Optimal Control for Fuzzy Markov Jump Singularly Perturbed Systems: A Hybrid Zero-Sum Game Iteration Approach

This paper addresses a novel optimal fuzzy control scheme for a category of nonlinear Markov jump singularly perturbed systems with mixed zero-sum game. Firstly, a Takagi-Sugeno fuzzy structure is employed to describe the nonlinear plant. On this basis, two types of value functions for multi-player mixed zero-sum game are developed and a series of fuzzy controllers are designed. Subsequently, a hybrid iteration approximation learning framework is constructed for approaching the solutions of the fuzzy game coupled algebraic Riccati equations. The hybrid iteration eliminates initial admissible control dependencies and has a desirable learning iteration rate, in contrast to the traditional policy iteration and value iteration. We present a novel model-based hybrid iteration scheme and further develop it to a model-free version. The model-free hybrid iteration scheme uses only online data collected along the system trajectories for controller design, and it eliminates the traditional model-dependent issues, which is more suitable for practical applications. Finally, the validity and flexibility of the proposed algorithm are verified by a simulation example.