PDE-based fault-tolerant control of swarm deployment while preserving connectedness

Abstract

The present study investigates PDE-based fault-tolerant control for a swarm system with a dynamic graph, wherein all agents maintain the communication connectivity and avoid collisions while being deployed along desired planar curves in the presence of actuator faults. Firstly, a switched parabolic system is established based on the switching of attractive potential functions between neighboring agents, occurring at the time instant when communication edges are generated between them. Secondly, a Lyapunov-based boundary controller is proposed to ensure that the switched PDE system achieves the desired planar deployment originating from equilibrium curves of this system. Finally, the finite-time stability of the closed-loop system is rigorously demonstrated to guarantee that all pairs of initially connected agents remain within each other’s sensing range for future finite time. Simulation results validate the effectiveness of the proposed research.