H∞ leader‐based consensus of non‐linear multi‐agents over switching graphs and disturbances using multiple Lyapunov functions

Abstract

This study deals with the multiple Lyapunov functions approach for the robust leader‐following consensus of one‐sided Lipschitz (OSL) multiagents, connected via switching topologies under external disturbances. Disturbances have been accounted for followers, connected via a directed graph with a spanning tree from the leader root. The authors stipulate two consensus protocols, based on the absence or existence of norm‐bounded reference input to the leader, and provide matrix inequalities for designing the parameters of consensus controllers. In the presence of L2 bounded disturbances, the proposed protocol ensures H∞ consensus criterion for minimisation of the effect of disturbances to the consensus error between the leader and followers. A remedy for striking robustness against external perturbations has been provided in the present work in contrast to the conventional consensus schemes on OSL agents. Switching OSL mobile agents and aircraft carriers consisting of a leader and five followers have been simulated in the existence of reference input and disturbances to demonstrate the empirical proficiency of the consensus protocol schemes.

Observer‐based leader‐following consensus of one‐sided Lipschitz multi‐agent systems over input saturation and directed graphs

“…The consensus problem for Lipschitz nonlinear MASs was addressed in [4,[14][15][16][17][18]. Recently, the consensus of systems having a more generalized form than the Lipschitz one, called the one-sided Lipschitz (OSL) dynamics, has been studied in [19][20][21]. OSL systems are less conservative than the conventional Lipschitz systems because the former form has a smaller magnitude of the nonlinearity parameter, and the relevant nonlinearity constant can have either a positive or a negative sign [22].…”

Communication constrained robust guidance strategy using quantized artificial time delay based control with input saturation

“…But, this approach appends an undesirable time lag into the system. A robust controller [14] based guidance strategy is discussed in [15], where the difficulty faced during solving the resulting Hamilton‐Jacobi (HJ) partial differential inequality raises doubts on its online applicability. Gain scheduling strategies [16, 17] have also been applied for designing robust guidance strategies, but this approach suffers from instability issues.…”