Lipschitz-Nonlinear Heterogeneous Multi-Agent Adaptive Distributed Time-Varying Formation-Tracking Control with Jointly Connected Topology

This paper studies the problem of time-varying formation-tracking control for a class of nonlinear multi-agent systems. A distributed adaptive controller that avoids the global non-zero minimum eigenvalue is designed for heterogeneous systems in which leaders and followers contain different nonlinear terms, and which relies only on the relative errors between adjacent agents. By adopting the Riccati inequality method, the adaptive adjustment factor in the controller is designed to solve the problem of automatically adjusting relative errors based solely on local information. Unlike existing research on time-varying formations with fixed and switching topologies, the method of jointly connected topological graphs is adopted to enable nonlinear followers to track the trajectories of leaders with different nonlinear terms and simultaneously achieve the control objective of the desired time-varying formation. The stability of the system under the jointly connected graph is proved by the Lyapunov stability proof method. Finally, numerical simulation experiments confirm the effectiveness of the proposed control method.