Nonfragile Output Feedback Tracking Control for Markov Jump Fuzzy Systems Based on Integral Reinforcement Learning Scheme

摘要

In this article, a novel integral reinforcement learning (RL)-based nonfragile output feedback tracking control algorithm is proposed for uncertain Markov jump nonlinear systems presented by the Takagi–Sugeno fuzzy model. The problem of nonfragile control is converted into solving the zero-sum games, where the control input and uncertain disturbance input can be regarded as two rival players. Based on the RL architecture, an offline parallel output feedback tracking learning algorithm is first designed to solve fuzzy stochastic coupled algebraic Riccati equations for Markov jump fuzzy systems. Furthermore, to overcome the requirement of a precise system information and transition probability, an online parallel integral RL-based algorithm is designed. Besides, the tracking object is achieved and the stochastically asymptotic stability, and expected <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> performance for considered systems is ensured via the Lyapunov stability theory and stochastic analysis method. Furthermore, the effectiveness of the proposed control algorithm is verified by a robot arm system.