Tracking control of heterogeneous Markov jump multi-agent systems based on PI observer

This paper discusses the problem of tracking control for heterogeneous Markov jump multi-agent systems (MASs) with directed communication topology. For each follower, a distributed Proportional-Integral (PI) observer is constructed. A synchronous tracking controller is developed by considering the state of the node itself and the observation state of the observer, in conjunction with the feedback control strategy. To address the inconsistency between the controller mode and the system mode, the hidden Markov model (HMM) is employed to describe the relationship between different modes, an asynchronous controller with dual-mode dependence is constructed to stabilize the system and the stability criterion is obtained. Simulation results demonstrate that, under the condition of system mode transitions satisfying Markov jumps, both controllers can effectively achieve the tracking control of heterogeneous MASs.