Inverse Reinforcement Learning H _∞ Optimal Control for Takagi-Sugeno Fuzzy Systems

This article presents an inverse reinforcement learning (RL) $H_{\infty } $ optimal control approach for a Takagi-Sugeno (T-S) fuzzy system (learner system) with disturbances. To reconstruct the expert system's cost function and imitate the expert system's behavior, a learner-expert framework and two inverse RL algorithms are proposed for the cases of the learner system's dynamics being known and unknown. The two developed learning algorithms are composed of three stages: an optimal control policy update stage, a gradient descent correction stage, and an inverse optimal control iteration stage. The first stage is to update the learner's optimal policies via game algebraic Riccati equations (GAREs), the second stage is to obtain the correction factor by observing the expert system's demonstrated trajectory, and the third stage is to adjust the state-penalty matrix. It is proven that the presented two algorithms are convergent, and the presented fuzzy inverse RL optimal control methodology can ensure the controlled system is asymptotically stable and achieve a Nash equilibrium solution. Finally, the presented fuzzy $H_{\infty } $ optimal control method is applied to an autonomous surface vehicle (ASV) system; the computer simulation and results illustrated the effectiveness of the developed methodology.