Distributed Sliding Mode Control for Nonlinear Multi‐Agent Consensus

ABSTRACT This article is concerned with the distributed control for consensus problems in nonlinear multi‐agent systems, with a focus on achieving global group behavior through only local interaction. We propose a novel distributed sliding mode control (DSMC) method for nonlinear heterogeneous multi‐agent systems under directed information exchange topologies. The DSMC constructs the topological sliding surface and reaching law via a so‐called “topological structured function”. The control law obtained by matching the topological sliding surface and topological reaching law is naturally distributed. Under this framework, topological diversity is explicitly incorporated and supported. Our method significantly simplifies the consensus problem by mapping interconnected higher‐order dynamics into an order sliding variable. Additionally, we propose a distributed observer for consensus problems with an active leader. We prove the asymptotic stability of DSMC under directed topologies containing a spanning tree and further prove finite‐time convergence under undirected topologies. Moreover, we extend the DSMC framework to Multiple‐Input Multiple‐Output (MIMO) systems. The effectiveness of DSMC is demonstrated under different topologies through numerical simulations, especially with an application to consensus of nonholonomic unicycle agents.