Self-Learning Control for Nonlinear Markov Jump Systems With Application to Quarter-Car Suspension Model

In this study, a novel self-learning control is proposed for nonlinear quarter-car suspension system (QCSS) based on Markov jump model with completely unknown dynamics to solve the optimal control issue. The interval type-2 (IT2) fuzzy method is used to overcome the uncertainty problem and the zero-sum game approach is adopted to transform the optimal control issue, so as to achieve Nash-equilibrium. Based on the framework of reinforcement learning (RL), an off-line policy iterative algorithm is proposed to solve the fuzzy random coupled algebraic Riccati equation (ARE). Due to the complexity and variability of the actual system, it is difficult to obtain the complete dynamic information. A self-learning algorithm is designed based on the off-line algorithm, which does not require any dynamic information of the system, relying on the system state and control input for iteration. Furthermore, the Lyapunov stability theory is adopted to ensure that the system is asymptotically stable with $H_{\infty }$ performance index. Finally, a simulation example is given to explain the effectiveness of the control method.