Design of Optimal Controller Using Reinforcement Learning in the Presence of Process and Measurement Noise

The design of stabilizing controller for a noisy system with an external disturbance is a challenging problem. The measurement noise associated with sensors and disturbances motivates the design of stabilizing linear quadratic design of controller and observer based on reinforcement learning (RL) methods. In this paper, a novel RL-based control algorithm is proposed for a class of continuous-time systems facing external disturbance and measurement noise. At first, a full-order observer has been developed to estimate all states using linear quadratic estimator problem in the scheme of RL algorithm by Generalized Policy Iteration (GPI) of dynamic programming. Then a full-state feedback controller using the linear quadratic Gaussian optimization problem has been presented and solved using GPI dynamic programming. By stating the Separation Principle, it is shown that the separated design of RL-based observer and controller is quite admissible. In the end, a simulation example is presented to demonstrate the effectiveness and applicability of the proposed method.