diff --git a/src/deepcpp/controller.cpp b/src/deepcpp/controller.cpp
index 3d2e768..6056ef2 100644
--- a/src/deepcpp/controller.cpp
+++ b/src/deepcpp/controller.cpp
@@ -137,18 +137,22 @@ void Controller::clear()
     y_ini.clear();
 }
 
-std::vector<VectorXd> Controller::apply(const std::vector<VectorXd> &target)
+std::vector<VectorXd> Controller::apply(const std::vector<VectorXd> &target, const std::vector<VectorXd> &offset)
 {
     if (!is_initialized())
         return {};
 
     check_dimensions(target, "target", target_size, output_dims);
 
+    if (!offset.empty())
+        check_dimensions(offset, "offset", target_size, input_dims);
+    
     // Flatten
     VectorXd target_ = concat(target);
+    VectorXd offset_ = offset.empty() ? VectorXd::Zero(target_size * output_dims) : concat(offset);
 
     auto x = concat(u_ini.get(), y_ini.get());
-    auto w = M_u.transpose() * Q * (target_ - M_x * x);
+    auto w = M_u.transpose() * Q * (target_ - M_x * x) + R * offset_;
     auto u_star = G.ldlt().solve(w).eval();
 
     if (input_constrain_fkt != nullptr)
@@ -163,7 +167,10 @@ std::vector<VectorXd> Controller::apply(const std::vector<VectorXd> &target)
     return split(u_star, target_size);
 }
 
-std::vector<VectorXd> Controller::apply(const VectorXd &target)
+std::vector<VectorXd> Controller::apply(const VectorXd &target, const VectorXd &offset)
 {
-    return apply(std::vector<VectorXd>{target});
+    return apply(
+        std::vector<VectorXd>{target},
+        offset.size() == 0 ? std::vector<VectorXd>{} : std::vector<VectorXd>{offset}
+    );
 }
diff --git a/src/deepcpp/controller.h b/src/deepcpp/controller.h
index 623890b..1e26bbc 100644
--- a/src/deepcpp/controller.h
+++ b/src/deepcpp/controller.h
@@ -74,6 +74,6 @@ class Controller
     bool is_initialized() const;
     void update(VectorXd u, VectorXd y);
     void clear();
-    std::vector<VectorXd> apply(const std::vector<VectorXd> &);
-    std::vector<VectorXd> apply(const VectorXd &);
+    std::vector<VectorXd> apply(const std::vector<VectorXd> &target, const std::vector<VectorXd> &offset = {});
+    std::vector<VectorXd> apply(const VectorXd &target, const VectorXd &offset = {});
 };
diff --git a/tests/deepcpp/test_controller.cpp b/tests/deepcpp/test_controller.cpp
index ca8e3c6..92bc4cb 100644
--- a/tests/deepcpp/test_controller.cpp
+++ b/tests/deepcpp/test_controller.cpp
@@ -76,12 +76,17 @@ void warm_up_controller(Controller& controller, DiscreteLTI& system, const Vecto
 
 // Control the system for a given number of time steps.
 // Returns the output of the system after the last time step.
-VectorXd control_system(Controller& controller, DiscreteLTI& system, const std::vector<VectorXd>& target, int time_steps)
+VectorXd control_system(
+    Controller& controller,
+    DiscreteLTI& system,
+    const std::vector<VectorXd>& target,
+    int time_steps,
+    const std::vector<VectorXd>& offset = {})
 {
     VectorXd u, y;
     for (int i = 0; i < time_steps; ++i)
     {
-        u = controller.apply(target).front();
+        u = controller.apply(target, offset).front();
         y = system.apply(u);
         controller.update(u, y);
     }
@@ -119,6 +124,14 @@ TEST_F(Test_1D_in_1D_out_LTI, Constrained)
     expect_near(y, target[0], 1e-5);
 }
 
+TEST_F(Test_1D_in_1D_out_LTI, Offset)
+{
+    Controller controller{u_d, y_d, T_ini, target.size(), /*Q*/1.0, /*R*/0.001};
+    warm_up_controller(controller, system, Vector(1));
+    VectorXd y = control_system(controller, system, target, T_ini, {Vector(10), Vector(10)});
+    expect_near(y, target[0], 0.02);
+}
+
 
 class Test_2D_in_3D_out_LTI : public ::testing::Test
 {
@@ -150,3 +163,11 @@ TEST_F(Test_2D_in_3D_out_LTI, Constrained)
     VectorXd y = control_system(controller, system, target, 2 * T_ini);
     expect_near(y, target[0], 0.05);
 }
+
+TEST_F(Test_2D_in_3D_out_LTI, Offset)
+{
+    Controller controller{u_d, y_d, T_ini, target.size(), /*Q*/1.0, /*R*/0.001};
+    warm_up_controller(controller, system, Vector(1, 1));
+    VectorXd y = control_system(controller, system, target, T_ini, {Vector(1, 1)});
+    expect_near(y, target[0], 0.05);
+}