Pinning consensus for multi‐agent systems with non‐linear dynamics and time‐varying delay under directed switching topology

Abstract

This paper studies the leader-following consensus problem in directed networks of agents with non-linear dynamics and time-varying coupling delay by using the pinning control method. The main contribution of this study is that we obtain two classes of sufficient leader-following consensus criteria without assuming that the topology among followers is strongly connected or has a spanning tree, and without assuming that the derivative of the time-varying communication delay is less than 1. In addition, to be more practical we consider the general network whose coupling topology is arbitrarily switching among a finite set of topologies. Based on the common Lyapunov theory and linear matrix inequalities approach, we prove that the leader-following consensus problem can be solved only with the assumption that the topology among the followers has p (p > 1) disjoint strong components or directed spanning trees and there is a directed path from the leader to each follower. Two examples are presented to show the applications of the criteria obtained in this study.

Globally asymptotic stability and synchronization analysis of uncertain multi‐agent systems with multiple time‐varying delays and impulses

“…To achieve the synchronization in MASs, numerous control schemes such as impulsive control, 29,40 pinning control, [41][42][43] sliding control, 44,45 and adaptive control 41,46 have been applied to reach a consensus of MASs. In this article, we focus on pinning control, where fractions of the agents are able to extract information from the leader.…”

A Lyapunov–Krasovskii Functional Approach to Stability and Linear Feedback Synchronization Control for Nonlinear Multi-Agent Systems with Mixed Time Delays

“…To achieve a multi-agent systems target, various control schemes such as impulsive control [39,40], pinning control [41,42], and adaptive control [41,43], in [44], He et al derived boundary vibration control of variable length crane systems in two-dimensional space with output constraints, in [45], Saravanakumar et al derived a finite-time sampled data control of the switched stochastic model with nondeterministic actuator faults and saturation nonlinearity, and in [46], He et al addressed an unified iterative learning control for flexible structures with input constraints. In [47], the robust finite-time composite nonlinear feedback control for synchronization of uncertain chaotic systems with nonlinearity and time delay has been implemented.…”

Exponential Consensus for Nonlinear Multi‐Agent Systems with Communication and Input Delays via Hybrid Control

“…The leader-following consensus for multi-agent systems with Lipschitz nonlinear dynamics under directed or undirected graph was investigated in [13][14][15][16][17], to cite a few. For example, the consensus problems are investigated for multi-agent systems only with communication delays (i.e., the delay related to the information transmission between the agents and their neighbors) in [19][20][21], only with input delays (i.e., the delay rooted in the dynamics of each agent) in [22,23], with both communication and input delays in [24][25][26]. It is well known to us that time-delay may arise inevitably during the communication process due to the limitation of transmission speed, the time taken for transportation of materials, the congestion of the communication channels, and so on.…”

“…Therefore, the consensus and the effect of time delay on coordination performance for delayed multi-agent systems have attracted a significant attention in recent years. For example, the consensus problems are investigated for multi-agent systems only with communication delays (i.e., the delay related to the information transmission between the agents and their neighbors) in [19][20][21], only with input delays (i.e., the delay rooted in the dynamics of each agent) in [22,23], with both communication and input delays in [24][25][26]. For the case of two types of time delays, it should be noticed that the existing studies mainly focused on linear systems and constant time delays.…”

“…For example, the consensus problems are investigated for multi‐agent systems only with communication delays ( i.e. , the delay related to the information transmission between the agents and their neighbors) in , only with input delays ( i.e. , the delay rooted in the dynamics of each agent) in , with both communication and input delays in .…”