This paper addresses the distributed containment control problem for a linear multi-leader multi-agent system with a directed communication topology. A new class of distributed observer-type containment protocols based only on the relative output measurements of the neighboring agents is proposed, removing the impractical assumption in some of the existing approaches that the observers embedded in the multiple dynamic agents have to share information with their neighbors. Under the mild assumption that, for each follower, there exists at least one leader having a directed path to that follower, some sufficient conditions are derived to guarantee the states of the followers to asymptotically converge to a convex hull formed by those of the dynamic leaders. Finally, some numerical simulations on containment of a multi-vehicle system are given to verify the effectiveness of the theoretical results.Index Terms-Networked system, multi-leader system, containment control, observer-type protocol, multi-vehicle system, communication.0018-9286 (c)
This technical note addresses the distributed fixed-time consensus protocol design problem for multi-agent systems with general linear dynamics over directed communication graphs. By using motion planning approaches, a class of distributed fixed-time consensus algorithms are developed, which rely only on the sampling information at some sampling instants. For linear multi-agent systems, the proposed algorithms solve the fixed-time consensus problem for any directed graph containing a directed spanning tree. In particular, the settling time can be off-line pre-assigned according to task requirements. Compared with the existing results for multi-agent systems, to our best knowledge, it is the first-time to solve fixedtime consensus problems for general linear multi-agent systems over directed graphs having a directed spanning tree. Extensions to the fixed-time formation flying are further studied for multiple satellites described by Hill equations.
This paper investigates the distributed finite-time tracking problem of networked agents with multiple Euler-Lagrange dynamics. To achieve finite-time tracking, a distributed finite-time protocol is first proposed on the basis of both relative position and relative velocity measurements. By using tools from homogeneous theory, it is theoretically shown that the proposed protocol can guarantee finite-time tracking in the presence of control input constraints. On the basis of the state feedback analysis and with the aid of second-order slidingmode observer approach, a new class of finite-time tracking protocols based only on the relative position measurements is developed and employed. It is proved that the multiple agents equipped with the designed protocols can track the target location in finite time. Furthermore, a decentralized finite-time protocol based on a distributed estimator is proposed to solve the finite-time tracking problems with a dynamic leader. The effectiveness of the theoretical results is finally illustrated by numerical simulations. DISTRIBUTED FINITE-TIME TRACKING SYSTEMS 1689 case of multiple leaders, the containment control problem arises, where the objective is to guarantee the states of followers to move into a convex hull spanned by those of leaders. Containment control problems were investigated in [5,21,22]. Note that most of the aforementioned works are primarily concerned with consensus in networks of agents with integrator-type dynamics. However, a large class of real mechanical systems should be described by Euler-Lagrange equations [23]. From this observation, consensus tracking problems of multiple Euler-Lagrange dynamics were studied in [24-28], respectively.In reality, convergence rate is a significant performance index for evaluating the effectiveness of a distributed tracking controller in the context of multi-agent systems. Numerous researchers endeavored to improve the convergence rate by enlarging the coupling strength, optimizing the system gain or designing better communication topology [29][30][31]. However, only some asymptotic tracking results can be yielded in the aforementioned literature. In practical applications, it is often desirable to achieve consensus in finite time. Therefore, it is essential to investigate how to construct finite-time consensus algorithms. Compared with the asymptotic control approach, finitetime control is an effective approach with high performance and good robustness to uncertainty and disturbance rejection. Finite-time consensus for multi-agent systems with first-order and secondorder dynamics was, respectively, studied in [32,33]. Then, in [34], one framework for constructing some effective distributed protocols was presented for solving finite-time consensus problems for multi-agent systems with first-order integrator dynamics. Distributed finite-time tracking control and containment control were addressed in [35][36][37][38] for integrator-type multi-agent systems, respectively. Recently, finite-time tracking and containment problems...
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