Reinforcement Learning Optimal Output Feedback Control for Takagi–Sugeno Fuzzy Systems With Disturbances

In this article, we study the reinforcement learning (RL) optimal output feedback control problem for Takagi–Sugeno (T–S) fuzzy systems with immeasurable states and disturbances. A fuzzy filtering observer is designed to estimate the immeasurable states, and then, based on the filtering observer, a fuzzy optimal output feedback control method is presented by employing zero-sum differential game theory. Since the analytical optimal control solutions are reduced to solving game algebraic Riccati equations (GAREs), which is difficult to obtain their analytical solutions, an output feedback model-free policy iteration (PI) learning algorithm is proposed. It is proved that the proposed algorithm is convergent and the proposed fuzzy RL optimal output feedback control approach can make the controlled systems be asymptotically stable and satisfy the disturbance attenuation condition. Finally, we apply the developed optimal control method to a mass–spring–damper system, and the simulation results verify the effectiveness of the developed method.