Parallel Optimal Tracking Control Schemes for Mode-Dependent Control of Coupled Markov Jump Systems via Integral RL Method

This article is concerned with the optimal tracking control problem of the coupled Markov jump system (CMJS) by using the reinforcement learning (RL) technique. Based on the conventional optimal tracking architecture, an offline tracking iteration algorithm is first designed to solve the coupled algebraic Riccati equation that can hardly be solved by mathematical methods directly. To overcome the crucial requirements and existing shortcomings in the offline tracking method, a novel integral RL (IRL) tracking algorithm is first proposed for CMJS, which develops a transition-probability-free optimal tracking control scheme with a reconstructed augmented system and discounted cost function. Both the requirements of transition probability πij and system matrix Ai are avoided via the designed IRL algorithm. The stability and convergence of the novel schemes are proved by the Lyapunov theory, and the tracking objective is achieved as desired. Finally, we apply the designed algorithms in a fourth-order Markov jump control problem and the stochastic mass, spring, and damper system to track continuous sinusoidal waveforms, and the simulation results are provided to show the effectiveness and applicability.