Adaptive Neural Design of Consensus Controllers for Nonlinear Multiagent Systems Under Switching Topologies
针对现有方法在切换拓扑下需线性增长条件的局限，提出一种状态依赖的自适应神经设计方法，保证稳定性并使同步误差收敛到可调残差，且无切换时误差渐近收敛到指定区间。
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> norm and moreover, once there are no more topology switchings, asymptotic convergence of synchronization errors to a prescribed interval recovers automatically.