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Author: attarmehran

All_AB.m

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+% Author:       Mehran Attar
+% Written:      08-March-2023
+% Last update:
+% Last revision:---
+
+%------------- BEGIN CODE --------------
+clc
+clear all
+close all
+%% system dynamics
+A=[0.7969 -0.2247;
+    0.1798 0.9767];
+B=[0.1271;0.0132];
+C = [1,0];
+D = 0;
+rand('seed',1);
+% define continuous time system
+% sys_c = ss(A,B,C,D);
+% % convert to discrete system
+% samplingtime = 0.01;
+% sys_d = c2d(sys_c,samplingtime);
+dim_x = size(A, 2);
+initpoints =1;
+%Number of time steps
+steps = 4;
+totalsamples = initpoints*steps;
+%% initial set and input
+% X0 = zonotope(zeros(dim_x,1),diag(ones(dim_x,1)));
+% X0 = zonotope(zeros(2,1),0.106*[0.999 -0.1;-1 -1]);
+U = zonotope(0,3);
+X0 = zonotope(zeros(2,1),10*eye(2));
+%noise zontope W
+W = zonotope(zeros(dim_x,1),0.005*eye(dim_x));
+
+%Construct matrix zonotpe \mathcal{M}_w
+index=1;
+for i=1:size(W.generators,2)
+    vec = W.Z(:,i+1);
+    GW{index}= [vec,zeros(dim_x,totalsamples-1)];
+    for j=1:totalsamples-1
+        GW{j+index}=  [GW{index+j-1}(:,2:end) GW{index+j-1}(:,1)];
+    end
+    index = j+index+1;
+end
+Wmatzono= matZonotope(zeros(dim_x,totalsamples),GW);
+
+% randomly choose constant inputs for each step / sampling time
+for i=1:totalsamples
+    u(i) = randPoint(U);
+end
+
+%simulate the system to get the data
+x0 = X0.center;
+x(:,1) = x0;
+index=1;
+for j=1:dim_x:initpoints*dim_x
+    x(j:j+dim_x-1,1) = randPoint(X0);
+    for i=1:steps
+        utraj(j,i) = u(index);
+        x(j:j+dim_x-1,i+1) = A*x(j:j+dim_x-1,i) + B*u(index) + randPoint(W);
+        index=index+1;
+    end
+end
+
+% concatenate the data trajectories
+index_0 =1;
+index_1 =1;
+for j=1:dim_x:initpoints*dim_x
+    for i=2:steps+1
+        x_meas_vec_1(:,index_1) = x(j:j+dim_x-1,i);
+        index_1 = index_1 +1;
+    end
+    for i=1:steps
+        u_mean_vec_0(:,index_0) = utraj(j,i);
+        x_meas_vec_0(:,index_0) = x(j:j+dim_x-1,i);
+        index_0 = index_0 +1;
+    end
+end
+
+% X_+ is X_1T
+% X_- is X_0T
+U_full = u_mean_vec_0(:,1:totalsamples); %same as u
+X_0T = x_meas_vec_0(:,1:totalsamples);
+X_1T = x_meas_vec_1(:,1:totalsamples);
+
+X1W_cen =  X_1T - Wmatzono.center;
+X1W = matZonotope(X1W_cen,Wmatzono.generator);
+% set of A and B
+AB = X1W * pinv([X_0T;U_full]);
+
+%%
+
+matrixCenter = [AB.center;zeros(1,3)];
+
+for i=1:AB.gens
+  G{i}=[AB.generator{i};zeros(1,3)];  
+end
+
+% instantiate matrix zonotope
+M_zono = matZonotope(matrixCenter, G);
+
+% obtain result of all vertices-------------------------
+V_AB = vertices(M_zono);
+
+save V_AB