Designing fixed-time tracking consensus protocols for networked Euler-Lagrangian systems with directed graphs
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https://doi.org/10.1007/s11431-019-1566-9
Designing fixed-time tracking consensus protocols for networked Euler-Lagrangian systems with directed graphs YAO LingLing1* & WANG He1,2 2 College
1 School of Mathematics, Southeast University, Nanjing 210096, China; of Engineering and Computer Science, Australian National University, Canberra ACT 2601, Australia
Received January 2, 2020; accepted March 18, 2020; published online July 20, 2020
In this paper, a class of disturbed networked Euler-Lagrangian systems is investigated to track a general virtual signal under a general directed communication network. Firstly, a class of fixed-time distributed observer is constructed to estimate the leader’s state. Secondly, a local anti-disturbance tracking control based on the previous distributed observer is proposed for each follower to achieve the tracking consensus in a fixed time. A simulation example is finally conducted to verify the proposed algorithm. fixed-time tracking, networked Euler-Lagrangian system, anti-disturbance control, directed network Citation:
Yao L L, Wang H. Designing fixed-time tracking consensus protocols for networked Euler-Lagrangian systems with directed graphs. Sci China Tech Sci, 2020, 63, https://doi.org/10.1007/s11431-019-1566-9
1 Introduction During the past two decades, cooperative control [1] of multiagent system has attracted much attention from not only academic community but also industrial community, owing to its widespread application in various fields such as mart grid [2, 3], unmanned air vehicle [4], and multi-vessels [5], and theoretical challenges aroused from these applications. Cooperative control problem generally refers to controlling a group of multi-agent system to achieve a common goal. As a fundamental research topic of cooperative control, consensus problem has been widely investigated recently. Consensus means that a collection of agents achieve an agreement on some certain variables through local interaction [6–9]. Generally speaking, consensus problems can be categorized into three classes: leaderless consensus without leader, tracking consensus with one leader, and containment control with two or more leaders [10–13]. Usually, a group of agents should be driven to follow an appointed agent or a *Corresponding author (email: [email protected])
predefined virtual signal so as to fulfill a specific task. Hence, in this paper, the authors mainly focus on the tracking consensus problem. A critical indicator to assess the performance of a consensus algorithm is the convergence rate. It has been revealed that the convergence rate of a consensus algorithm depends not merely on control gains and dynamics, but also on the communication network among all the agents and the number of the agents in the network [6, 14]. Massive effort has been made to improve convergence rate, among which finite-time consensus algorithm [15–19] is a significant class since in most real applications consensus should be achieved in finite time. Nevertheless, the conve
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