Optimal Tracking Control for Markov Jump Systems via Reinforcement Learning

This paper puts forward a reinforcement learning (RL)-based algorithm specifically tailored for the online solution of the optimal tracking problem in Markov jump systems (MJSs) where the system models are only partially known. To address the challenges posed by the partial unknownness and jump characteristics of MJSs, the research first elaborately designs a system augmentation method under the premise of decoupled subsystem conditions. On this basis, it conducts a rigorous theoretical demonstration to verify the equivalence between the optimal tracking problem of the original MJSs and the linear quadratic tracking (LQT) problem of the constructed coupled augmented systems (CASs). Leveraging the inherent jumping attributes of MJSs, the complex overall system is then effectively decomposed into multiple independent continuous-time linear subsystems, which simplifies the subsequent solution process. Afterwards, reinforcement learning techniques are employed to numerically solve the Riccati equation closely related to the augmented system, realizing the online computation of the optimal tracking strategy. Finally, through comprehensive numerical simulations, the tracking performance and convergence properties of the proposed online algorithm are extensively validated.