Fault-tolerant control for swarm systems: A geometric-based PDE planning approach

This paper investigates the issue of fault-tolerant control for swarm systems subject to switched graphs, actuator faults and obstacles. A geometric-based partial differential equation (PDE) framework is proposed to unify collision-free trajectory generation and fault-tolerant control. To deal with the fault-induced force imbalances, the Riemannian metric is proposed to coordinate nominal controllers and the global one. Then, Riemannian-based trajectory length optimization is solved by gradient’s dynamic model–heat flow PDE, under which a feasible trajectory satisfying motion constraints is achieved to guide the faulty system. Such virtual control force emerges autonomously through this metric adjustments. Further, the tracking error is rigorously proven to be exponential boundedness. Simulation results confirm the validity of these theoretical findings.