Leader-Following Consensus of Non-linear Multi-agent Systems with Interval Time-Varying Delay via Impulsive Control
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Leader-Following Consensus of Non-linear Multi-agent Systems with Interval Time-Varying Delay via Impulsive Control M. Syed Ali1 · R. Agalya1 · Zeynep Orman2 · Sabri Arik2 Accepted: 23 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis. Keywords Multi-agent systems (MASs) · Leader following consensus · Impulsive control
The work of author was supported by SERB – MATRICS Project No. MTR/2018/000931.
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Zeynep Orman [email protected] M. Syed Ali [email protected] Sabri Arik [email protected]
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Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu 632115, India
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Department of Computer Engineering, Faculty of Engineering, Istanbul University-Cerrahpasa, 34320 Avcilar, Istanbul, Turkey
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M. S. Ali et al.
1 Introduction For the past few decades, many endeavors have been made by many researchers to investigate the stability and consensus criteria for multi-agent system due to its wide application in various common fields like physics, sciences and mathematics especially in car platoons, surveillance robots, satellite imaging formations, sensor networks, unmanned aerial vehicles, world wide web, fish school etc., [1–6]. Based on the existence of the number of leaders in the multi-agent systems, the cooperative control of multi-agent systems can be divided into two parts, namely, leaderless consensus problem and leader-following consensus problem [7–9]. The dynamics of the other following agents are controlled by the leader (which receives no information from any follower) to complete a difficult task in the leader following consensus problem. Specifically the leader following consensus of MASs with communication noise is examined in [10] and the containment control (multiple leader) of MASs in both continuous time domain and discrete time domain is well discussed in [11]. The c
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