Adaptive Time-Varying Formation Control for High-Order LTI Multi-agent Systems

In this paper, distributed time-varying formation control problems for general high-order linear time invariant (LTI) multi-agent systems are studied using an adaptive based approach. Firstly, constructed by the states of neighboring agents, a time-varying formation control protocol is proposed, where the adaptive gain scheduling technique is employed to adjusting the coupling weights between neighboring agents. Secondly, an algorithm with two steps is presented to design the distributed adaptive formation control protocol, where a description of the feasible time-varying formation set is given. In contrast to the existing results on formation control, no global information about the interaction topologies is required. Then, the stability of the algorithm is proved using the Lyapunov theory. If the predefined time-varying formation belongs to the feasible formation set, time-varying formation is shown to be achieved by general high-order LTI multi-agent systems using the distributed adaptive formation protocol designed in the proposed algorithm. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical results.