Distributed fixed-time fault-tolerant tracking and containment of second-order multi-agent systems

This article addresses the fixed-time fault-tolerant consensus problem for second-order multi-agent systems under actuator faults and directed topologies. A novel sliding-mode control framework is proposed, integrating fixed-time observers to estimate actuator faults and distributed protocols to achieve tracking and containment objectives. Particularly, the key innovations include a singularity-free sliding manifold with prescribed-time convergence and a unified control design applicable to both single- and multi-leader scenarios. Numerical examples are carried out to validate the theoretical results.