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This paper presents some necessary and sufficient conditions for the synchronization of second-order interconnected networks, where fixed inner-linked connections with information communication exist. First, a novel derivation of the conditions for a second-order polynomial with complex coefficients to be Hurwitz is provided. Based on this, a sufficient and necessary condition is proposed for the synchronization of the coupled complex network. Next, the design method of the synchronization protocol is constructively given, where the upper and lower bounds of the control gains are obtained through the properties of the polynomial. In addition, we consider some special cases where the second-order model is a double integrator, or general multiagent model without fixed interactions. Finally, the simulation result is given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

A wide range of multi-agent coordination problems including reference tracking and disturbance rejection requirements can be formulated as distributed output regulation problem. The general framework captures typical tasks such as output synchronization, leader-following, formation keeping, and many more. We present a distributed regulator for groups of identical and non-identical linear agents subject to global external signals affecting all agents as well as local external signals affecting individual agents. Both signal types comprise references and disturbances. The main contribution is a novel coupling among the agents based on their transient state components, or estimates thereof in the output feedback case. The transient synchronization improves the cooperative behavior in transient phases and guarantees a desired decay rate of the synchronization error, which leads to a cooperative reaction on local disturbances acting on individual agents. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the distributed coordination problem for multiple Lagrangian systems in the presence of parametric uncertainties under a directed graph without using neighbors’ velocity information in the absence of communication. We consider two cases, namely, the distributed containment control problem with multiple stationary leaders and the leaderless synchronization problem. In both cases, distributed adaptive control algorithms without using neighbors’ velocity information are proposed. The control gains in the algorithms are varying with distributed updating laws. Furthermore, necessary and sufficient conditions on the directed graph are presented, respectively, such that all followers converge to the stationary convex hull spanned by the stationary leaders asymptotically in the containment control problem and the systems synchronize asymptotically in the leaderless synchronization problem. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, we study the distributed coordination for second-order multi-agent systems with intrinsic nonlinear dynamics under an undirected graph that characterizes the interaction among the agents or followers. Both the leaderless consensus problem and the coordinated tracking problem with a dynamic leader are considered. By introducing a distributed filter for each agent or follower, the proposed control algorithms use only relative position measurements in the absence of communication. In the special case without the intrinsic nonlinear dynamics, i.e., for multi-agent systems with double-integrator dynamics, we further derive a necessary and sufficient condition for the leaderless consensus problem under a general directed graph. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, we study the distributed containment control problem for networked Lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers. We propose a distributed adaptive control algorithm combined with distributed sliding-mode estimators. A necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically. As a byproduct, we show a necessary and sufficient condition on leaderless consensus for networked Lagrangian systems under a directed graph. Numerical simulation results are given to show the effectiveness of the proposed control algorithms. [Copyright &y& Elsevier]

This brief studies distributed containment control for double-integrator dynamics in the presence of both stationary and dynamic leaders. In the case of stationary leaders, we propose a distributed containment control algorithm and study conditions on the network topology and the control gains to guarantee asymptotic containment control in any dimensional space. In the case of dynamic leaders, we study two cases: leaders with an identical velocity and leaders with nonidentical velocities. For the first case, we propose two distributed containment control algorithms to solve, respectively, asymptotic containment control under a switching directed network topology and finite-time containment control under a fixed directed network topology. In particular, asymptotic containment control can be achieved for any dimensional space if the network topology is fixed and for only the 1-D space if the network topology is switching. For the second case, we propose a distributed containment control algorithm under a fixed network topology where the communication patterns among the followers are undirected and derive conditions on the network topology and the control gains to guarantee asymptotic containment control for any dimensional space. Both simulation results and experimental results on a multi-robot platform are provided to validate some theoretical results. [ABSTRACT FROM AUTHOR]