Distributed time-varying group formation tracking for cluster systems under switching topologies

Abstract

Distributed formation control is one of the basic important subjects of cluster intelligent control. Denial environments and multi-task requirements present new challenges to formation control. This paper investigates the time-varying group formation tracking control problem for high-order linear cluster systems. It divides the agents in the cluster systems into three classes: the virtual leader, the group leaders, and the followers. The virtual leader provides reference trajectories or tracking instructions for the macro-movement of the cluster systems. The group leaders track these trajectories and instructions and ensure the coordination among the subgroups by communicating with each other. The followers track the state of the subgroup leaders and realize the desired formation. Under switching topologies and external disturbances, a distributed time-varying group formation tracking control protocol is constructed based on the neighboring information feedback among agents and the sliding mode control theory, and an algorithm is proposed to determine the unknown parameters of this protocol. Then, the closed-loop stability of such cluster systems is proven by using the Lyapunov theory. Finally, numerical simulations demonstrate that the proposed approach can achieve time-varying group formation tracking for high-order linear cluster systems.