diff --git a/benchmarks/control_theory/ball_beam/kill_hold.prob b/benchmarks/control_theory/ball_beam/kill_hold.prob new file mode 100644 index 0000000..8966621 --- /dev/null +++ b/benchmarks/control_theory/ball_beam/kill_hold.prob @@ -0,0 +1,55 @@ +# system state +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# controller state +z1 = 1 +z2 = 1 + +# measurements +y1 = 0.5 * x1 +y2 = 0.25 * x3 + +# Failure probabilities +ps = 0 +pc = 0 +pa = 0 + +while true: + # old values + x1o = x1 + x2o = x2 + x3o = x3 + z1o = z1 + z2o = z2 + + # system evolution + x1 = x1o + 0.015*x2o + 0.0003*x3o + 0.000029*u + x2 = x2o + 0.045*x3o + 0.0058*u + x3 = x3o + 0.256*u + + overrun = Bernoulli(pc) + actuation_fail = Bernoulli(pa) + + # controller evolution + if overrun == 0: + z1 = z1o + 0.025 * y1 + z2 = 0.9685*z2o - 0.2608 * y1 + end + + # new command + if overrun == 0 && actuation_fail == 0: + u = -0.108*z1o - 0.2608*z2o - 2.43*y1 - 3*y2 + end + + # measurements + sensor_fail = Bernoulli(ps) + if sensor_fail == 0: + y1 = 0.5 * x1 + y2 = 0.25 * x3 + end +end diff --git a/benchmarks/control_theory/ball_beam/kill_zero.prob b/benchmarks/control_theory/ball_beam/kill_zero.prob new file mode 100644 index 0000000..c9653e8 --- /dev/null +++ b/benchmarks/control_theory/ball_beam/kill_zero.prob @@ -0,0 +1,57 @@ +# system state +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# controller state +z1 = 1 +z2 = 1 + +# measurements +y1 = 0.5 * x1 +y2 = 0.25 * x3 + +# Failure probabilities +#ps = 0 +pc = 0 +#pa = 0 + +while true: + # old values + x1o = x1 + x2o = x2 + x3o = x3 + z1o = z1 + z2o = z2 + + # system evolution + x1 = x1o + 0.015*x2o + 0.0003*x3o + 0.000029*u + x2 = x2o + 0.045*x3o + 0.0058*u + x3 = x3o + 0.256*u + + overrun = Bernoulli(pc) + actuation_fail = Bernoulli(pa) + + # controller evolution + if overrun == 0: + z1 = z1o + 0.025 * y1 + z2 = 0.9685*z2o - 0.2608 * y1 + end + + # new command + if overrun == 0 && actuation_fail == 0: + u = -0.108*z1o - 0.2608*z2o - 2.43*y1 - 3*y2 + else: + u = 0 + end + + # measurements + sensor_fail = Bernoulli(ps) + if sensor_fail == 0: + y1 = 0.5 * x1 + y2 = 0.25 * x3 + end +end diff --git a/benchmarks/control_theory/ball_beam/skip_hold.prob b/benchmarks/control_theory/ball_beam/skip_hold.prob new file mode 100644 index 0000000..2427141 --- /dev/null +++ b/benchmarks/control_theory/ball_beam/skip_hold.prob @@ -0,0 +1,55 @@ +# system state +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# controller state +z1 = 1 +z2 = 1 + +# measurements +y1 = 0.5 * x1 +y2 = 0.25 * x3 + +# Failure probabilities +ps = 0 +pc = 0 +pa = 0 + +while true: + # old values + x1o = x1 + x2o = x2 + x3o = x3 + z1o = z1 + z2o = z2 + + # system evolution + x1 = x1o + 0.015*x2o + 0.0003*x3o + 0.000029*u + x2 = x2o + 0.045*x3o + 0.0058*u + x3 = x3o + 0.256*u + + overrun = Bernoulli(pc) + actuation_fail = Bernoulli(pa) + + # controller evolution + if overrun == 0: + z1 = z1o + 0.025 * y1 + z2 = 0.9685*z2o - 0.2608 * y1 + end + + # new command + if overrun == 0 && actuation_fail == 0: + u = -0.108*z1o - 0.2608*z2o - 2.43*y1 - 3*y2 + end + + # measurements + sensor_fail = Bernoulli(ps) + if sensor_fail == 0 && overrun == 0: + y1 = 0.5 * x1 + y2 = 0.25 * x3 + end +end diff --git a/benchmarks/control_theory/ball_beam/skip_zero.prob b/benchmarks/control_theory/ball_beam/skip_zero.prob new file mode 100644 index 0000000..b0646dd --- /dev/null +++ b/benchmarks/control_theory/ball_beam/skip_zero.prob @@ -0,0 +1,57 @@ +# system state +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# controller state +z1 = 1 +z2 = 1 + +# measurements +y1 = 0.5 * x1 +y2 = 0.25 * x3 + +# Failure probabilities +ps = 0 +pc = 0 +pa = 0 + +while true: + # old values + x1o = x1 + x2o = x2 + x3o = x3 + z1o = z1 + z2o = z2 + + # system evolution + x1 = x1o + 0.015*x2o + 0.0003*x3o + 0.000029*u + x2 = x2o + 0.045*x3o + 0.0058*u + x3 = x3o + 0.256*u + + overrun = Bernoulli(pc) + actuation_fail = Bernoulli(pa) + + # controller evolution + if overrun == 0: + z1 = z1o + 0.025 * y1 + z2 = 0.9685*z2o - 0.2608 * y1 + end + + # new command + if overrun == 0 && actuation_fail == 0: + u = -0.108*z1o - 0.2608*z2o - 2.43*y1 - 3*y2 + else: + u = 0 + end + + # measurements + sensor_fail = Bernoulli(ps) + if sensor_fail == 0 && overrun == 0: + y1 = 0.5 * x1 + y2 = 0.25 * x3 + end +end diff --git a/benchmarks/control_theory/ball_beam/system.prob b/benchmarks/control_theory/ball_beam/system.prob new file mode 100644 index 0000000..da4b92d --- /dev/null +++ b/benchmarks/control_theory/ball_beam/system.prob @@ -0,0 +1,40 @@ +# system state +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# controller state +z1 = 1 +z2 = 1 + +# measurements +y1 = 0.5 * x1 +y2 = 0.25 * x3 + +while true: + # old values + x1o = x1 + x2o = x2 + x3o = x3 + z1o = z1 + z2o = z2 + + # system evolution + x1 = x1o + 0.015*x2o + 0.0003*x3o + 0.000029*u + x2 = x2o + 0.045*x3o + 0.0058*u + x3 = x3o + 0.256*u + + # controller evolution + z1 = z1o + 0.025 * y1 + z2 = 0.9685*z2o - 0.2608 * y1 + + # new command + u = -0.108*z1o - 0.2608*z2o - 2.43*y1 - 3*y2 + + # measurements + y1 = 0.5 * x1 + y2 = 0.25 * x3 +end diff --git a/benchmarks/control_theory/cruise_control/kill_hold.prob b/benchmarks/control_theory/cruise_control/kill_hold.prob new file mode 100644 index 0000000..063d829 --- /dev/null +++ b/benchmarks/control_theory/cruise_control/kill_hold.prob @@ -0,0 +1,45 @@ +# state vector +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# measurements +y1 = x1 +y2 = x2 +y3 = x3 + +# Failure probabilities +ps = 0 +pc = 0 +pa = 0 + +while true: + # store old values + x1o = x1 + x2o = x2 + x3o = x3 + + # state update + x1 = 1*x1o + 0.01*x2o + 0*x3o + 0.0001*u + x2 = -0.0003*x1o + 0.9997*x2o + 0.01*x3o + 0.0001*u + x3 = -0.0604*x1o - 0.0531*x2o + 0.9974*x3o + 0.0247*u + + overrun = Bernoulli(pc) + + # command update + actuation_fail = Bernoulli(pa) + if overrun == 0 && actuation_fail == 0: + u = -872.54*y1 - 131.49*y2 - 10.097*y3 + end + + # measurements + sensor_fail = Bernoulli(ps) + if sensor_fail == 0: + y1 = x1 + y2 = x2 + y3 = x3 + end +end diff --git a/benchmarks/control_theory/cruise_control/kill_zero.prob b/benchmarks/control_theory/cruise_control/kill_zero.prob new file mode 100644 index 0000000..5ab7851 --- /dev/null +++ b/benchmarks/control_theory/cruise_control/kill_zero.prob @@ -0,0 +1,47 @@ +# state vector +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# measurements +y1 = x1 +y2 = x2 +y3 = x3 + +# Failure probabilities +ps = 0 +pc = 0 +pa = 0 + +while true: + # store old values + x1o = x1 + x2o = x2 + x3o = x3 + + # state update + x1 = 1*x1o + 0.01*x2o + 0*x3o + 0.0001*u + x2 = -0.0003*x1o + 0.9997*x2o + 0.01*x3o + 0.0001*u + x3 = -0.0604*x1o - 0.0531*x2o + 0.9974*x3o + 0.0247*u + + overrun = Bernoulli(pc) + + # command update + actuation_fail = Bernoulli(pa) + if overrun == 0 && actuation_fail == 0: + u = -872.54*y1 - 131.49*y2 - 10.097*y3 + else: + u = 0 + end + + # measurements + sensor_fail = Bernoulli(ps) + if sensor_fail == 0: + y1 = x1 + y2 = x2 + y3 = x3 + end +end diff --git a/benchmarks/control_theory/cruise_control/skip_hold.prob b/benchmarks/control_theory/cruise_control/skip_hold.prob new file mode 100644 index 0000000..8dca4ce --- /dev/null +++ b/benchmarks/control_theory/cruise_control/skip_hold.prob @@ -0,0 +1,45 @@ +# state vector +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# measurements +y1 = x1 +y2 = x2 +y3 = x3 + +# Failure probabilities +ps = 0 +pc = 0.5 +pa = 0 + +while true: + # store old values + x1o = x1 + x2o = x2 + x3o = x3 + + # state update + x1 = 1*x1o + 0.01*x2o + 0*x3o + 0.0001*u + x2 = -0.0003*x1o + 0.9997*x2o + 0.01*x3o + 0.0001*u + x3 = -0.0604*x1o - 0.0531*x2o + 0.9974*x3o + 0.0247*u + + overrun = Bernoulli(pc) + + # command update + actuation_fail = Bernoulli(pa) + if overrun == 0 && actuation_fail == 0: + u = -872.54*y1 - 131.49*y2 - 10.097*y3 + end + + # measurements + sensor_fail = Bernoulli(ps) + if sensor_fail == 0 && overrun == 0: + y1 = x1 + y2 = x2 + y3 = x3 + end +end diff --git a/benchmarks/control_theory/cruise_control/skip_zero.prob b/benchmarks/control_theory/cruise_control/skip_zero.prob new file mode 100644 index 0000000..78f4b04 --- /dev/null +++ b/benchmarks/control_theory/cruise_control/skip_zero.prob @@ -0,0 +1,47 @@ +# state vector +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# measurements +y1 = x1 +y2 = x2 +y3 = x3 + +# Failure probabilities +ps = 0 +pc = 0 +pa = 0 + +while true: + # store old values + x1o = x1 + x2o = x2 + x3o = x3 + + # state update + x1 = 1*x1o + 0.01*x2o + 0*x3o + 0.0001*u + x2 = -0.0003*x1o + 0.9997*x2o + 0.01*x3o + 0.0001*u + x3 = -0.0604*x1o - 0.0531*x2o + 0.9974*x3o + 0.0247*u + + overrun = Bernoulli(pc) + + # command update + actuation_fail = Bernoulli(pa) + if overrun == 0 && actuation_fail == 0: + u = -872.54*y1 - 131.49*y2 - 10.097*y3 + else: + u = 0 + end + + # measurements + sensor_fail = Bernoulli(ps) + if sensor_fail == 0 && overrun == 0: + y1 = x1 + y2 = x2 + y3 = x3 + end +end diff --git a/benchmarks/control_theory/cruise_control/system.prob b/benchmarks/control_theory/cruise_control/system.prob new file mode 100644 index 0000000..4de9bb1 --- /dev/null +++ b/benchmarks/control_theory/cruise_control/system.prob @@ -0,0 +1,33 @@ +# state vector +x1 = 1 +x2 = 1 +x3 = 1 + +# command +u = 1 + +# measurements +y1 = x1 +y2 = x2 +y3 = x3 + +while true: + # store old values + x1o = x1 + x2o = x2 + x3o = x3 + uo = u + + # state update + x1 = 1*x1o + 0.01*x2o + 0*x3o + 0.0001*uo + x2 = -0.0003*x1o + 0.9997*x2o + 0.01*x3o + 0.0001*uo + x3 = -0.0604*x1o - 0.0531*x2o + 0.9974*x3o + 0.0247*uo + + # command update + u = -872.54*x1o - 131.49*x2o - 10.097*x3o + + # measurements + y1 = x1 + y2 = x2 + y3 = x3 +end diff --git a/cli/argument_parser.py b/cli/argument_parser.py index 60a563d..e9b39a6 100644 --- a/cli/argument_parser.py +++ b/cli/argument_parser.py @@ -11,7 +11,6 @@ def _set_settings(args): settings.type_fp_iterations = args.type_fp_iterations settings.numeric_roots = args.numeric_roots settings.numeric_croots = args.numeric_croots - settings.numeric_eps = args.numeric_eps settings.trivial_guard = args.trivial_guard settings.exact_func_moments = args.exact_func_moments @@ -199,13 +198,6 @@ def __init__(self): default=settings.numeric_croots, help="If set the complex roots in the recurrence computation will be computed numerically", ) - self.argument_parser.add_argument( - "--numeric_eps", - dest="numeric_eps", - default=settings.numeric_eps, - type=float, - help="Interval epsilon for the potential approximation of roots", - ) self.argument_parser.add_argument( "--tail_bound_moments", dest="tail_bound_moments", diff --git a/control_system/__init__.py b/control_system/__init__.py new file mode 100644 index 0000000..dbfa834 --- /dev/null +++ b/control_system/__init__.py @@ -0,0 +1,5 @@ +from .control_system import ControlSystem +from .controller import Controller +from .sensor import Sensor +from .actuator import Actuator, ActuatorFaultStrategy +from .cs_converter import CSConverter diff --git a/control_system/actuator.py b/control_system/actuator.py new file mode 100644 index 0000000..29d2fb3 --- /dev/null +++ b/control_system/actuator.py @@ -0,0 +1,28 @@ +from sympy import Matrix, Expr, sympify +from enum import Enum, auto + + +class ActuatorFaultStrategy(Enum): + ZERO = auto() + HOLD = auto() + + +class Actuator: + effect: Matrix + symbol: str + variables: [str] + fault_probability: Expr + fault_strategy: ActuatorFaultStrategy + + def __init__(self, symbol: str = "u"): + self.symbol = symbol + + def set_effect(self, e: Matrix): + self.effect = e + self.variables = [self.symbol + str(i) for i in range(e.cols)] + + def set_fault_probability(self, p: Expr | float): + self.fault_probability = sympify(p) + + def set_fault_strategy(self, fs: ActuatorFaultStrategy): + self.fault_strategy = fs diff --git a/control_system/control_system.py b/control_system/control_system.py new file mode 100644 index 0000000..0df6961 --- /dev/null +++ b/control_system/control_system.py @@ -0,0 +1,31 @@ +from .actuator import Actuator +from .controller import Controller +from .sensor import Sensor + +from sympy import Matrix + + +class ControlSystem: + actuator: Actuator + sensor: Sensor + controller: Controller + + dynamics: Matrix + state_symbol: str + state_variables: [str] + + def __init__(self, state_symbol: str = "x"): + self.state_symbol = state_symbol + + def add_actuator(self, a: Actuator): + self.actuator = a + + def add_sensor(self, s: Sensor): + self.sensor = s + + def add_controller(self, c: Controller): + self.controller = c + + def set_dynamics(self, d: Matrix): + self.dynamics = d + self.state_variables = [self.state_symbol + str(i) for i in range(d.rows)] diff --git a/control_system/controller.py b/control_system/controller.py new file mode 100644 index 0000000..d40a8af --- /dev/null +++ b/control_system/controller.py @@ -0,0 +1,51 @@ +from sympy import Matrix, Expr, sympify +from typing import Tuple +from enum import Enum, auto + +from .sensor import Sensor +from .actuator import Actuator + +StateEffect = Matrix +StateInfluence = Matrix +ActuatorEffect = Matrix + + +class ControllerFaultStrategy(Enum): + SKIP = auto() + KILL = auto() + + +class Controller: + name: str + dynamics: Matrix = None + state_symbol: str + state_variables: [str] = [] + sensor: Tuple[Sensor, StateEffect, ActuatorEffect] + actuator: Tuple[Actuator, StateInfluence] + fault_probability: Expr + fault_strategy: ControllerFaultStrategy + + def __init__(self, state_symbol: str = "z", name: str = "c"): + self.state_symbol = state_symbol + self.name = name + + def set_dynamics(self, d: Matrix): + self.dynamics = d + self.state_variables = [self.state_symbol + str(i) for i in range(d.rows)] + + def set_sensor( + self, + sensor: Sensor, + state_effect: StateEffect = None, + actuator_effect: ActuatorEffect = None, + ): + self.sensor = (sensor, state_effect, actuator_effect) + + def set_actuator(self, actuator: Actuator, state_influence: StateInfluence = None): + self.actuator = (actuator, state_influence) + + def set_fault_probability(self, p: Expr | float): + self.fault_probability = sympify(p) + + def set_fault_strategy(self, fs: ControllerFaultStrategy): + self.fault_strategy = fs diff --git a/control_system/cs_converter.py b/control_system/cs_converter.py new file mode 100644 index 0000000..ddff62d --- /dev/null +++ b/control_system/cs_converter.py @@ -0,0 +1,91 @@ +from program import Program, normalize_program +from program.assignment import PolyAssignment +from program.condition import TrueCond +from utils import make_assigns_parallel +from .control_system import ControlSystem +from sympy import Matrix, zeros + + +class CSConverter: + control_system: ControlSystem + is_probabilistic: bool + + def __init__(self, control_system: ControlSystem): + self.control_system = control_system + self.is_probabilistic = False + self.loop_body = [] + + def construct_program(self) -> Program: + self._add_system_dynamics_assigns() + self._add_controller_assigns() + self._add_sensor_assigns() + program = Program( + [], [], [], [], TrueCond(), self.loop_body, self.is_probabilistic + ) + return normalize_program(program) + + def _add_system_dynamics_assigns(self): + state_vars = self.control_system.state_variables + expressions = self.control_system.dynamics * Matrix(state_vars) + if self.control_system.actuator is not None: + acc = self.control_system.actuator + expressions += acc.effect * Matrix(acc.variables) + assignments = [ + PolyAssignment.deterministic(v, e) for v, e in zip(state_vars, expressions) + ] + assignments = make_assigns_parallel(assignments) + self.loop_body += assignments + + def _add_controller_assigns(self): + if self.control_system.controller is None: + return + + controller = self.control_system.controller + actuator, state_influence = controller.actuator + sensor, state_effect, act_effect = controller.sensor + + # Add variables for sensor inputs + sensor_input_variables = [sv + controller.name for sv in sensor.variables] + sensor_input_assigns = [ + PolyAssignment.deterministic(iv, sv) + for iv, sv in zip(sensor_input_variables, sensor.variables) + ] + self.loop_body += sensor_input_assigns + + # Add assignments for actuator + act_expressions = Matrix.zeros(len(actuator.variables), 1) + if state_influence is not None: + act_expressions += state_influence * Matrix(controller.state_variables) + if act_effect is not None: + act_expressions += act_effect * Matrix(sensor_input_variables) + act_assigns = [ + PolyAssignment.deterministic(v, e) + for v, e in zip(actuator.variables, act_expressions) + ] + act_assigns = make_assigns_parallel(act_assigns) + self.loop_body += act_assigns + + # Add assignments for controller state + if controller.dynamics is not None: + expressions = controller.dynamics * Matrix(controller.state_variables) + if state_effect is not None: + expressions += state_effect * Matrix(sensor_input_variables) + assigns = [ + PolyAssignment.deterministic(v, e) + for v, e in zip(controller.state_variables, expressions) + ] + assigns = make_assigns_parallel(assigns) + self.loop_body += assigns + + def _add_sensor_assigns(self): + if self.control_system.sensor is None: + return + + sensor = self.control_system.sensor + state_vars = self.control_system.state_variables + expressions = sensor.measurement * Matrix(state_vars) + assignments = [ + PolyAssignment.deterministic(v, e) + for v, e in zip(sensor.variables, expressions) + ] + self.loop_body += assignments diff --git a/control_system/sensor.py b/control_system/sensor.py new file mode 100644 index 0000000..98805e7 --- /dev/null +++ b/control_system/sensor.py @@ -0,0 +1,18 @@ +from sympy import Matrix, Expr, sympify + + +class Sensor: + measurement: Matrix + symbol: str + variables: [str] + fault_probability: Expr + + def __init__(self, symbol: str = "y"): + self.symbol = symbol + + def set_measurement(self, m: Matrix): + self.measurement = m + self.variables = [self.symbol + str(i) for i in range(m.rows)] + + def set_fault_probability(self, p: Expr | float): + self.fault_probability = sympify(p) diff --git a/recurrences/rec_builder.py b/recurrences/rec_builder.py index f660777..36979fe 100644 --- a/recurrences/rec_builder.py +++ b/recurrences/rec_builder.py @@ -1,7 +1,7 @@ from functools import lru_cache from math import prod -from typing import Set, List -from symengine.lib.symengine_wrapper import Expr, Symbol, sympify, One, Zero +from typing import List, Set +from symengine.lib.symengine_wrapper import Expr, Symbol, sympify, One from program import Program from program.assignment import Assignment from program.type import Finite @@ -23,13 +23,12 @@ def __init__(self, program: Program): self.program = program @lru_cache(maxsize=None) - def get_recurrences(self, monomial: Expr) -> Recurrences: + def get_recurrences(self, *monomials: Expr | str) -> Recurrences: """ Constructs a complete system of linear recurrences (over expected values) completely describing - the expected value of "monomial". + the expected value(s) of "monomials". """ - monomial = sympify(monomial) - to_process = {monomial} + to_process = {sympify(m) for m in monomials} processed = set() recurrence_dict = {} while to_process: diff --git a/recurrences/recurrences.py b/recurrences/recurrences.py index 08e7a06..d104e9b 100644 --- a/recurrences/recurrences.py +++ b/recurrences/recurrences.py @@ -15,13 +15,20 @@ class Recurrences: program: Program recurrence_dict: Dict[Expr, Expr] init_values_dict: Dict[Expr, Expr] - recurrence_matrix: Matrix - init_values_vector: Matrix monomials: List[Expr] dependencies: Dict[Expr, Set[Expr]] is_acyclic: bool is_inhomogeneous = False constant_symbols: List[Symbol] + # Stores the recurrence in homogenous form + # i.e: Recurrence is recurrence_matrix^n * init_values_vector + recurrence_matrix: Matrix + init_values_vector: Matrix + # Stores the recurrence in inhomogeneous form + # i.e: Recurrence equation is f(n+1) = A*f(n) + b with initial values x (b might be 0) + A: Matrix + b: Matrix + x: Matrix def __init__( self, @@ -77,14 +84,21 @@ def _init_data(self): initial_values = [self.init_values_dict[v] for v in self.monomials] - # If the system is inhomogeneous (constant inhomogeneous part). Then we need to fill - # up those recurrence coefficients which are homogeneous with "0". if self.is_inhomogeneous: + # If the system is inhomogeneous (constant inhomogeneous part). Then we need to fill + # up those recurrence coefficients which are homogeneous with "0". initial_values.append(sympify(1)) for cs in coefficients: if len(cs) == len(self.monomials): cs.append(sympify(0)) coefficients.append([sympify(0) for _ in self.monomials] + [sympify(1)]) + self.A = Matrix(coefficients)[:-1, :-1] + self.b = Matrix(coefficients)[:-1, -1] + self.x = Matrix(initial_values) + else: + self.A = Matrix(coefficients) + self.b = Matrix([sympify(0) for _ in self.monomials]) + self.x = Matrix(initial_values) self.init_values_vector = Matrix(initial_values) self.recurrence_matrix = Matrix(coefficients) diff --git a/recurrences/solver/cyclic_solver.py b/recurrences/solver/cyclic_solver.py index e68fe04..bc7b669 100644 --- a/recurrences/solver/cyclic_solver.py +++ b/recurrences/solver/cyclic_solver.py @@ -21,7 +21,6 @@ class CyclicSolver(Solver): gen_sol_unknowns_set: Set[Symbol] numeric_roots: bool numeric_croots: bool - numeric_eps: float _is_exact: bool def __init__( @@ -29,7 +28,6 @@ def __init__( recurrences: Recurrences, numeric_roots: bool = None, numeric_croots: bool = None, - numeric_eps: float = None, ): self.n = symbols("n", integer=True) self.recurrences = recurrences @@ -39,7 +37,6 @@ def __init__( self.numeric_croots = ( settings.numeric_croots if numeric_croots is None else numeric_croots ) - self.numeric_eps = settings.numeric_eps if numeric_eps is None else numeric_eps self.monomials = set(recurrences.monomials) self.monom_to_index = { m: i @@ -54,7 +51,6 @@ def _compute_general_solution(self): self.characteristic_poly, self.numeric_roots, self.numeric_croots, - self.numeric_eps, ) solution = sympify(0) count = 0 diff --git a/recurrences/solver/recurrence_solver.py b/recurrences/solver/recurrence_solver.py index 4b35f0b..e9e26a1 100644 --- a/recurrences/solver/recurrence_solver.py +++ b/recurrences/solver/recurrence_solver.py @@ -12,15 +12,12 @@ def __init__( recurrences: Recurrences, numeric_roots: bool = None, numeric_croots: bool = None, - numeric_eps: float = None, force_cyclic_solver: bool = False, ): if recurrences.is_acyclic and not force_cyclic_solver: self.solver = AcyclicSolver(recurrences) else: - self.solver = CyclicSolver( - recurrences, numeric_roots, numeric_croots, numeric_eps - ) + self.solver = CyclicSolver(recurrences, numeric_roots, numeric_croots) @property def is_exact(self) -> bool: diff --git a/scripts/api_ball_beam.py b/scripts/api_ball_beam.py new file mode 100644 index 0000000..40979fb --- /dev/null +++ b/scripts/api_ball_beam.py @@ -0,0 +1,36 @@ +from control_system import * +from sympy import Matrix + + +ball_beam_system = ControlSystem() + +# Setup control system +ball_beam_system.set_dynamics(Matrix([[1, 0.015, 0.0003], [0, 1, 0.045], [0, 0, 1]])) + +# Construct and add sensor +sensor = Sensor() +sensor.set_measurement(Matrix([[0.5, 0, 0], [0, 0, 0.25]])) +sensor.set_fault_probability(0.2) +ball_beam_system.add_sensor(sensor) + +# Construct and add actuator +actuator = Actuator() +actuator.set_effect(Matrix([2.9e-5, 0.0058, 0.256])) +actuator.set_fault_probability(0.3) +actuator.set_fault_strategy(ActuatorFaultStrategy.HOLD) +ball_beam_system.add_actuator(actuator) + +# Construct and add controller +controller = Controller() +controller.set_dynamics(Matrix([[1, 0], [0, 0.9685]])) +sensor_state_effect = Matrix([[0.025, 0], [-0.2608, 0]]) +sensor_act_effect = Matrix([-2.43, -3]).T +controller.set_sensor(sensor, sensor_state_effect, sensor_act_effect) +state_influence = Matrix([-0.108, -0.2608]).T +controller.set_actuator(actuator, state_influence) +controller.set_fault_probability(0.5) +ball_beam_system.add_controller(controller) + +converter = CSConverter(ball_beam_system) +program = converter.construct_program() +print(program) diff --git a/scripts/api_cruise_control.py b/scripts/api_cruise_control.py new file mode 100644 index 0000000..de283f0 --- /dev/null +++ b/scripts/api_cruise_control.py @@ -0,0 +1,32 @@ +from control_system import * +from sympy import Matrix + +# Setup control system +cc_system = ControlSystem() +cc_system.set_dynamics( + Matrix([[1, 0.01, 0], [-0.0003, 0.9997, 0.01], [-0.0604, -0.0531, 0.9974]]) +) + +# Construct and add sensor +sensor = Sensor() +sensor.set_measurement(Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])) +sensor.set_fault_probability(0.1) +cc_system.add_sensor(sensor) + +# Construct and add actuator +actuator = Actuator() +actuator.set_effect(Matrix([0.0001, 0.0001, 0.0247])) +actuator.set_fault_probability(0.2) +actuator.set_fault_strategy(ActuatorFaultStrategy.ZERO) +cc_system.add_actuator(actuator) + +# Construct and add controller +controller = Controller() +sensor_act_effect = Matrix([-872.54, -131.49, -10.097]).T +controller.set_sensor(sensor, actuator_effect=sensor_act_effect) +controller.set_actuator(actuator) +cc_system.add_controller(controller) + +converter = CSConverter(cc_system) +program = converter.construct_program() +print(program) diff --git a/scripts/ball_beam.py b/scripts/ball_beam.py new file mode 100644 index 0000000..b263258 --- /dev/null +++ b/scripts/ball_beam.py @@ -0,0 +1,11629 @@ +from inputparser import Parser +from program import normalize_program +from recurrences.rec_builder import RecBuilder +from symengine.lib.symengine_wrapper import sympify, Symbol +from stability_analysis import NumericStabilityAnalyzer + +import numpy as np +import matplotlib.pyplot as plt +from matplotlib import cm +from progress.bar import Bar + + +def get_rho(strategy, ps=0.0, pc=0.0, pa=0.0): + file_path = f"../benchmarks/control_theory/ball_beam/{strategy}.prob" + program = Parser().parse_file(file_path) + for assign in program.initial: + if str(assign.variable) == "ps": + assign.polynomials = [sympify(ps)] + if str(assign.variable) == "pc": + assign.polynomials = [sympify(pc)] + if str(assign.variable) == "pa": + assign.polynomials = [sympify(pa)] + + program = normalize_program(program) + + rec_builder = RecBuilder(program) + recurrences = rec_builder.get_recurrences( + "x1", "x2", "x3", "x1**2", "x2**2", "x3**2" + ) + + analyzer = NumericStabilityAnalyzer(recurrences) + return analyzer.get_rho() + + +def compute_single_variations(strategy): + # vary ps + ps_data = [] + with Bar("Varying ps ... ") as bar: + for ps in np.arange(0, 1, 0.01): + ps_data.append(get_rho(strategy, ps=ps)) + bar.next() + print(f"ps data for {strategy}:") + print(ps_data) + + # vary pc + pc_data = [] + with Bar("Varying pc ... ") as bar: + for pc in np.arange(0, 1, 0.01): + pc_data.append(get_rho(strategy, pc=pc)) + bar.next() + print(f"pc data for {strategy}:") + print(pc_data) + + # vary pa + pa_data = [] + with Bar("Varying pa ... ") as bar: + for pa in np.arange(0, 1, 0.01): + pa_data.append(get_rho(strategy, pa=pa)) + bar.next() + print(f"pa data for {strategy}:") + print(pa_data) + + +def compute_double_variations(strategy): + density = 0.1 + xs = np.arange(0, 1, density) + ys = np.arange(0, 1, density) + xs, ys = np.meshgrid(xs, ys) + zs = np.zeros(xs.shape) + with Bar("Varying pa and ps ...", max=int((1 / density) ** 2)) as bar: + for i in range(zs.shape[0]): + for j in range(zs.shape[1]): + pa = xs[i, j] + ps = ys[i, j] + zs[i, j] = get_rho(strategy, pa=pa, ps=ps) + bar.next() + print("2D values:") + print(zs.tolist()) + + +def compute_double_variations_fast(): + file_path = f"../benchmarks/control_theory/ball_beam/kill_zero.prob" + program = Parser().parse_file(file_path) + + program = normalize_program(program) + + rec_builder = RecBuilder(program) + recurrences = rec_builder.get_recurrences( + "x1", "x2", "x3", "x1**2", "x2**2", "x3**2" + ) + kill_zero_matrix = recurrences.A + + density = 0.01 + xs = np.arange(0, 1, density) + ys = np.arange(0, 1, density) + xs, ys = np.meshgrid(xs, ys) + zs = np.zeros(xs.shape) + with Bar("Varying pa and ps ...", max=int((1 / density) ** 2)) as bar: + for i in range(zs.shape[0]): + for j in range(zs.shape[1]): + pa = xs[i, j] + ps = ys[i, j] + matrix = kill_zero_matrix.subs({"pa": pa, "ps": ps}) + matrix = np.array(matrix).astype(np.float64) + eigvs = np.linalg.eigvals(matrix) + zs[i, j] = max([abs(ev) for ev in eigvs]) + bar.next() + print("2D values:") + print(zs.tolist()) + + +def plot_fig6(): + # Kill and Zero plot + ps_data_kill_zero = [ + 0.9978984860292592, + 0.9978984862817318, + 0.9978984865393534, + 0.9978984868022858, + 0.9978984870707013, + 0.9978984873447672, + 0.9978984876246627, + 0.9978984879105776, + 0.9978984882027102, + 0.9978984885012605, + 0.9978984888064465, + 0.9978984891184925, + 0.9978984894376304, + 0.9978984897641039, + 0.9978984900981687, + 0.9978984904400983, + 0.997898490790167, + 0.9978984911486719, + 0.9978984915159202, + 0.9978984918922374, + 0.9978984922779635, + 0.9978984926734559, + 0.9978984930790898, + 0.9978984934952583, + 0.9978984939223797, + 0.9978984943608907, + 0.9978984948112563, + 0.9978984952739571, + 0.9978984957495161, + 0.9978984962384689, + 0.9978984967413932, + 0.9978984972588949, + 0.9978984977916199, + 0.9978984983402501, + 0.9978984989055008, + 0.9978984994881483, + 0.9978985000890029, + 0.9978985007089362, + 0.997898501348865, + 0.9978985020097788, + 0.9978985026927241, + 0.9978985033988178, + 0.9978985041292661, + 0.9978985048853428, + 0.9978985056684271, + 0.997898506479988, + 0.9978985073216065, + 0.9978985081949873, + 0.9978985091019632, + 0.9978985100445085, + 0.9978985110247592, + 0.9978985120450219, + 0.997898513107799, + 0.997898514215805, + 0.9978985153719862, + 0.9978985165795626, + 0.9978985178420263, + 0.9978985191632185, + 0.9978985205473302, + 0.9978985219989677, + 0.9978985235231876, + 0.9978985251255823, + 0.9978985268123244, + 0.9978985285902459, + 0.9978985304669554, + 0.9978985324509151, + 0.9978985345515892, + 0.9978985367795916, + 0.9978985391468598, + 0.997898541666876, + 0.9978985443549092, + 0.9978985472283517, + 0.9978985503070611, + 0.9978985536138556, + 0.9978985571750534, + 0.9978985610211909, + 0.9978985651878864, + 0.9978985697169624, + 0.9978985746578349, + 0.9978985800693504, + 0.9978985860221151, + 0.9978985926016063, + 0.9986281596844219, + 1.005814579163735, + 1.0131157921056069, + 1.0203442696626326, + 1.0274517936122698, + 1.0344084590943294, + 1.0411871515029416, + 1.0477579183109071, + 1.0540846614018, + 1.0601218552238083, + 1.0658100856500947, + 1.071069080399318, + 1.075785880940787, + 1.0797931012490305, + 1.082824812325663, + 1.084413875174669, + 1.0835969881279695, + 1.0776664649891043, + ] + pc_data_kill_zero = [ + 0.9978984860292592, + 0.9979123705259259, + 0.9979266402895767, + 0.9979412795310291, + 0.9979562730754816, + 0.9979716063452087, + 0.9979872653417252, + 0.9980032366276284, + 0.9980195073082606, + 0.9980360650133242, + 0.9980528978785647, + 0.9980699945275785, + 0.9980873440538651, + 0.9981049360031801, + 0.9981227603562149, + 0.9981408075116717, + 0.9981590682697692, + 0.9981775338161819, + 0.9981961957064579, + 0.9982150458509048, + 0.9982340764999846, + 0.998253280230179, + 0.9982726499303743, + 0.9982921787887128, + 0.9983118602799553, + 0.9983316881533045, + 0.9983516564207165, + 0.9983717593456556, + 0.9983919914323297, + 0.9984123474153322, + 0.9984328222497144, + 0.9984534111014983, + 0.9984741093385603, + 0.9984949125219091, + 0.9985158163973288, + 0.9985368168874046, + 0.9985579100838573, + 0.9985790922402277, + 0.998600359764895, + 0.998621709214359, + 0.998643137286847, + 0.9986646408161951, + 0.9986862167659909, + 0.9987078622239691, + 0.9987295743966583, + 0.9987513506042712, + 0.9987731882757953, + 0.9987950849443166, + 0.9988170382425379, + 0.9988390458984995, + 0.9988611057314775, + 0.998889801846288, + 0.9991029900723533, + 0.9993175823848738, + 0.9995335935251446, + 0.9997510354728203, + 1.0000709785178143, + 1.000514402587103, + 1.000961081224321, + 1.0014110305645458, + 1.0018642597894931, + 1.0023207689777776, + 1.002780547252751, + 1.0032435709528833, + 1.003709801696857, + 1.0041791842675596, + 1.004651644257645, + 1.0051270854247445, + 1.0056053867026677, + 1.0060863988091193, + 1.0065699403806903, + 1.0070557935525146, + 1.0075436988821167, + 1.0080333494939708, + 1.0085243842911327, + 1.009016380041351, + 1.009508842093565, + 1.0100011934129225, + 1.010492761531483, + 1.0109827628891508, + 1.0114702838713054, + 1.0119542576172171, + 1.012433435346025, + 1.0129063504804134, + 1.0133712731694207, + 1.0138261518067673, + 1.0142685366192825, + 1.0146954780392607, + 1.0151033888105823, + 1.015487852584605, + 1.0158433511956724, + 1.0161628640048554, + 1.0164372575413192, + 1.0166543138742006, + 1.0167970970520674, + 1.0168410075738814, + 1.016747950515479, + 1.0164531489575306, + 1.01582843291876, + 1.0145303757667365, + ] + pa_data_kill_zero = [ + 0.9978984860292592, + 0.9978982337083446, + 0.9978979761880671, + 0.9978977133060668, + 0.9978974448931709, + 0.9978971707730036, + 0.9978968907616139, + 0.9978966046670679, + 0.9978963122889885, + 0.9978960134181214, + 0.997895707835802, + 0.9978953953134525, + 0.9978950756119886, + 0.9978947484812202, + 0.997894413659195, + 0.997894070871516, + 0.9978937198305657, + 0.9978933602347186, + 0.9978929917674745, + 0.9978926140965342, + 0.9978922268727923, + 0.9978918297292716, + 0.9978914222799463, + 0.9978910041185264, + 0.9978905748170666, + 0.9978901339245434, + 0.9978896809652443, + 0.9978892154370843, + 0.9978887368097438, + 0.9978882445226441, + 0.99788773798278, + 0.9978872165623165, + 0.9978866795960197, + 0.997886126378423, + 0.9978855561607295, + 0.9978849681474398, + 0.9978843614926691, + 0.9978837352960728, + 0.997883088598421, + 0.9978824203766744, + 0.9978817295386222, + 0.9978810149169189, + 0.9978802752625244, + 0.9978795092374247, + 0.9978787154065868, + 0.9978778922289826, + 0.9978770380476619, + 0.9978761510786117, + 0.9978752293983723, + 0.9978742709301459, + 0.9978732734282134, + 0.9978722344604253, + 0.9978711513884513, + 0.9978700213454871, + 0.9978688412109997, + 0.997867607582047, + 0.9978663167406195, + 0.9978649646163605, + 0.9978635467438584, + 0.9978620582135854, + 0.9978604936153551, + 0.9978588469728988, + 0.9978571116679721, + 0.9978552803518939, + 0.9978533448420802, + 0.9978512960005177, + 0.9978491235903731, + 0.9978468161060401, + 0.9978443605707171, + 0.9978417422940145, + 0.9978389445801669, + 0.9978359483746516, + 0.9978327318335983, + 0.9978292697955998, + 0.9978255331292064, + 0.9978214879207145, + 0.997817094454925, + 0.997812305924841, + 0.9978070667828608, + 0.9978013106122325, + 0.9977949573488758, + 0.9979622411430684, + 0.9982239456097534, + 0.9984901538115333, + 0.9987605994098896, + 0.9990349853294376, + 0.9995177442719444, + 1.0001477447359568, + 1.0007896336142619, + 1.001443420477501, + 1.0021093091820772, + 1.0027878049903634, + 1.0034798491972945, + 1.0041869471264913, + 1.0049111470842644, + 1.0056543943325655, + 1.006415818683618, + 1.0071828641350455, + 1.007904327181489, + 1.0083908590088804, + ] + x_range = np.arange(0, 1, 0.01) + + fig, ax = plt.subplots() + ax.axhline(y=1, color="grey", ls="solid", lw=1) + ax.plot(x_range, ps_data_kill_zero, label="ps", ls="solid", lw=3) + ax.plot(x_range, pc_data_kill_zero, label="pc", ls="dashdot", lw=3) + ax.plot(x_range, pa_data_kill_zero, label="pa", ls="dotted", lw=3) + ax.set_title("Kill and Zero") + ax.set_xlabel("px") + ax.set_ylabel("rho") + ax.legend() + plt.show() + + # Kill and Hold plot + ps_data_kill_hold = [ + 0.9978984860292592, + 0.9978984862817318, + 0.9978984865393534, + 0.9978984868022858, + 0.9978984870707013, + 0.9978984873447672, + 0.9978984876246627, + 0.9978984879105776, + 0.9978984882027102, + 0.9978984885012605, + 0.9978984888064465, + 0.9978984891184925, + 0.9978984894376304, + 0.9978984897641039, + 0.9978984900981687, + 0.9978984904400983, + 0.997898490790167, + 0.9978984911486719, + 0.9978984915159202, + 0.9978984918922374, + 0.9978984922779635, + 0.9978984926734559, + 0.9978984930790898, + 0.9978984934952583, + 0.9978984939223797, + 0.9978984943608907, + 0.9978984948112563, + 0.9978984952739571, + 0.9978984957495161, + 0.9978984962384689, + 0.9978984967413932, + 0.9978984972588949, + 0.9978984977916199, + 0.9978984983402501, + 0.9978984989055008, + 0.9978984994881483, + 0.9978985000890029, + 0.9978985007089362, + 0.997898501348865, + 0.9978985020097788, + 0.9978985026927241, + 0.9978985033988178, + 0.9978985041292661, + 0.9978985048853428, + 0.9978985056684271, + 0.997898506479988, + 0.9978985073216065, + 0.9978985081949873, + 0.9978985091019632, + 0.9978985100445085, + 0.9978985110247592, + 0.9978985120450219, + 0.997898513107799, + 0.997898514215805, + 0.9978985153719862, + 0.9978985165795626, + 0.9978985178420263, + 0.9978985191632185, + 0.9978985205473302, + 0.9978985219989677, + 0.9978985235231876, + 0.9978985251255823, + 0.9978985268123244, + 0.9978985285902459, + 0.9978985304669554, + 0.9978985324509151, + 0.9978985345515892, + 0.9978985367795916, + 0.9978985391468598, + 0.997898541666876, + 0.9978985443549092, + 0.9978985472283517, + 0.9978985503070611, + 0.9978985536138556, + 0.9978985571750534, + 0.9978985610211909, + 0.9978985651878864, + 0.9978985697169624, + 0.9978985746578349, + 0.9978985800693504, + 0.9978985860221151, + 0.9978985926016063, + 0.9986281596844219, + 1.005814579163735, + 1.0131157921056069, + 1.0203442696626326, + 1.0274517936122698, + 1.0344084590943294, + 1.0411871515029416, + 1.0477579183109071, + 1.0540846614018, + 1.0601218552238083, + 1.0658100856500947, + 1.071069080399318, + 1.075785880940787, + 1.0797931012490305, + 1.082824812325663, + 1.084413875174669, + 1.0835969881279695, + 1.0776664649891043, + ] + pc_data_kill_hold = [ + 0.9978984860292592, + 0.9979126112653465, + 0.9979271037089629, + 0.9979419483312584, + 0.9979571307108627, + 0.9979726370136309, + 0.997988453972389, + 0.9980045688667076, + 0.9980209695029331, + 0.9980376441944303, + 0.9980545817421955, + 0.9980717714158958, + 0.9980892029352973, + 0.9981068664522256, + 0.9981247525330199, + 0.9981428521414988, + 0.9981611566224986, + 0.9981796576859516, + 0.9981983473914939, + 0.9982172181336756, + 0.9982362626276661, + 0.9982554738955516, + 0.9982748452531268, + 0.9982943702972323, + 0.9983140428935999, + 0.9983338571651906, + 0.9983538074810219, + 0.9983738884454492, + 0.998394094887934, + 0.9984144218532021, + 0.9984348645918716, + 0.9984554185514615, + 0.998476079367783, + 0.9984968428567441, + 0.9985177050064711, + 0.9985386619698055, + 0.9985597100571175, + 0.9985808457294477, + 0.9986020655919392, + 0.998623366387581, + 0.9986447449911948, + 0.9986661984037235, + 0.9986877237467502, + 0.9987093182572621, + 0.9987309792826533, + 0.9987527042759343, + 0.9987744907911659, + 0.9987963364790733, + 0.9988182390828777, + 0.9988401964342761, + 0.9988622064496255, + 0.9988842671262667, + 0.9989063765390249, + 0.9989285328368434, + 0.9989507342395604, + 0.9989729790348408, + 0.9989952655752121, + 0.99901759227523, + 0.9990399576087657, + 0.9990623601064045, + 0.9990847983529437, + 0.9991072709849851, + 0.999129776688639, + 0.9991523141973033, + 0.9991748822895423, + 0.9991974797870288, + 0.9992201055525811, + 0.9992427584882694, + 0.9992654375335726, + 0.9992881416636329, + 0.9993108698875546, + 0.9993336212467593, + 0.9993563948134025, + 0.9993791896888545, + 0.9994195459291113, + 0.999558409451343, + 0.9996978344852497, + 0.9998379059448115, + 1.0000297885536367, + 1.0003137036164256, + 1.0006019528710535, + 1.0008997193960245, + 1.0012535378489382, + 1.0055260783243236, + 1.01290130355763, + 1.0201938457881885, + 1.0273562563071506, + 1.0343666442587687, + 1.0412023091764322, + 1.0478363258551944, + 1.054235386532086, + 1.0603571464833703, + 1.066146296428981, + 1.0715282924566574, + 1.0763986895539588, + 1.0806035957527016, + 1.083900191546168, + 1.0858652561517894, + 1.0856330647647126, + 1.0807823307315607, + ] + pa_data_kill_hold = [ + 0.9978984860292592, + 0.9978984862817281, + 0.9978984865393543, + 0.9978984868022875, + 0.997898487070702, + 0.9978984873447659, + 0.9978984876246634, + 0.997898487910578, + 0.9978984882027095, + 0.9978984885012607, + 0.997898488806446, + 0.9978984891184937, + 0.9978984894376299, + 0.997898489764103, + 0.99789849009817, + 0.9978984904400998, + 0.9978984907901691, + 0.9978984911486708, + 0.9978984915159195, + 0.9978984918922366, + 0.9978984922779631, + 0.9978984926734554, + 0.9978984930790854, + 0.9978984934952563, + 0.9978984939223793, + 0.9978984943608911, + 0.9978984948112544, + 0.9978984952739576, + 0.9978984957495157, + 0.9978984962384672, + 0.9978984967413924, + 0.9978984972588961, + 0.9978984977916201, + 0.9978984983402501, + 0.9978984989054998, + 0.9978984994881481, + 0.9978985000890045, + 0.9978985007089344, + 0.9978985013488667, + 0.9978985020097789, + 0.9978985026927234, + 0.9978985033988196, + 0.9978985041292661, + 0.9978985048853468, + 0.9978985056684264, + 0.9978985064799872, + 0.9978985073216076, + 0.9978985081949879, + 0.9978985091019636, + 0.9978985100445074, + 0.9978985110247587, + 0.9978985120450216, + 0.9978985131077971, + 0.9978985142158028, + 0.9978985153719866, + 0.9978985165795595, + 0.9978985178420279, + 0.9978985191632204, + 0.9978985205473282, + 0.9978985219989642, + 0.9978985235231874, + 0.9978985251255816, + 0.9978985268123234, + 0.9978985285902467, + 0.997898530466956, + 0.9978985324509142, + 0.9978985345515892, + 0.9978985367795932, + 0.9978985391468606, + 0.9978985416668759, + 0.9978985443549087, + 0.9978985472283487, + 0.9978985503070598, + 0.9978985536138554, + 0.9978985571750544, + 0.9978985610211893, + 0.9978985651878866, + 0.9978985697169596, + 0.9978985746578358, + 0.9978985800693498, + 0.997898586022116, + 0.9978985926016035, + 0.9984542080845076, + 1.0059833293452622, + 1.0134029079422973, + 1.0206985134834754, + 1.0278540499268765, + 1.034850595395227, + 1.0416653459437988, + 1.0482702865046438, + 1.0546303278690317, + 1.060700554010665, + 1.066421973991321, + 1.0717146467594005, + 1.076465895459925, + 1.0805085718925576, + 1.0835768817251614, + 1.0852034425335202, + 1.0844230589562682, + 1.0785159431192144, + ] + x_range = np.arange(0, 1, 0.01) + + fig, ax = plt.subplots() + ax.axhline(y=1, color="grey", ls="solid", lw=1) + ax.plot(x_range, ps_data_kill_hold, label="ps", ls="solid", lw=3) + ax.plot(x_range, pc_data_kill_hold, label="pc", ls="dashdot", lw=3) + ax.plot(x_range, pa_data_kill_hold, label="pa", ls="dotted", lw=3) + ax.set_title("Kill and Hold") + ax.set_xlabel("px") + ax.set_ylabel("rho") + ax.legend() + plt.show() + + # Skip and Zero plot + ps_data_skip_zero = [ + 0.9978984860292592, + 0.9978984862817318, + 0.9978984865393534, + 0.9978984868022858, + 0.9978984870707013, + 0.9978984873447672, + 0.9978984876246627, + 0.9978984879105776, + 0.9978984882027102, + 0.9978984885012605, + 0.9978984888064465, + 0.9978984891184925, + 0.9978984894376304, + 0.9978984897641039, + 0.9978984900981687, + 0.9978984904400983, + 0.997898490790167, + 0.9978984911486719, + 0.9978984915159202, + 0.9978984918922374, + 0.9978984922779635, + 0.9978984926734559, + 0.9978984930790898, + 0.9978984934952583, + 0.9978984939223797, + 0.9978984943608907, + 0.9978984948112563, + 0.9978984952739571, + 0.9978984957495161, + 0.9978984962384689, + 0.9978984967413932, + 0.9978984972588949, + 0.9978984977916199, + 0.9978984983402501, + 0.9978984989055008, + 0.9978984994881483, + 0.9978985000890029, + 0.9978985007089362, + 0.997898501348865, + 0.9978985020097788, + 0.9978985026927241, + 0.9978985033988178, + 0.9978985041292661, + 0.9978985048853428, + 0.9978985056684271, + 0.997898506479988, + 0.9978985073216065, + 0.9978985081949873, + 0.9978985091019632, + 0.9978985100445085, + 0.9978985110247592, + 0.9978985120450219, + 0.997898513107799, + 0.997898514215805, + 0.9978985153719862, + 0.9978985165795626, + 0.9978985178420263, + 0.9978985191632185, + 0.9978985205473302, + 0.9978985219989677, + 0.9978985235231876, + 0.9978985251255823, + 0.9978985268123244, + 0.9978985285902459, + 0.9978985304669554, + 0.9978985324509151, + 0.9978985345515892, + 0.9978985367795916, + 0.9978985391468598, + 0.997898541666876, + 0.9978985443549092, + 0.9978985472283517, + 0.9978985503070611, + 0.9978985536138556, + 0.9978985571750534, + 0.9978985610211909, + 0.9978985651878864, + 0.9978985697169624, + 0.9978985746578349, + 0.9978985800693504, + 0.9978985860221151, + 0.9978985926016063, + 0.9986281596844219, + 1.005814579163735, + 1.0131157921056069, + 1.0203442696626326, + 1.0274517936122698, + 1.0344084590943294, + 1.0411871515029416, + 1.0477579183109071, + 1.0540846614018, + 1.0601218552238083, + 1.0658100856500947, + 1.071069080399318, + 1.075785880940787, + 1.0797931012490305, + 1.082824812325663, + 1.084413875174669, + 1.0835969881279695, + 1.0776664649891043, + ] + pc_data_skip_zero = [ + 0.9978984860292592, + 0.9979123707853905, + 0.9979266408240767, + 0.9979412803513606, + 0.9979562741882387, + 0.9979716077532703, + 0.997987267044712, + 0.9980032386223362, + 0.9980195095890375, + 0.9980360675724222, + 0.998052900706441, + 0.9980699976131984, + 0.9980873473849512, + 0.9981049395664361, + 0.9981227641375471, + 0.998140811496372, + 0.9981590724426761, + 0.9981775381618314, + 0.9981962002092133, + 0.9982150504950804, + 0.9982340812699381, + 0.9982532851104169, + 0.9982726549056097, + 0.9982921838439575, + 0.9983118654005607, + 0.9983316933250176, + 0.9983516616297293, + 0.9983717645786339, + 0.9983919966764446, + 0.9984123526582772, + 0.9984328274797462, + 0.9984534163074273, + 0.9984741145097762, + 0.9984949176483799, + 0.9985158214696168, + 0.998536821896645, + 0.9985579150217793, + 0.9985790970991412, + 0.9986003645376806, + 0.9986217138944706, + 0.9986431418682924, + 0.9986646452935367, + 0.9986862211343182, + 0.9987078664789077, + 0.9987295785343396, + 0.9987513546213204, + 0.9987731921693213, + 0.9987950887118971, + 0.9988170418822022, + 0.9988390494087129, + 0.99886110911112, + 0.9989744341973246, + 0.9991955895508934, + 0.9994187415686175, + 0.9996439435707286, + 0.9998825945367704, + 1.0003449935613404, + 1.000812248861758, + 1.001284489110021, + 1.0017618441017602, + 1.0022444423534438, + 1.0027324092901724, + 1.0032258655424604, + 1.003724925146868, + 1.0042296935359374, + 1.0047402652342363, + 1.0052567211857466, + 1.005779125636134, + 1.0063075224852849, + 1.0068419310122592, + 1.0073823408566687, + 1.0079287061164504, + 1.0084809383914763, + 1.0090388985626693, + 1.0096023870451645, + 1.0101711321871025, + 1.0107447763979778, + 1.0113228594728714, + 1.0119047984213811, + 1.0124898628949852, + 1.0130771450091762, + 1.0136655219408806, + 1.0142536090899994, + 1.0148397007390253, + 1.0154216938872758, + 1.015996989049489, + 1.0165623589144404, + 1.0171137712105802, + 1.0176461447725598, + 1.0181530055358503, + 1.0186259879587638, + 1.0190540890459523, + 1.0194225093936136, + 1.0197107690159848, + 1.0198894674933248, + 1.0199143006024287, + 1.0197139119682963, + 1.0191617142908933, + 1.017995663323188, + 1.015485675838009, + ] + pa_data_skip_zero = [ + 0.9978984860292592, + 0.9978982337083446, + 0.9978979761880671, + 0.9978977133060668, + 0.9978974448931709, + 0.9978971707730036, + 0.9978968907616139, + 0.9978966046670679, + 0.9978963122889885, + 0.9978960134181214, + 0.997895707835802, + 0.9978953953134525, + 0.9978950756119886, + 0.9978947484812202, + 0.997894413659195, + 0.997894070871516, + 0.9978937198305657, + 0.9978933602347186, + 0.9978929917674745, + 0.9978926140965342, + 0.9978922268727923, + 0.9978918297292716, + 0.9978914222799463, + 0.9978910041185264, + 0.9978905748170666, + 0.9978901339245434, + 0.9978896809652443, + 0.9978892154370843, + 0.9978887368097438, + 0.9978882445226441, + 0.99788773798278, + 0.9978872165623165, + 0.9978866795960197, + 0.997886126378423, + 0.9978855561607295, + 0.9978849681474398, + 0.9978843614926691, + 0.9978837352960728, + 0.997883088598421, + 0.9978824203766744, + 0.9978817295386222, + 0.9978810149169189, + 0.9978802752625244, + 0.9978795092374247, + 0.9978787154065868, + 0.9978778922289826, + 0.9978770380476619, + 0.9978761510786117, + 0.9978752293983723, + 0.9978742709301459, + 0.9978732734282134, + 0.9978722344604253, + 0.9978711513884513, + 0.9978700213454871, + 0.9978688412109997, + 0.997867607582047, + 0.9978663167406195, + 0.9978649646163605, + 0.9978635467438584, + 0.9978620582135854, + 0.9978604936153551, + 0.9978588469728988, + 0.9978571116679721, + 0.9978552803518939, + 0.9978533448420802, + 0.9978512960005177, + 0.9978491235903731, + 0.9978468161060401, + 0.9978443605707171, + 0.9978417422940145, + 0.9978389445801669, + 0.9978359483746516, + 0.9978327318335983, + 0.9978292697955998, + 0.9978255331292064, + 0.9978214879207145, + 0.997817094454925, + 0.997812305924841, + 0.9978070667828608, + 0.9978013106122325, + 0.9977949573488758, + 0.9979622411430684, + 0.9982239456097534, + 0.9984901538115333, + 0.9987605994098896, + 0.9990349853294376, + 0.9995177442719444, + 1.0001477447359568, + 1.0007896336142619, + 1.001443420477501, + 1.0021093091820772, + 1.0027878049903634, + 1.0034798491972945, + 1.0041869471264913, + 1.0049111470842644, + 1.0056543943325655, + 1.006415818683618, + 1.0071828641350455, + 1.007904327181489, + 1.0083908590088804, + ] + x_range = np.arange(0, 1, 0.01) + + fig, ax = plt.subplots() + ax.axhline(y=1, color="grey", ls="solid", lw=1) + ax.plot(x_range, ps_data_skip_zero, label="ps", ls="solid", lw=3) + ax.plot(x_range, pc_data_skip_zero, label="pc", ls="dashdot", lw=3) + ax.plot(x_range, pa_data_skip_zero, label="pa", ls="dotted", lw=3) + ax.set_title("Skip and Zero") + ax.set_xlabel("px") + ax.set_ylabel("rho") + ax.legend() + plt.show() + + # Skip and Hold plot + ps_data_skip_hold = [ + 0.9978984860292592, + 0.9978984862817318, + 0.9978984865393534, + 0.9978984868022858, + 0.9978984870707013, + 0.9978984873447672, + 0.9978984876246627, + 0.9978984879105776, + 0.9978984882027102, + 0.9978984885012605, + 0.9978984888064465, + 0.9978984891184925, + 0.9978984894376304, + 0.9978984897641039, + 0.9978984900981687, + 0.9978984904400983, + 0.997898490790167, + 0.9978984911486719, + 0.9978984915159202, + 0.9978984918922374, + 0.9978984922779635, + 0.9978984926734559, + 0.9978984930790898, + 0.9978984934952583, + 0.9978984939223797, + 0.9978984943608907, + 0.9978984948112563, + 0.9978984952739571, + 0.9978984957495161, + 0.9978984962384689, + 0.9978984967413932, + 0.9978984972588949, + 0.9978984977916199, + 0.9978984983402501, + 0.9978984989055008, + 0.9978984994881483, + 0.9978985000890029, + 0.9978985007089362, + 0.997898501348865, + 0.9978985020097788, + 0.9978985026927241, + 0.9978985033988178, + 0.9978985041292661, + 0.9978985048853428, + 0.9978985056684271, + 0.997898506479988, + 0.9978985073216065, + 0.9978985081949873, + 0.9978985091019632, + 0.9978985100445085, + 0.9978985110247592, + 0.9978985120450219, + 0.997898513107799, + 0.997898514215805, + 0.9978985153719862, + 0.9978985165795626, + 0.9978985178420263, + 0.9978985191632185, + 0.9978985205473302, + 0.9978985219989677, + 0.9978985235231876, + 0.9978985251255823, + 0.9978985268123244, + 0.9978985285902459, + 0.9978985304669554, + 0.9978985324509151, + 0.9978985345515892, + 0.9978985367795916, + 0.9978985391468598, + 0.997898541666876, + 0.9978985443549092, + 0.9978985472283517, + 0.9978985503070611, + 0.9978985536138556, + 0.9978985571750534, + 0.9978985610211909, + 0.9978985651878864, + 0.9978985697169624, + 0.9978985746578349, + 0.9978985800693504, + 0.9978985860221151, + 0.9978985926016063, + 0.9986281596844219, + 1.005814579163735, + 1.0131157921056069, + 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pc_data_skip_hold, label="pc", ls="dashdot", lw=3) + ax.plot(x_range, pa_data_skip_hold, label="pa", ls="dotted", lw=3) + ax.set_title("Skip and Hold") + ax.set_xlabel("px") + ax.set_ylabel("rho") + ax.legend() + plt.show() + + +def plot_fig8(): + density = 0.01 + xs = np.arange(0, 1, density) + ys = np.arange(0, 1, density) + xs, ys = np.meshgrid(xs, ys) + zs = np.array( + [ + [ + 0.9978984860292597, + 0.997898233708345, + 0.9978979761880651, + 0.997897713306067, + 0.9978974448931713, + 0.9978971707730043, + 0.9978968907616153, + 0.9978966046670669, + 0.9978963122889899, + 0.9978960134181192, + 0.9978957078358042, + 0.9978953953134542, + 0.997895075611987, + 0.9978947484812196, + 0.9978944136591978, + 0.9978940708715154, + 0.9978937198305644, + 0.997893360234718, + 0.9978929917674739, + 0.9978926140965364, + 0.9978922268727954, + 0.9978918297292699, + 0.9978914222799469, + 0.997891004118527, + 0.9978905748170674, + 0.9978901339245414, + 0.9978896809652418, + 0.9978892154370852, + 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1.0443966410128387, + 1.0437383637591384, + 1.0430765783753435, + 1.042411222687827, + 1.0417422341823872, + 1.0410695502143545, + 1.040393108252864, + 1.039712846161209, + 1.0390287025149112, + 1.0383406169570109, + 1.0376485305881349, + 1.0369523863850139, + 1.036252129635762, + 1.0355477083726459, + 1.0348390737713737, + 1.0341261804709392, + 1.0334089867450957, + 1.0326874544267761, + 1.0319615484439, + 1.0312312357681526, + 1.0304964835004409, + 1.0297572557124297, + 1.0290135085252827, + 1.0282651827242772, + 1.0275121929697184, + 1.0267544123565466, + 1.025991650677696, + 1.025223624235615, + 1.0244499143806267, + 1.023669911068282, + 1.022882736487218, + 1.0220871419588748, + 1.0212813683268709, + 1.0204629548617905, + 1.019628472052578, + 1.0187731346046134, + 1.017890211058146, + 1.0169700566425346, + 1.015998374142783, + 1.0149526865086416, + 1.0137939418117854, + 1.0124413723178065, + 1.010660838021691, + ], + ] + ) + + fig, ax = plt.subplots(subplot_kw={"projection": "3d"}) + surf = ax.plot_surface(xs, ys, zs, cmap=cm.coolwarm, linewidth=0, antialiased=False) + fig.colorbar(surf, shrink=0.5, aspect=5) + ax.invert_xaxis() + ax.set_xlabel("pa") + ax.set_ylabel("ps") + plt.show() + + +def print_table2(): + print(f"Kill+Zero: {get_rho('kill_zero', ps=0.15, pc=0.4, pa=0.05)}") + print(f"Kill+Hold: {get_rho('kill_hold', ps=0.15, pc=0.4, pa=0.05)}") + print(f"Skip+Zero: {get_rho('skip_zero', ps=0.15, pc=0.4, pa=0.05)}") + print(f"Skip+Hold: {get_rho('skip_zero', ps=0.15, pc=0.4, pa=0.05)}") + + +if __name__ == "__main__": + # compute_single_variations("skip_hold") + # compute_double_variations("kill_zero") + # compute_double_variations_fast() + # plot_fig6() + # print_table2() + # plot_fig8() + pcs = np.arange(0.6, 0.8, 0.01) + for pc in pcs: + print(f"{pc}: {get_rho('skip_hold', pc=pc)}") diff --git a/scripts/cruise_control.py b/scripts/cruise_control.py new file mode 100644 index 0000000..881164b --- /dev/null +++ b/scripts/cruise_control.py @@ -0,0 +1,11596 @@ +from inputparser import Parser +from program import normalize_program +from recurrences.rec_builder import RecBuilder +from symengine.lib.symengine_wrapper import sympify +from stability_analysis import NumericStabilityAnalyzer, SymbolicStabilityAnalyzer + +import numpy as np +import matplotlib.pyplot as plt +from matplotlib import cm +from progress.bar import Bar + + +def get_rho(strategy, ps=0.0, pc=0.0, pa=0.0): + file_path = f"../benchmarks/control_theory/cruise_control/{strategy}.prob" + program = Parser().parse_file(file_path) + for assign in program.initial: + if str(assign.variable) == "ps": + assign.polynomials = [sympify(ps)] + if str(assign.variable) == "pc": + assign.polynomials = [sympify(pc)] + if str(assign.variable) == "pa": + assign.polynomials = [sympify(pa)] + + program = normalize_program(program) + + rec_builder = RecBuilder(program) + recurrences = rec_builder.get_recurrences( + "x1", "x2", "x3", "x1**2", "x2**2", "x3**2" + ) + + analyzer = SymbolicStabilityAnalyzer(recurrences) + return float(analyzer.get_rho()) + + +def compute_single_variations(strategy): + # vary ps + ps_data = [] + with Bar("Varying ps ... ") as bar: + for ps in np.arange(0, 1, 0.01): + ps_data.append(get_rho(strategy, ps=ps)) + bar.next() + print(f"ps data for {strategy}:") + print(ps_data) + + # vary pc + pc_data = [] + with Bar("Varying pc ... ") as bar: + for pc in np.arange(0, 1, 0.01): + pc_data.append(get_rho(strategy, pc=pc)) + bar.next() + print(f"pc data for {strategy}:") + print(pc_data) + + # vary pa + pa_data = [] + with Bar("Varying pa ... ") as bar: + for pa in np.arange(0, 1, 0.01): + pa_data.append(get_rho(strategy, pa=pa)) + bar.next() + print(f"pa data for {strategy}:") + print(pa_data) + + +def compute_double_variations(strategy): + density = 0.01 + xs = np.arange(0, 1, density) + ys = np.arange(0, 1, density) + xs, ys = np.meshgrid(xs, ys) + zs = np.zeros(xs.shape) + with Bar("Varying pc and ps ...", max=int((1 / density) ** 2)) as bar: + for i in range(zs.shape[0]): + for j in range(zs.shape[1]): + pc = xs[i, j] + ps = ys[i, j] + zs[i, j] = get_rho(strategy, pc=pc, ps=ps) + bar.next() + print("2D values:") + print(zs.tolist()) + + +def plot_fig2(): + # Kill and Zero plot + ps_data_kill_zero = [ + 0.9507846751471404, + 0.950763753079543, + 0.9507424127949756, + 0.9507206418171972, + 0.9506984271776994, + 0.9506757553917314, + 0.9506526124329601, + 0.9506289837066203, + 0.9506048540211449, + 0.95058020755812, + 0.9505550278404666, + 0.9505292976987124, + 0.9505029992352793, + 0.9504761137865855, + 0.9504486218828819, + 0.9504205032055834, + 0.9503917365420607, + 0.9503622997375295, + 0.9503321696440722, + 0.950301322066358, + 0.9502697317040206, + 0.950237372090363, + 0.950204215527187, + 0.9501702330154487, + 0.9501353941814954, + 0.9500996671985247, + 0.9500630187030398, + 0.9500254137058483, + 0.9499868154973475, + 0.9499471855466497, + 0.9499064833941966, + 0.9498646665374388, + 0.9498216903091175, + 0.9497775077477918, + 0.9497320694600249, + 0.9496853234739272, + 0.9496372150835005, + 0.9495876866833363, + 0.9495366775933484, + 0.9494841238730239, + 0.9494299581249772, + 0.94937410928753, + 0.9493165024161715, + 0.9492570584540148, + 0.9491956939914065, + 0.9491323210153103, + 0.9490668466493087, + 0.9489991728856313, + 0.9489291963111305, + 0.9488568078300641, + 0.9487818923873134, + 0.9487043286971398, + 0.948623988984039, + 0.9485407387442819, + 0.9484544365393669, + 0.9483649338357129, + 0.9482720749089825, + 0.9539373084375898, + 0.9629811862395585, + 0.9719874972840551, + 0.9809525483078207, + 0.9898733729482746, + 0.9987473282298689, + 1.007571886825178, + 1.016344517816983, + 1.0250626101173923, + 1.0337234171078307, + 1.0423240116304244, + 1.0508612453404207, + 1.059331708782899, + 1.067731689701585, + 1.0760571276135364, + 1.084303562857684, + 1.0924660782740503, + 1.1005392314446911, + 1.1085169750375223, + 1.116392562221101, + 1.1241584333190764, + 1.131806078771986, + 1.1393258719603683, + 1.146706863343357, + 1.1539365244251787, + 1.1610004258795934, + 1.167881828122957, + 1.1745611537444447, + 1.1810152978754558, + 1.1872167121232302, + 1.1931321654894578, + 1.1987210335140657, + 1.2039328795271274, + 1.2087039400352693, + 1.2129518504708885, + 1.2165674201022914, + 1.2194011918341174, + 1.2212401675875582, + 1.221764394696108, + 1.2204575684119403, + 1.2163954161946386, + 1.2076246480567658, + 1.1884542022795663, + ] + pc_data_kill_zero = [ + 0.9507846751471404, + 0.9508004479300163, + 0.9508192629201162, + 0.950841398602657, + 0.9508671590334299, + 0.950896876215339, + 0.9509309126718473, + 0.9509696642238268, + 0.9510135629733136, + 0.9510630804930384, + 0.951118731214751, + 0.9511810760012258, + 0.9512507258765027, + 0.9513283458755291, + 0.9514146589577307, + 0.9515104499084239, + 0.9516165691269753, + 0.9517339361710965, + 0.9518635428921333, + 0.9520064559575019, + 0.9521638185138557, + 0.952336850700305, + 0.9525268486773927, + 0.9527351817988647, + 0.9529632875247788, + 0.9532126636635667, + 0.9534848575453622, + 0.9537814517786423, + 0.9541040463359393, + 0.9544542368593566, + 0.9548335892758254, + 0.9552436110633836, + 0.9556857198007477, + 0.956161209943174, + 0.9566712190656637, + 0.9572166950629782, + 0.9577983659522656, + 0.9584167139533253, + 0.9590719553985143, + 0.9597640277453611, + 0.9604925845480372, + 0.9612569987309777, + 0.9620563739560749, + 0.9628895633488687, + 0.9637551944079311, + 0.9646516986099031, + 0.9655773440625989, + 0.966530269550222, + 0.967508518437827, + 0.9685100711233663, + 0.9695328750056691, + 0.9705748712378246, + 0.9716340178260569, + 0.9727083088912621, + 0.9737957901211833, + 0.9748945706002696, + 0.976002831313217, + 0.9771188306827616, + 0.9782409075300328, + 0.9793674818454278, + 0.9804970537373376, + 0.9816282008923576, + 0.982759574839131, + 0.9838898962631798, + 0.98501794957494, + 0.9861425768892257, + 0.9872626715332168, + 0.9883771711611623, + 0.9894850505180751, + 0.9905853138604289, + 0.9927444536328506, + 0.9950133022297394, + 0.9972639277487634, + 0.9994947215945512, + 1.001704044701955, + 1.0038902079248502, + 1.0060514499863153, + 1.0081859122531185, + 1.010291609374355, + 1.0123663945185486, + 1.0144079175193554, + 1.0164135736412836, + 1.0183804398170826, + 1.020305193952987, + 1.022184011026986, + 1.0240124268578796, + 1.0257851559841553, + 1.0274958429856293, + 1.029136714856655, + 1.0306980820233653, + 1.0321676000544866, + 1.0335291380614007, + 1.0347609702686547, + 1.0358327365033224, + 1.0367000054531617, + 1.0372937494478511, + 1.037497723590286, + 1.0370922102034312, + 1.0355792158791284, + 1.0313687959641955, + ] + pa_data_kill_zero = [ + 0.9507846751471404, + 0.9508004479300163, + 0.9508192629201162, + 0.950841398602657, + 0.9508671590334299, + 0.950896876215339, + 0.9509309126718473, + 0.9509696642238268, + 0.9510135629733136, + 0.9510630804930384, + 0.951118731214751, + 0.9511810760012258, + 0.9512507258765027, + 0.9513283458755291, + 0.9514146589577307, + 0.9515104499084239, + 0.9516165691269753, + 0.9517339361710965, + 0.9518635428921333, + 0.9520064559575019, + 0.9521638185138557, + 0.952336850700305, + 0.9525268486773927, + 0.9527351817988647, + 0.9529632875247788, + 0.9532126636635667, + 0.9534848575453622, + 0.9537814517786423, + 0.9541040463359393, + 0.9544542368593566, + 0.9548335892758254, + 0.9552436110633836, + 0.9556857198007477, + 0.956161209943174, + 0.9566712190656637, + 0.9572166950629782, + 0.9577983659522656, + 0.9584167139533253, + 0.9590719553985143, + 0.9597640277453611, + 0.9604925845480372, + 0.9612569987309777, + 0.9620563739560749, + 0.9628895633488687, + 0.9637551944079311, + 0.9646516986099031, + 0.9655773440625989, + 0.966530269550222, + 0.967508518437827, + 0.9685100711233663, + 0.9695328750056691, + 0.9705748712378246, + 0.9716340178260569, + 0.9727083088912621, + 0.9737957901211833, + 0.9748945706002696, + 0.976002831313217, + 0.9771188306827616, + 0.9782409075300328, + 0.9793674818454278, + 0.9804970537373376, + 0.9816282008923576, + 0.982759574839131, + 0.9838898962631798, + 0.98501794957494, + 0.9861425768892257, + 0.9872626715332168, + 0.9883771711611623, + 0.9894850505180751, + 0.9905853138604289, + 0.9927444536328506, + 0.9950133022297394, + 0.9972639277487634, + 0.9994947215945512, + 1.001704044701955, + 1.0038902079248502, + 1.0060514499863153, + 1.0081859122531185, + 1.010291609374355, + 1.0123663945185486, + 1.0144079175193554, + 1.0164135736412836, + 1.0183804398170826, + 1.020305193952987, + 1.022184011026986, + 1.0240124268578796, + 1.0257851559841553, + 1.0274958429856293, + 1.029136714856655, + 1.0306980820233653, + 1.0321676000544866, + 1.0335291380614007, + 1.0347609702686547, + 1.0358327365033224, + 1.0367000054531617, + 1.0372937494478511, + 1.037497723590286, + 1.0370922102034312, + 1.0355792158791284, + 1.0313687959641955, + ] + x_range = np.arange(0, 1, 0.01) + + fig, ax = plt.subplots() + ax.axhline(y=1, color="grey", ls="solid", lw=1) + ax.plot(x_range, ps_data_kill_zero, label="ps", ls="solid", lw=3) + ax.plot(x_range, pc_data_kill_zero, label="pc", ls="dashdot", lw=3) + ax.plot(x_range, pa_data_kill_zero, label="pa", ls="dotted", lw=3) + ax.set_title("Kill and Zero") + ax.set_xlabel("px") + ax.set_ylabel("rho") + ax.legend() + plt.show() + + # Kill and Hold plot + ps_data_kill_hold = [ + 0.9507846751471404, + 0.950763753079543, + 0.9507424127949756, + 0.9507206418171972, + 0.9506984271776994, + 0.9506757553917314, + 0.9506526124329601, + 0.9506289837066203, + 0.9506048540211449, + 0.95058020755812, + 0.9505550278404666, + 0.9505292976987124, + 0.9505029992352793, + 0.9504761137865855, + 0.9504486218828819, + 0.9504205032055834, + 0.9503917365420607, + 0.9503622997375295, + 0.9503321696440722, + 0.950301322066358, + 0.9502697317040206, + 0.950237372090363, + 0.950204215527187, + 0.9501702330154487, + 0.9501353941814954, + 0.9500996671985247, + 0.9500630187030398, + 0.9500254137058483, + 0.9499868154973475, + 0.9499471855466497, + 0.9499064833941966, + 0.9498646665374388, + 0.9498216903091175, + 0.9497775077477918, + 0.9497320694600249, + 0.9496853234739272, + 0.9496372150835005, + 0.9495876866833363, + 0.9495366775933484, + 0.9494841238730239, + 0.9494299581249772, + 0.94937410928753, + 0.9493165024161715, + 0.9492570584540148, + 0.9491956939914065, + 0.9491323210153103, + 0.9490668466493087, + 0.9489991728856313, + 0.9489291963111305, + 0.9488568078300641, + 0.9487818923873134, + 0.9487043286971398, + 0.948623988984039, + 0.9485407387442819, + 0.9484544365393669, + 0.9483649338357129, + 0.9482720749089825, + 0.9539373084375898, + 0.9629811862395585, + 0.9719874972840551, + 0.9809525483078207, + 0.9898733729482746, + 0.9987473282298689, + 1.007571886825178, + 1.016344517816983, + 1.0250626101173923, + 1.0337234171078307, + 1.0423240116304244, + 1.0508612453404207, + 1.059331708782899, + 1.067731689701585, + 1.0760571276135364, + 1.084303562857684, + 1.0924660782740503, + 1.1005392314446911, + 1.1085169750375223, + 1.116392562221101, + 1.1241584333190764, + 1.131806078771986, + 1.1393258719603683, + 1.146706863343357, + 1.1539365244251787, + 1.1610004258795934, + 1.167881828122957, + 1.1745611537444447, + 1.1810152978754558, + 1.1872167121232302, + 1.1931321654894578, + 1.1987210335140657, + 1.2039328795271274, + 1.2087039400352693, + 1.2129518504708885, + 1.2165674201022914, + 1.2194011918341174, + 1.2212401675875582, + 1.221764394696108, + 1.2204575684119403, + 1.2163954161946386, + 1.2076246480567658, + 1.1884542022795663, + ] + pc_data_kill_hold = [ + 0.9507846751471404, + 0.9507637530795425, + 0.9507424127949781, + 0.9507206418171984, + 0.9506984271776981, + 0.9506757553917323, + 0.9506526124329636, + 0.9506289837066186, + 0.9506048540211447, + 0.9505802075581207, + 0.9505550278404648, + 0.9505292976987101, + 0.9505029992352784, + 0.9504761137865853, + 0.9504486218828846, + 0.9504205032055832, + 0.9503917365420559, + 0.9503622997375312, + 0.9503321696440756, + 0.9503013220663603, + 0.9502697317040243, + 0.9502373720903645, + 0.9502042155271861, + 0.9501702330154452, + 0.950135394181494, + 0.9500996671985221, + 0.9500630187030374, + 0.9500254137058542, + 0.9499868154973486, + 0.949947185546645, + 0.9499064833941936, + 0.9498646665374387, + 0.9498216903091183, + 0.9497775077477868, + 0.9497320694600271, + 0.9496853234739265, + 0.9496372150834993, + 0.9495876866833343, + 0.9495366775933446, + 0.949484123873023, + 0.9494299581249779, + 0.9493741092875286, + 0.9493165024161725, + 0.9492570584540152, + 0.949195693991405, + 0.9491323210153109, + 0.9490668466493097, + 0.9489991728856355, + 0.9489291963111297, + 0.9488568078300589, + 0.9487818923873126, + 0.9487043286971436, + 0.9486239889840421, + 0.9485407387442798, + 0.9484544365393638, + 0.9483649338357081, + 0.9482720749089801, + 0.9539373084375896, + 0.9629811862395642, + 0.9719874972840314, + 0.9809525483078136, + 0.9898733729482728, + 0.9987473282298677, + 1.0075718868251669, + 1.0163445178169788, + 1.0250626101173843, + 1.0337234171078402, + 1.0423240116304302, + 1.0508612453404174, + 1.0593317087828968, + 1.0677316897015758, + 1.076057127613531, + 1.0843035628576794, + 1.092466078274051, + 1.1005392314446925, + 1.1085169750375166, + 1.1163925622210995, + 1.1241584333190724, + 1.1318060787719892, + 1.1393258719603692, + 1.1467068633433617, + 1.1539365244251767, + 1.1610004258796038, + 1.1678818281229515, + 1.174561153744437, + 1.1810152978754493, + 1.187216712123229, + 1.1931321654894527, + 1.1987210335140477, + 1.2039328795271265, + 1.2087039400352724, + 1.2129518504708927, + 1.216567420102295, + 1.2194011918341137, + 1.2212401675875653, + 1.2217643946961014, + 1.220457568411925, + 1.2163954161946473, + 1.207624648056774, + 1.1884542022795688, + ] + pa_data_kill_hold = [ + 0.9507846751471404, + 0.9507637530795425, + 0.9507424127949781, + 0.9507206418171984, + 0.9506984271776981, + 0.9506757553917323, + 0.9506526124329636, + 0.9506289837066186, + 0.9506048540211447, + 0.9505802075581207, + 0.9505550278404648, + 0.9505292976987101, + 0.9505029992352784, + 0.9504761137865853, + 0.9504486218828846, + 0.9504205032055832, + 0.9503917365420559, + 0.9503622997375312, + 0.9503321696440756, + 0.9503013220663603, + 0.9502697317040243, + 0.9502373720903645, + 0.9502042155271861, + 0.9501702330154452, + 0.950135394181494, + 0.9500996671985221, + 0.9500630187030374, + 0.9500254137058542, + 0.9499868154973486, + 0.949947185546645, + 0.9499064833941936, + 0.9498646665374387, + 0.9498216903091183, + 0.9497775077477868, + 0.9497320694600271, + 0.9496853234739265, + 0.9496372150834993, + 0.9495876866833343, + 0.9495366775933446, + 0.949484123873023, + 0.9494299581249779, + 0.9493741092875286, + 0.9493165024161725, + 0.9492570584540152, + 0.949195693991405, + 0.9491323210153109, + 0.9490668466493097, + 0.9489991728856355, + 0.9489291963111297, + 0.9488568078300589, + 0.9487818923873126, + 0.9487043286971436, + 0.9486239889840421, + 0.9485407387442798, + 0.9484544365393638, + 0.9483649338357081, + 0.9482720749089801, + 0.9539373084375896, + 0.9629811862395642, + 0.9719874972840314, + 0.9809525483078136, + 0.9898733729482728, + 0.9987473282298677, + 1.0075718868251669, + 1.0163445178169788, + 1.0250626101173843, + 1.0337234171078402, + 1.0423240116304302, + 1.0508612453404174, + 1.0593317087828968, + 1.0677316897015758, + 1.076057127613531, + 1.0843035628576794, + 1.092466078274051, + 1.1005392314446925, + 1.1085169750375166, + 1.1163925622210995, + 1.1241584333190724, + 1.1318060787719892, + 1.1393258719603692, + 1.1467068633433617, + 1.1539365244251767, + 1.1610004258796038, + 1.1678818281229515, + 1.174561153744437, + 1.1810152978754493, + 1.187216712123229, + 1.1931321654894527, + 1.1987210335140477, + 1.2039328795271265, + 1.2087039400352724, + 1.2129518504708927, + 1.216567420102295, + 1.2194011918341137, + 1.2212401675875653, + 1.2217643946961014, + 1.220457568411925, + 1.2163954161946473, + 1.207624648056774, + 1.1884542022795688, + ] + x_range = np.arange(0, 1, 0.01) + + fig, ax = plt.subplots() + ax.axhline(y=1, color="grey", ls="solid", lw=1) + ax.plot(x_range, ps_data_kill_hold, label="ps", ls="solid", lw=3) + ax.plot(x_range, pc_data_kill_hold, label="pc", ls="dashdot", lw=3) + ax.plot(x_range, pa_data_kill_hold, label="pa", ls="dotted", lw=3) + ax.set_title("Kill and Hold") + ax.set_xlabel("px") + ax.set_ylabel("rho") + ax.legend() + plt.show() + + # Skip and Zero plot + ps_data_skip_zero = [ + 0.9507846751471404, + 0.950763753079543, + 0.9507424127949756, + 0.9507206418171972, + 0.9506984271776994, + 0.9506757553917314, + 0.9506526124329601, + 0.9506289837066203, + 0.9506048540211449, + 0.95058020755812, + 0.9505550278404666, + 0.9505292976987124, + 0.9505029992352793, + 0.9504761137865855, + 0.9504486218828819, + 0.9504205032055834, + 0.9503917365420607, + 0.9503622997375295, + 0.9503321696440722, + 0.950301322066358, + 0.9502697317040206, + 0.950237372090363, + 0.950204215527187, + 0.9501702330154487, + 0.9501353941814954, + 0.9500996671985247, + 0.9500630187030398, + 0.9500254137058483, + 0.9499868154973475, + 0.9499471855466497, + 0.9499064833941966, + 0.9498646665374388, + 0.9498216903091175, + 0.9497775077477918, + 0.9497320694600249, + 0.9496853234739272, + 0.9496372150835005, + 0.9495876866833363, + 0.9495366775933484, + 0.9494841238730239, + 0.9494299581249772, + 0.94937410928753, + 0.9493165024161715, + 0.9492570584540148, + 0.9491956939914065, + 0.9491323210153103, + 0.9490668466493087, + 0.9489991728856313, + 0.9489291963111305, + 0.9488568078300641, + 0.9487818923873134, + 0.9487043286971398, + 0.948623988984039, + 0.9485407387442819, + 0.9484544365393669, + 0.9483649338357129, + 0.9482720749089825, + 0.9539373084375898, + 0.9629811862395585, + 0.9719874972840551, + 0.9809525483078207, + 0.9898733729482746, + 0.9987473282298689, + 1.007571886825178, + 1.016344517816983, + 1.0250626101173923, + 1.0337234171078307, + 1.0423240116304244, + 1.0508612453404207, + 1.059331708782899, + 1.067731689701585, + 1.0760571276135364, + 1.084303562857684, + 1.0924660782740503, + 1.1005392314446911, + 1.1085169750375223, + 1.116392562221101, + 1.1241584333190764, + 1.131806078771986, + 1.1393258719603683, + 1.146706863343357, + 1.1539365244251787, + 1.1610004258795934, + 1.167881828122957, + 1.1745611537444447, + 1.1810152978754558, + 1.1872167121232302, + 1.1931321654894578, + 1.1987210335140657, + 1.2039328795271274, + 1.2087039400352693, + 1.2129518504708885, + 1.2165674201022914, + 1.2194011918341174, + 1.2212401675875582, + 1.221764394696108, + 1.2204575684119403, + 1.2163954161946386, + 1.2076246480567658, + 1.1884542022795663, + ] + pc_data_skip_zero = [ + 0.9507846751471404, + 0.9507789470553917, + 0.9507746124312688, + 0.9507718210406172, + 0.9507707380482425, + 0.9507715457386796, + 0.9507744454464271, + 0.950779659722532, + 0.9507874347679334, + 0.950798043167783, + 0.9508117869650623, + 0.950829001116487, + 0.9508500573784036, + 0.9508753686755304, + 0.9509053940106654, + 0.95094064397828, + 0.9509816869498354, + 0.9510291560019294, + 0.9510837566605448, + 0.9511462755338608, + 0.9512175899011811, + 0.9512986783149822, + 0.951390632253754, + 0.9514946688325644, + 0.951612144531685, + 0.9517445698356498, + 0.9518936245804009, + 0.9520611736763167, + 0.9522492827033153, + 0.9524602326526491, + 0.9526965328135338, + 0.9529609304703451, + 0.9532564156957202, + 0.9535862191174075, + 0.9539538001446094, + 0.9543628228303049, + 0.9548171164194172, + 0.9553206178176927, + 0.9558772938579769, + 0.9564910424742761, + 0.9571655737942406, + 0.9579042746823087, + 0.9587100631840307, + 0.9595852422029892, + 0.9605313639784734, + 0.9615491178674739, + 0.9626382530545178, + 0.9637975449585756, + 0.9650248096030185, + 0.9663169648489845, + 0.9676701322060612, + 0.969079768920666, + 0.9705408178561609, + 0.9720478624866212, + 0.9735952758318435, + 0.9751773547751575, + 0.976788434258004, + 0.9784229787644584, + 0.9800756509199401, + 0.9817413587628221, + 0.9834152843051527, + 0.9854548753686175, + 0.9889328364867414, + 0.9923894994975835, + 0.9958189570896228, + 0.9992156148548627, + 1.002574142292494, + 1.0058894238154716, + 1.0091565099934225, + 1.0123705689884412, + 1.015526837910062, + 1.0186205736157485, + 1.0216470022956567, + 1.0246012669903222, + 1.0274783719782528, + 1.0302731227190391, + 1.0329800597225962, + 1.0355933843060627, + 1.0381068736561643, + 1.0405137818786308, + 1.0428067227034383, + 1.0449775281034641, + 1.0470170750826275, + 1.0489150700131724, + 1.0506597756812586, + 1.0522376598956247, + 1.0536329348705855, + 1.0548269414757503, + 1.0557973080467797, + 1.0565167727752016, + 1.0569514882781434, + 1.057058499604154, + 1.0567818444593708, + 1.0560462334438956, + 1.0547461962942402, + 1.0527260102902916, + 1.0497387718554474, + 1.0453508095793087, + 1.0386684189670017, + 1.0272552760452847, + ] + pa_data_skip_zero = [ + 0.9507846751471404, + 0.9508004479300163, + 0.9508192629201162, + 0.950841398602657, + 0.9508671590334299, + 0.950896876215339, + 0.9509309126718473, + 0.9509696642238268, + 0.9510135629733136, + 0.9510630804930384, + 0.951118731214751, + 0.9511810760012258, + 0.9512507258765027, + 0.9513283458755291, + 0.9514146589577307, + 0.9515104499084239, + 0.9516165691269753, + 0.9517339361710965, + 0.9518635428921333, + 0.9520064559575019, + 0.9521638185138557, + 0.952336850700305, + 0.9525268486773927, + 0.9527351817988647, + 0.9529632875247788, + 0.9532126636635667, + 0.9534848575453622, + 0.9537814517786423, + 0.9541040463359393, + 0.9544542368593566, + 0.9548335892758254, + 0.9552436110633836, + 0.9556857198007477, + 0.956161209943174, + 0.9566712190656637, + 0.9572166950629782, + 0.9577983659522656, + 0.9584167139533253, + 0.9590719553985143, + 0.9597640277453611, + 0.9604925845480372, + 0.9612569987309777, + 0.9620563739560749, + 0.9628895633488687, + 0.9637551944079311, + 0.9646516986099031, + 0.9655773440625989, + 0.966530269550222, + 0.967508518437827, + 0.9685100711233663, + 0.9695328750056691, + 0.9705748712378246, + 0.9716340178260569, + 0.9727083088912621, + 0.9737957901211833, + 0.9748945706002696, + 0.976002831313217, + 0.9771188306827616, + 0.9782409075300328, + 0.9793674818454278, + 0.9804970537373376, + 0.9816282008923576, + 0.982759574839131, + 0.9838898962631798, + 0.98501794957494, + 0.9861425768892257, + 0.9872626715332168, + 0.9883771711611623, + 0.9894850505180751, + 0.9905853138604289, + 0.9927444536328506, + 0.9950133022297394, + 0.9972639277487634, + 0.9994947215945512, + 1.001704044701955, + 1.0038902079248502, + 1.0060514499863153, + 1.0081859122531185, + 1.010291609374355, + 1.0123663945185486, + 1.0144079175193554, + 1.0164135736412836, + 1.0183804398170826, + 1.020305193952987, + 1.022184011026986, + 1.0240124268578796, + 1.0257851559841553, + 1.0274958429856293, + 1.029136714856655, + 1.0306980820233653, + 1.0321676000544866, + 1.0335291380614007, + 1.0347609702686547, + 1.0358327365033224, + 1.0367000054531617, + 1.0372937494478511, + 1.037497723590286, + 1.0370922102034312, + 1.0355792158791284, + 1.0313687959641955, + ] + x_range = np.arange(0, 1, 0.01) + + fig, ax = plt.subplots() + ax.axhline(y=1, color="grey", ls="solid", lw=1) + ax.plot(x_range, ps_data_skip_zero, label="ps", ls="solid", lw=3) + ax.plot(x_range, pc_data_skip_zero, label="pc", ls="dashdot", lw=3) + ax.plot(x_range, pa_data_skip_zero, label="pa", ls="dotted", lw=3) + ax.set_title("Skip and Zero") + ax.set_xlabel("px") + ax.set_ylabel("rho") + ax.legend() + plt.show() + + # Skip and Hold plot + ps_data_skip_hold = [ + 0.9507846751471404, + 0.950763753079543, + 0.9507424127949756, + 0.9507206418171972, + 0.9506984271776994, + 0.9506757553917314, + 0.9506526124329601, + 0.9506289837066203, + 0.9506048540211449, + 0.95058020755812, + 0.9505550278404666, + 0.9505292976987124, + 0.9505029992352793, + 0.9504761137865855, + 0.9504486218828819, + 0.9504205032055834, + 0.9503917365420607, + 0.9503622997375295, + 0.9503321696440722, + 0.950301322066358, + 0.9502697317040206, + 0.950237372090363, + 0.950204215527187, + 0.9501702330154487, + 0.9501353941814954, + 0.9500996671985247, + 0.9500630187030398, + 0.9500254137058483, + 0.9499868154973475, + 0.9499471855466497, + 0.9499064833941966, + 0.9498646665374388, + 0.9498216903091175, + 0.9497775077477918, + 0.9497320694600249, + 0.9496853234739272, + 0.9496372150835005, + 0.9495876866833363, + 0.9495366775933484, + 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ax.plot(x_range, pc_data_skip_hold, label="pc", ls="dashdot", lw=3) + ax.plot(x_range, pa_data_skip_hold, label="pa", ls="dotted", lw=3) + ax.set_title("Skip and Hold") + ax.set_xlabel("px") + ax.set_ylabel("rho") + ax.legend() + plt.show() + + +def plot_fig4(): + density = 0.01 + xs = np.arange(0, 1, density) + ys = np.arange(0, 1, density) + xs, ys = np.meshgrid(xs, ys) + zs = np.array( + [ + [ + 0.9507846751471404, + 0.950742858555921, + 0.9507002638895056, + 0.9506568714019266, + 0.9506126607904426, + 0.9505676111844323, + 0.9505217011348324, + 0.9504749086044056, + 0.9504272109589903, + 0.9503785849598997, + 0.9503290067577377, + 0.9502784518878906, + 0.9502268952679442, + 0.9501743111974502, + 0.9501206733603386, + 0.9500659548304785, + 0.9500101280808411, + 0.9499531649968131, + 0.9498950368943602, + 0.949835714543634, + 0.94977516819893, + 0.94971336763589, + 0.9496502821968502, + 0.9495858808456553, + 0.9495201322330936, + 0.949453004774482, + 0.9493844667409318, + 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1.1521434267288961, + 1.151169265657713, + 1.1501702245662546, + 1.149145000458528, + 1.1480921816173506, + 1.1470102349553892, + 1.1458974914510187, + 1.1447521293080343, + 1.143572154394773, + 1.1423553774135162, + 1.1410993871159292, + 1.1398015187065145, + 1.1384588163489244, + 1.1370679883915882, + 1.1356253535320762, + 1.134126775606758, + 1.132567583967073, + 1.1309424754056614, + 1.1292453922018952, + 1.1274693688797666, + 1.1256063374234846, + 1.1236468765137322, + 1.1215798840821576, + 1.1193921428803941, + 1.1170677336650874, + 1.1145872261863965, + 1.1119265373602563, + 1.1090552751989113, + 1.1059342587185454, + 1.1025116590668271, + 1.0987167097426858, + 1.0944488445893514, + 1.0895574988015964, + 1.0838006538913825, + 1.0767470650360997, + 1.067490444550895, + 1.053408216577705, + ], + ] + ) + + fig, ax = plt.subplots(subplot_kw={"projection": "3d"}) + surf = ax.plot_surface(xs, ys, zs, cmap=cm.coolwarm, linewidth=0, antialiased=False) + fig.colorbar(surf, shrink=0.5, aspect=5) + ax.invert_xaxis() + ax.set_xlabel("pc") + ax.set_ylabel("ps") + plt.show() + + +def print_table1(): + print(f"Kill+Zero: {get_rho('kill_zero', ps=0.15, pc=0.4, pa=0.05)}") + print(f"Kill+Hold: {get_rho('kill_hold', ps=0.15, pc=0.4, pa=0.05)}") + print(f"Skip+Zero: {get_rho('skip_zero', ps=0.15, pc=0.4, pa=0.05)}") + print(f"Skip+Hold: {get_rho('skip_zero', ps=0.15, pc=0.4, pa=0.05)}") + + +if __name__ == "__main__": + # compute_single_variations("skip_hold") + # plot_fig2() + # print_table1() + # compute_double_variations("skip_hold") + # plot_fig4() + pcs = np.arange(0.4, 0.6, 0.01) + for pc in pcs: + print(f"{pc}: {get_rho('skip_hold', pc=pc)}") diff --git a/scripts/cruise_controll_sh.py b/scripts/cruise_controll_sh.py new file mode 100644 index 0000000..88c239f --- /dev/null +++ b/scripts/cruise_controll_sh.py @@ -0,0 +1,46 @@ +import numpy as np +from progress.bar import Bar + + +def run_process(): + x1 = 1 + x2 = 1 + x3 = 1 + u = 1 + y1 = x1 + y2 = x2 + y3 = x3 + pc = 0.5 + for _ in range(100): + # store old values + x1o = x1 + x2o = x2 + x3o = x3 + + # state update + x1 = 1 * x1o + 0.01 * x2o + 0 * x3o + 0.0001 * u + x2 = -0.0003 * x1o + 0.9997 * x2o + 0.01 * x3o + 0.0001 * u + x3 = -0.0604 * x1o - 0.0531 * x2o + 0.9974 * x3o + 0.0247 * u + + is_overrun = np.random.choice([True, False], p=[pc, 1 - pc]) + + if not is_overrun: + u = -872.54 * y1 - 131.49 * y2 - 10.097 * y3 + + if not is_overrun: + y1 = x1 + y2 = x2 + y3 = x3 + return x1**2 + + +if __name__ == "__main__": + data = [] + num_samples = 10**7 + with Bar("Computing samples", max=num_samples) as bar: + for i in range(num_samples): + data.append(run_process()) + bar.next() + if (i + 1) % 1000 == 0: + print(" ", np.average(data)) + print(np.average(data)) diff --git a/scripts/stability.ipynb b/scripts/stability.ipynb new file mode 100644 index 0000000..3169e62 --- /dev/null +++ b/scripts/stability.ipynb @@ -0,0 +1,108 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "source_code = \"\"\"\n", + "# dynamical system parameters\n", + "a11 = 0.999\n", + "a12 = 0.003002\n", + "a21 = 0.002001\n", + "a22 = 1.002\n", + "b1 = 0.01003\n", + "b2 = 0.02003\n", + "c1 = 1\n", + "c2 = 0.5\n", + "period = 0.1\n", + "\n", + "# initialization\n", + "x1, x2 = 1, -1\n", + "y = c1*x1 + c2*x2\n", + "y_measure = y\n", + "z, error = 0, 0\n", + "setpoint = 1\n", + "\n", + "# control parameters\n", + "kp = 10\n", + "ki = 0.5\n", + "\n", + "while true:\n", + "\n", + " # execution of the controller\n", + " error = setpoint - y_measure # input of the controller\n", + " z = z + period*error\n", + " u = kp*error + ki*z\n", + "\n", + " # execution of dynamical system\n", + " x1, x2 = a11*x1 + a12*x2 + b1*u, a21*x1 + a22*x2 + b2*u\n", + " y = c1*x1 + c2*x2\n", + " g = Normal(0, 1)\n", + " y_measure = y + g\n", + "\n", + "end\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "outputs": [], + "source": [ + "from inputparser import Parser\n", + "from program import normalize_program\n", + "\n", + "program = Parser().parse_string(source_code)\n", + "program = normalize_program(program)" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + } + }, + { + "cell_type": "code", + "execution_count": 8, + "outputs": [], + "source": [ + "from recurrences.rec_builder import RecBuilder\n", + "\n", + "rec_builder = RecBuilder(program)\n", + "recurrences = rec_builder.get_recurrences(\"y_measure\")" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/scripts/stability.py b/scripts/stability.py new file mode 100644 index 0000000..a0f7071 --- /dev/null +++ b/scripts/stability.py @@ -0,0 +1,63 @@ +from inputparser import Parser +from program import normalize_program +from recurrences.rec_builder import RecBuilder + +from stability_analysis import SymbolicStabilityAnalyzer, NumericStabilityAnalyzer + +import time + +start = time.time() + +source_code = """ +# dynamical system parameters +a11 = 0.999 +a12 = 0.003002 +a21 = 0.002001 +a22 = 1.002 +b1 = 0.01003 +b2 = 0.02003 +c1 = 1 +c2 = 0.5 +period = 0.1 + +# initialization +x1, x2 = 1, -1 +y = c1*x1 + c2*x2 +y_measure = y +z, error = 0, 0 +setpoint = 1 + +# control parameters +kp = 10 +ki = 0.5 + +while true: + + # execution of the controller + error = setpoint - y_measure # input of the controller + z = z + period*error + u = kp*error + ki*z + + # execution of dynamical system + x1, x2 = a11*x1 + a12*x2 + b1*u, a21*x1 + a22*x2 + b2*u + y = c1*x1 + c2*x2 + g = Normal(0, 1) + y_measure = y + g + +end +""" + +program = Parser().parse_string(source_code) +program = normalize_program(program) + +rec_builder = RecBuilder(program) +recurrences = rec_builder.get_recurrences("y_measure") + +analyzer = NumericStabilityAnalyzer(recurrences) +print(analyzer.is_globally_stable()) +print(analyzer.is_unstable()) +print(analyzer.is_lyapunov_stable()) +print(analyzer.get_equilibrium()) + +end = time.time() +print(f"{end - start} seconds") diff --git a/settings.py b/settings.py index 87a908d..dcb6dfb 100644 --- a/settings.py +++ b/settings.py @@ -16,9 +16,6 @@ # If true, the complex roots in the recurrence computation will be computed numerically numeric_croots: bool = False -# Interval epsilon for the potential approximation of roots -numeric_eps: float = 1e-10 - # If set any loop guard will be overridden with 'true' trivial_guard: bool = False diff --git a/stability_analysis/__init__.py b/stability_analysis/__init__.py new file mode 100644 index 0000000..b75b449 --- /dev/null +++ b/stability_analysis/__init__.py @@ -0,0 +1,3 @@ +from .symbolic_stability_analyzer import StabilityAnalyzer +from .symbolic_stability_analyzer import SymbolicStabilityAnalyzer +from .numeric_stability_analyzer import NumericStabilityAnalyzer diff --git a/stability_analysis/numeric_stability_analyzer.py b/stability_analysis/numeric_stability_analyzer.py new file mode 100644 index 0000000..bfe77b7 --- /dev/null +++ b/stability_analysis/numeric_stability_analyzer.py @@ -0,0 +1,55 @@ +from functools import lru_cache +from recurrences import Recurrences +from stability_analysis.stability_analyzer import StabilityAnalyzer +import numpy as np + + +class NumericStabilityAnalyzer(StabilityAnalyzer): + recurrences: Recurrences + A: np.ndarray + b: np.ndarray + + def __init__(self, recurrences: Recurrences): + self.recurrences = recurrences + self.A = np.array(self.recurrences.A).astype(np.float64) + self.b = np.array(self.recurrences.b).astype(np.float64) + + @lru_cache(maxsize=None) + def _get_eigenvalues(self): + eigvs = np.linalg.eigvals(self.A) + result = {} + for ev in eigvs: + if ev in result: + result[ev] += 1 + else: + result[ev] = 1 + return result + + @lru_cache(maxsize=None) + def get_rho(self): + eigvs = self._get_eigenvalues() + return max([abs(ev) for ev in eigvs.keys()]) + + @lru_cache(maxsize=None) + def is_globally_stable(self) -> bool: + eigvs = self._get_eigenvalues() + return all([abs(ev) < 1 for ev in eigvs.keys()]) + + @lru_cache(maxsize=None) + def is_unstable(self) -> bool: + eigvs = self._get_eigenvalues() + return any([abs(ev) > 1 for ev in eigvs.keys()]) + + @lru_cache(maxsize=None) + def is_lyapunov_stable(self) -> bool: + if self.is_globally_stable(): + return True + eigvs = self._get_eigenvalues() + if any([mult > 1 for mult in eigvs.values()]): + return False + return all([c <= 1 for c in eigvs.keys()]) + + @lru_cache(maxsize=None) + def get_equilibrium(self): + I = np.identity(self.A.shape[0]) + return np.dot(np.linalg.inv(I - self.A), self.b) diff --git a/stability_analysis/stability_analyzer.py b/stability_analysis/stability_analyzer.py new file mode 100644 index 0000000..4ba7baa --- /dev/null +++ b/stability_analysis/stability_analyzer.py @@ -0,0 +1,23 @@ +from abc import ABC, abstractmethod + + +class StabilityAnalyzer(ABC): + @abstractmethod + def is_globally_stable(self) -> bool: + pass + + @abstractmethod + def is_unstable(self) -> bool: + pass + + @abstractmethod + def is_lyapunov_stable(self) -> bool: + pass + + @abstractmethod + def get_equilibrium(self): + pass + + @abstractmethod + def get_rho(self): + pass diff --git a/stability_analysis/symbolic_stability_analyzer.py b/stability_analysis/symbolic_stability_analyzer.py new file mode 100644 index 0000000..f7eda3b --- /dev/null +++ b/stability_analysis/symbolic_stability_analyzer.py @@ -0,0 +1,51 @@ +from functools import lru_cache +from sympy import eye, Max +from recurrences import Recurrences +from stability_analysis.stability_analyzer import StabilityAnalyzer + + +class SymbolicStabilityAnalyzer(StabilityAnalyzer): + recurrences: Recurrences + + def __init__(self, recurrences: Recurrences): + self.recurrences = recurrences + + @lru_cache(maxsize=None) + def _get_eigenvalues(self): + return self.recurrences.A.eigenvals() + + @lru_cache(maxsize=None) + def _compare_eigenvalues_with(self, k: int): + return [abs(ev).compare(k) for ev in self._get_eigenvalues().keys()] + + @lru_cache(maxsize=None) + def get_rho(self): + eigvs = self._get_eigenvalues() + return Max(*[abs(ev) for ev in eigvs.keys()]) + + @lru_cache(maxsize=None) + def is_globally_stable(self) -> bool: + comparisons = self._compare_eigenvalues_with(1) + return all([c == -1 for c in comparisons]) + + @lru_cache(maxsize=None) + def is_unstable(self) -> bool: + comparisons = self._compare_eigenvalues_with(1) + return any([c == 1 for c in comparisons]) + + @lru_cache(maxsize=None) + def is_lyapunov_stable(self) -> bool: + if self.is_globally_stable(): + return True + eigv_multiplicities = self._get_eigenvalues().values() + if any([m > 1 for m in eigv_multiplicities]): + return False + comparisons = self._compare_eigenvalues_with(1) + return all([c <= 0 for c in comparisons]) + + @lru_cache(maxsize=None) + def get_equilibrium(self): + A = self.recurrences.A + b = self.recurrences.b + I = eye(A.shape[0]) + return ((I - A) ** (-1)) * b diff --git a/tests/unsolvable-tests/non-lin-markov-1-synth-1.txt b/tests/unsolvable-tests/non-lin-markov-1-synth-1.txt deleted file mode 100644 index 74c9b74..0000000 --- a/tests/unsolvable-tests/non-lin-markov-1-synth-1.txt +++ /dev/null @@ -1,37 +0,0 @@ - -8888888b. .d88888b. 888 d8888 8888888b. -888 Y88b d88P" "Y88b 888 d88888 888 Y88b -888 888 888 888 888 d88P888 888 888 -888 d88P 888 888 888 d88P 888 888 d88P -8888888P" 888 888 888 d88P 888 8888888P" -888 888 888 888 d88P 888 888 T88b -888 Y88b. .d88P 888 d8888888888 888 T88b -888 "Y88888P" 88888888 d88P 888 888 T88b - -By the ProbInG group - - - -------------------- -- Analysis Result - -------------------- - -I found a solution. Maybe I won't tell you. -Synthesized solvable loop: -types - s : Finite(0, 1) -end -_t9 = s0 -_s8 = x0*_u5 - y0*_u5 -s = _t9 -while true: - _t9 = 1/2 - _s8 = (5/6)*_s8 - s = _t9 -end - -Invariant used: -(x*_u5 - y*_u5, (x0 - y0)*(5/6)**n*_u5) - - -Elapsed time: 0.354628324508667 s diff --git a/tests/unsolvable-tests/squares-synth-1.txt b/tests/unsolvable-tests/squares-synth-1.txt deleted file mode 100644 index f4e94e3..0000000 --- a/tests/unsolvable-tests/squares-synth-1.txt +++ /dev/null @@ -1,37 +0,0 @@ - -8888888b. .d88888b. 888 d8888 8888888b. -888 Y88b d88P" "Y88b 888 d88888 888 Y88b -888 888 888 888 888 d88P888 888 888 -888 d88P 888 888 888 d88P 888 888 d88P -8888888P" 888 888 888 d88P 888 8888888P" -888 888 888 888 d88P 888 888 T88b -888 Y88b. .d88P 888 d8888888888 888 T88b -888 "Y88888P" 88888888 d88P 888 888 T88b - -By the ProbInG group - - - -------------------- -- Analysis Result - -------------------- - -I found a solution. Maybe I won't tell you. -Synthesized solvable loop: -types - z : Finite(0, 1) -end -_t6 = 0 -_s5 = (1/3)*x0*_u3 + (1/3)*y0*_u3 -z = _t6 -while true: - _t6 = 1 - z - _s5 = 2*_s5 + _u3 - z*_u3 - z = _t6 -end - -Invariant used: -((1/3)*x*_u3 + (1/3)*y*_u3, (1/6)*_u3*(2*2**n*(x0 + y0) + 3*2**_k7*n*(1 - (-1)**(-_k7 + n)))) - - -Elapsed time: 0.7448279857635498 s diff --git a/utils/__init__.py b/utils/__init__.py index e421361..4a5d14b 100644 --- a/utils/__init__.py +++ b/utils/__init__.py @@ -22,6 +22,7 @@ from .special_polys import ce_bell_poly, prob_hermite_poly from .solvers import solve_rec_by_summing from .graph import Graph +from .assignments import make_assigns_parallel from .algebraic_numbers import ( faccin_height, faccin_bound, diff --git a/utils/assignments.py b/utils/assignments.py new file mode 100644 index 0000000..4e24b40 --- /dev/null +++ b/utils/assignments.py @@ -0,0 +1,22 @@ +from typing import TYPE_CHECKING + +if TYPE_CHECKING: + from program.assignment import Assignment +from .identifiers import get_unique_var + + +def make_assigns_parallel(assigns: ["Assignment"]): + from program.assignment import PolyAssignment + + if len(assigns) <= 1: + return assigns + + substitutions = {} + tmp_assigns = [] + for assign in assigns: + tmp_var = get_unique_var("t") + substitutions[assign.variable] = tmp_var + tmp_assigns.append(PolyAssignment.deterministic(tmp_var, assign.variable)) + for assign in assigns: + assign.subs(substitutions) + return tmp_assigns + assigns diff --git a/utils/expressions.py b/utils/expressions.py index 745f750..1a322cf 100644 --- a/utils/expressions.py +++ b/utils/expressions.py @@ -20,21 +20,13 @@ def float_to_rational(expr: Expr): return sympy2symengine(Rational(str(expr))) -def get_all_roots(poly: Poly, numeric=False, numeric_croots=False, eps=1e-10): - exact = True +def get_all_roots(poly: Poly, numeric=False, numeric_croots=False): if numeric: - poly_roots = poly.intervals(eps=eps) - if isinstance(poly_roots, tuple): - tmp = [] - for r in poly_roots: - tmp += r - poly_roots = tmp - result = [] - for (h, l), m in poly_roots: - result.append(((h + l) / 2, m)) - if h != l: - exact = False - return result, exact + poly_roots = poly.nroots() + result = {} + for root in poly_roots: + result[root] = 1 if root not in result else result[root] + 1 + return list(result.items()), False try: poly_roots = poly.all_roots(multiple=False) @@ -195,6 +187,9 @@ def solve_by_equating_coefficients(poly: Expr, variables, k: Symbol): def eval_re(n, expression): + import sys + + sys.set_int_max_str_digits(0) result = expression.xreplace({symbols("n"): n, symbols("n", integer=True): n}) return re(result.expand())