Connectivity-Preserving Formation Control of Multiagent Systems Under Time-Varying Topology

This paper addresses the formation stability and connectivity preservation problem for nonlinear multiagent systems (MASs) with unknown control directions under limited communication ranges. Distinct from existing studies, the communication topology exhibits state-dependent time-varying properties, rather than the traditional binary edge weight model. Under these conditions, a novel distributed connectivity-preserving control framework is proposed. First, a prescribed performance observer and prescribed-time reference signal generator are designed to reconstruct the underlying topology and leader signals under time-varying connectivity. Subsequently, a variable-gain controller is developed based on an integral multiplicative barrier Lyapunov function (IMBLF) of the Laplacian eigenvalue. This method relaxes the conventional local connectivity constraints while ensuring: 1) Connectivity is preserved within predefined bounds even in the presence of uncertainties affecting transient coordination errors. 2) With connectivity being maintained, the communication edges can be dynamically adjusted based on real-time distance, leading to great flexibility of topology. Finally, the feasibility of the proposed scheme is illustrated by simulation.