RL-based tracking control for discrete Markov jump singularly perturbed systems with application

In this paper, a model-free tracking control algorithm is proposed for discrete-time Markov jump singularly perturbed systems. To overcome the severe numerical stiffness and ill-conditioning problems inherent in the singularly perturbed parameter, the original system is first decoupled into fast and slow subsystems via the time-scale separation method. By embedding dynamic reference signals into the subsystems, augmented matrix systems are constructed, thereby converting the original tracking task into a stabilization problem. Subsequently, an improved data-driven policy iteration algorithm is designed. By reconstructing the value function, this algorithm effectively solves the coupled algebraic Riccati equations for the subsystems without relying on any system dynamic information. Furthermore, a suboptimal composite controller is formulated to achieve the desired tracking objective. Finally, the effectiveness and applicability of the proposed control method are validated through simulation on a tunnel diode circuit model.