Inverse Reinforcement Learning Optimal Control for Takagi-Sugeno Fuzzy Systems

Inverse reinforcement learning optimal control is under the framework of learner-expert. The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function, so it can handle optimal control problems effectively. This paper proposes an inverse reinforcement learning optimal control method for Takagi-Sugeno (T-S) fuzzy systems. Based on learner systems, an expert system is constructed, where the learner system only knows the expert system's optimal control policy. To reconstruct the unknown cost function, we firstly develop a model-based inverse reinforcement learning algorithm for the case that systems dynamics are known. The developed model-based learning algorithm is consists of two learning stages: an inner reinforcement learning loop and an outer inverse optimal control loop. The inner loop desires to obtain optimal control policy via learner's cost function and the outer loop aims to update learner's state-penalty matrices via only using expert's optimal control policy. Then, to eliminate the requirement that the system dynamics must be known, a data-driven integral learning algorithm is presented. It is proved that the presented two algorithms are convergent and the developed inverse reinforcement learning optimal control scheme can ensure the controlled fuzzy learner systems to be asymptotically stable. Finally, we apply the proposed fuzzy optimal control to the truck-trailer system, and the computer simulation results verify the effectiveness of the presented approach.