A novel approach for adaptive H_∞ leader-following consensus of higher-order locally Lipschitz multi-agent systems

This paper addresses the design of fully-distributed edge-based leader-following consensus controller for the higher-order locally Lipschitz nonlinear multi-agents. The proposed fully-distributed consensus approach deals with the local scenario as compared to the traditional consensus control for the globally Lipschitz models. The dynamics of nonlinear systems are considered to satisfy the Lipschitz condition locally and an adaptive fully-distributed relative-state consensus protocol has been established for ensuring a coherent behavior of agents. A local leader-following adaptive consensus controller design condition, for obtaining the adaptive consensus protocol gain, has been formulated using the proposed local treatment, adaptation law for coupling weights, ellipsoidal regional investigation, asymptotic stability consideration, and Lyapunov redesign. The developed results are enriched for attaining a robust adaptive consensus of the locally Lipschitz multi-agents against disturbances by using the local L₂ stability approach. This developed technique can be effective for minimizing the effect of external disturbances on the consensus error. From technical point of view, the proposed method can be used for the locally Lipschitz models, like systems having polynomial approximations in their models. Further, the proposed approach adapts (similar to routing in communication) in accordance with the requirement of control gains for a communication topology. Furthermore, our method can be applied to deal with the unwanted disturbance (like change in air flow speed or direction and external perturbations) for attaining a robust design. In contrast to existing studies, the proposed results consider adaptive and H_∞ consensus schemes for the higher-order locally Lipschitz multi-agents. The developed results are verified for a network of six vendor pol multi-agent systems and modified Chua's circuits.