Reinforcement learning-based linear quadratic tracking control for partially unknown Markov jump singular interconnected systems

In this paper, an online policy iteration algorithm is adopted to solve the linear quadratic tracking control problem for a class of partially unknown Markov jump singular interconnected systems. Firstly, due to the singular systems consisting of dynamic parts and static parts, Markov jump singular interconnected systems can be described as regular systems composed of dynamic parts by utilizing a linear non-singular transformation approach. On this basis, a subsystem transformation technique is employed to reconstruct Markov jump singular interconnected systems owing to the stochastic jump characteristics of Markov jump systems. Subsequently, through decoupling the Markov jump singular interconnected system, an augmented system with tracking signals is established. Furthermore, considering the coupling relationship between interconnected subsystems and partial system dynamics, the reinforcement learning-based parallel policy iteration algorithm is used to obtain the control policy. The convergence of the designed algorithm is also demonstrated. Finally, the feasibility and effectiveness of the devised algorithms are verified by a numerical example.