Adaptive Neural Design of Consensus Controllers for Nonlinear Multiagent Systems Under Switching Topologies

Existing adaptive neural control methods for nonlinear multiagent systems (MASs) are only applicable under a fixed topology or are applicable under switching topologies but require some linear growth conditions on the nonlinear functions. Motivated by these limitations, a state-dependent adaptive neural design method is proposed in this article. Technically, our method is developed from a state-dependent Lyapunov function candidate, a switched control law, and a projection-based adaptation mechanism. To overcome the stability analysis difficulty caused by the new design of the Lyapunov function, a nonswitched compensation approach and a modified multiple Lyapunov functions method are proposed to derive a dwell-time condition, under which stability can be preserved. It is proved that in addition to stability, synchronization errors converge to a tunable residual around zero. Besides, the proposed scheme achieves the improvement of transient performance in terms of $L_{2}$ norm and moreover, once there are no more topology switchings, asymptotic convergence of synchronization errors to a prescribed interval recovers automatically.