Time-varying formation of discrete-time heterogeneous multi-agent systems with non-uniform communication delay and switching topology

In this paper, a distributed time-varying formation (TVF) control protocol is designed based on the consensus theory of multi-agents for the TVF control problem of discrete heterogeneous multi-agent systems (MASs) according to the position and velocity information of the agent itself and its neighboring agents, considering that the system has non-uniform communication delays and switching directed topologies, and that the heterogeneous system is composed of first-order and second-order agents. First, the feasibility of the formation of discrete heterogeneous MASs is analyzed using the state transition method and random matrix characteristics. Secondly, a TVF control protocol is designed for discrete-time heterogeneous MASs, taking into account its switching directed topologies and non-uniform communication delays. Furthermore, the necessary and sufficient conditions for the TVF of discrete-time heterogeneous MASs are derived and proved. Finally, the effectiveness of the control protocol designed in this study in the TVF control of MASs under discrete and heterogeneous conditions is verified by simulation experiments.