Time-Varying Formation-Containment Control via PDE Backstepping Technique

This paper focuses on the formation-containment (FC) control for multi-agent systems (MASs) with long input delay under jointly connected switching topologies. The considered MASs contain one virtual leader, multiple leaders and followers. The leaders complete the formation first, then the followers move into the formation created by the leaders. Compared with existing FC control, each agent in the considered MASs can have different dynamics. To handle long input delay, based on the partial differential equation (PDE) backstepping technique, a new distributed predictor feedback control method is proposed. Utilizing this method and the certainty equivalence principle, the MASs with long input delay can be mapped into new coupled ODE-PDE target systems. Then, Lyapunov-Krasovskii functions are used to prove the stability of the system. Simulations verify the validity of the proposed results.Note to Practitioners—In actual applications, multiple agents need to perform complex tasks together. These agents can be divided into leaders and followers. The leaders need to establish a time-varying formation (TVF) around a virtual leader to adapt to the changing circumstances, then the followers can move into the multiple leaders’ spanning convex hull so they can be protected from outside obstacles. In practical, input delays frequently occur in MASs due to network transmission, which brings difficulties to the FC control. Although there are plenty of works on FC control, research on the FC control of MASs with long input delay is still lacking.