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

Abstract

This paper aims to investigate the exponential leader-following consensus for nonlinear multi-agent systems with time-varying communication and input delays by using hybrid control. Based on the Lyapunov functional method, impulsive differential equation theory and matrix analysis, we show that all the followers can achieve leader-following consensus with the virtual leader exponentially even if only a fraction of followers can obtain the leader's information. Two classes of exponential consensus criteria as well as the convergence rates for the controlled multi-agent systems are presented under very relaxed interaction topology conditions, i.e., the directed interaction topology among the followers is only required to have p (p > 1) disjoint strong components. Finally, two numerical examples are given to validate the proposed theoretical results.

Leader‐following consensus of heterogenous fractional‐order multi‐agent systems under input delays

“…Figure 6 shows that under lower control gains, the agents with fractional orders are more tolerant than those with integer orders, while under high control gains, the agents with integer orders are more tolerant th an those with fractional orders. Here, the order of the leader is assumed as = 0.8, the order of the follower is assumed as = 0.9, the control gain is chosen as = 1, the dynamic 2and (12), which can verify the correctness of Theorem 2. Besides, Figure 7 shows that if the input delay increases, the time to fulfill leader-following consensus of the HFOMASs (2) and (12) will increase.…”

“…, is the input delay with identical value for each follower, the definitions of other parameters and variables in (12) are the same as those of (3) and (5). (2) and (12) can be achieved if and only if…”

“…For example, different kinds of control algorithms have been designed to achieve the consensus, such as event-triggered control [5,6], adaptive control [3,7], and observer-based control [8]. On the other hand, few different constraints have been taken into account due to different working environment, such as the time delay [9][10][11][12], parameter uncertainty [13,14], external disturbances [5].…”

“…The undesirable instability and poor performance can easily happen due to the existence of time delays. Nowadays, many results about the leader-following consensus of integer-order delayed MASs have been obtained, which can be referred to [10][11][12]. Some results about the consensus of delayed FOMASs has been obtained [25][26][27].…”

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

“…e authors discussed in [11,12]. Dynamic structures are often subjected to several disturbances in functional applications, such as communication delays.…”