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In this paper, the event-triggered consensus problem is studied for multi-agent systems with general linear dynamics under a general directed graph. Based on state feedback, we propose a decentralized event-triggered consensus controller (ETCC) for each agent to achieve consensus, without requiring continuous communication among agents. Each agent only needs to monitor its own state continuously to determine when to trigger an event and broadcast its states to its out-neighbors. The agent updates its controller when it broadcasts its states to its out-neighbors or receives new information from its in-neighbors. The ETCC can be implemented in multiple steps. it is proved that under the proposed ETCC there is no Zeno behavior exhibited. To relax the requirement of continuous monitoring of each agent’s own states, we further propose a self-triggered consensus controller (STCC). Simulation results are given to illustrate the theoretical analysis and show the advantages of the event-triggered and self-triggered controllers proposed in this paper. [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 problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies. First, when the leaders are stationary and all followers share an inertial coordinate frame, we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is fixed, we partition the (nonsymmetric) Laplacian matrix and explore its properties to derive the convergence results. When the directed network topology is switching, the commonly adopted decoupling technique based on the Kronecker product in a high-dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results. The proposed coordinate transformation technique also has potential applications in other high-dimensional distributed control scenarios and might be used to simplify the analysis of a high-dimensional system to that of a one-dimensional system when the decoupling technique based on the Kronecker product cannot be applied. Second, when the leaders are dynamic and all followers share an inertial coordinate frame, we propose a distributed tracking control algorithm without velocity measurements. When the directed network topology is fixed, we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is switching, we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high-dimensional space. We also show via some counterexamples that it is, in general, impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high-dimensional space. Simulation results are presented as a proof of concept. [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]

Abstract: This paper considers the consensus problem for multi-agent systems with inherent nonlinear dynamics under directed topologies. A variable transformation method is used to convert the consensus problem to a partial stability problem. Both first-order and second-order systems are investigated under fixed and switching topologies, respectively. It is assumed that the inherent nonlinear terms satisfy the Lipshitz condition. Sufficient conditions on the feedback gains are given based on a Lyapunov function method. For first-order systems under a fixed topology, the consensus is achieved if the feedback gain related to the agents’ positions is large enough. For first-order systems under switching topologies, the effect of the minimum dwell time for the switching signal on the consensus achievement is considered. For second-order systems under a fixed topology, the consensus is achieved if the feedback gains related to the agents’ positions and velocities, respectively, are both large enough. For second-order systems under switching topologies, a switching variable transformation is given. Then, the consensus problem is investigated when all the digraphs are strongly connected and weighted balanced with a common weighted vector. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results. [Copyright &y& Elsevier]