Integral Reinforcement Learning-Based Tracking Control for Nonlinear Markov Jump Systems With Unknown Dynamics

In this work, a new tracking control algorithm based on integral reinforcement learning (IRL) is proposed for nonlinear Markov jump systems (MJSs) represented by interval type-2 fuzzy (IT2F) model. The adoption of IT2F approach to describe nonlinear objects can overcome the uncertainty problem of traditional Takagi–Sugeno (T-S) fuzzy model. The control input and external disturbance are considered as two opposing competitors, and the optimal control problem is transformed into a zero-sum game problem. Furthermore, a mode-free IRL algorithm is designed to solve the fuzzy-coupled algebraic Riccati equations without the system dynamics information. The stability and the convergence of new scheme are demonstrated through Lyapunov theory, and the desired tracking goal is achieved. Finally, the designed model-free IRL algorithm is applied to a typical mass-spring-damper mechanical system and the implementation results demonstrate the practicality and effectiveness of the proposed method.