Event-Triggered Consensus Control for Linear Multi-agent Systems Using Output Feedback

This paper investigates the periodic event-triggered asymmetric bipartite consensus problem of multi-agent systems (MASs) under structurally balanced undirected signed graphs. In order to reduce the consumption of communication resources and continuous detection in the control process of MASs, a novel periodic detection event-triggered asymmetric bipartite consensus control protocol is proposed. In particular, each agent samples only in a fixed period. For each agent, two event conditions are given, and only when state error satisfies this event condition can the event be triggered. A new type of Laplacian matrix is constructed to achieve asymmetric bipartite consensus. The control method can guarantee the performance of MASs and have less communication resources. Based on the Lyapunov stability theorem and algebraic graph theory, the proposed periodic event-triggered control strategy is able to implement the asymmetric bipartite consensus when the topology is structurally balanced undirected signed graphs. The proposed method in this paper can reduce the restriction on the sampling period and automatically exclude Zeno behavior. Finally, the validity of the conclusion is verified by numerical simulation.

This paper examines the event-triggered consensus problem of the multi-agent system on signed networks. An event-based distributed control protocol is proposed for multiagent networks where the dynamics of each agent is characterized by a controllable linear time-invariant system ( $A, B$ ). By exploring the Gauge transformation between Laplacian matrix and signed Laplacian matrix, we show that the bipartite consensus and trivial consensus can be achieved, respectively, in terms of the structural balance of the underlying signed network. Furthermore, the Zeno phenomenon of the closed-loop system is shown to be non-existed when employing the proposed event-based control protocol. Simulation results are finally provided to demonstrate our results.

Consensus conditions for heterogeneous multi-agent sampled-data control systems with nonlinearities and inter-agent communication delay.

This paper addresses the distributed leaderless and leader-following consensus problems for multi-agent systems with general linear dynamics and unknown external disturbances. With the aid of extended state observer technique, both the local states and disturbance are estimated simultaneously, then the distributed consensus protocols are proposed based on information of relative estimated states of neighbor agents and the estimated disturbance. It has been shown that, with the proposed consensus protocols, all agents can reach consensus under undirected and connected communication graphs. Finally, simulation examples are included to demonstrate the effectiveness of the proposed protocols.

This brief exploits the adaptive dynamic event-triggered (ADET) consensus problem for multi-agent systems (MASs). Firstly, we propose a novel ADET protocol which improves the existing dynamic event-triggered (DET) protocol and adaptive event-triggered (AET) protocol based on sampling control. The possibility that linear matrix inequalities (LMIs) have no feasible solution is reduced by presetting an adaptive maximum threshold. The asymptotic stability criterion is obtained. Subsequently, the controller gain and ADET parameters are obtained. Finally, the validity of the theoretical results in this brief is verified by a numerical simulation.

As a new area of research, consensus problems for multi-agent systems have been studied extensively in the literature. It is usually assumed that all agents share a common one-dimensional state space. The authors of this study concentrate on the consensus problems of multi-agent systems in the framework of high-dimensional state space. As a basis for the analysis, a general model is first introduced by presenting two typical examples along with some necessary and sufficient conditions for the system to solve a consensus problem. Then the structures of consensus functions are investigated and some algebraic characterisations are given. Finally, a class of switched multi-agent systems are discussed and some sufficient conditions for the possession of the consensus property are provided. Several examples to illustrate the effectiveness of theoretical results are given.

This paper investigates event-triggered control strategy for the consensus problem of multi-agent systems with time-varying delays. The state of each agent is sampled and transmitted to its neighbors when a certain event condition is satisfied. Two kinds of decentralized event conditions are proposed. Sufficient conditions in terms of Linear Matrix Inequalities (LMIs) are established to ensure the consensus of the multi-agent systems with the event-triggered control feedbacks. Simulation example is given to demonstrate the effectiveness of the theoretical results.

This study focuses on distributed event-triggered consensus control under the scenario where only inaccurate agent model information is available. By designing a novel triggering error, a distributed dynamic event-triggered consensus (DETC) protocol is proposed for multiagent systems (MASs) with general linear dynamics over digraphs, without accurate a priori information of agent models. To improve the efficiency of the dynamic triggering law, a mixed triggering threshold is designed with a resilient function integrated to further enlarge interevent intervals. Within the proposed DETC protocol, the computational cost is significantly reduced especially for MASs with nonsparse and high-dimensional agent system matrices. In addition, for each individual agent, the states of neighboring agents used for triggering detections or controller updates are required in an on-demand (instead of continuous) way, which preserves communication resources and facilitates practical implementation. The feasibility of the designed DETC protocol is corroborated by rigorous theoretical analysis on consensus convergence and Zeno behavior exclusion. Finally, simulations are shown to demonstrate the effectiveness of the studied theory.

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.

This paper considers the distributed consensus problems for multi-agent systems with general linear and Lipschitz nonlinear dynamics. Distributed relative-state consensus protocols with an adaptive law for adjusting the coupling weights between neighboring agents are designed for both the linear and nonlinear cases, under which consensus is reached for all undirected connected communication graphs. Extensions to the case with a leader-follower communication graph are further studied. In contrast to the existing results in the literature, the adaptive consensus protocols here can be implemented by each agent in a fully distributed fashion without using any global information.

This article investigates adaptive control problems for unknown second-order nonlinear multiagent systems (MASs) via an event-triggered approach. An adaptive event-triggered consensus controller is given to second-order MAS with unknown nonlinear dynamics. We prove that the proposed consensus controller is free from Zeno behavior. Next, an adaptive event-triggered tracking controller is developed for leader-follower MAS with the leader having bounded nonzero control input. Both consensus and tracking controllers are fully distributed, which means that event-triggered controllers only use local cooperative information. Finally, an unknown second-order nonlinear MAS is used to verify the given event-triggered controllers.

This paper investigates the consensus problem for multiagent systems with time-varying delays. The bounded delays can be arbitrarily fast time-varying. The communication topology is assumed to be undirected and fixed. With general linear dynamics under average state feedback protocols, the consensus problem is then transformed into the robust control problem. Further, sufficient frequency domain criteria are established in terms of small gain theorem by analyzing the delay dependent gains for both continuous-time and discrete-time systems. The controller synthesis problems can be solved by applying the frequency domain design methods. Numerical examples are demonstrated to verify the effectiveness of the proposed approaches.

In this paper, we investigate the fault-tolerant consensus problems for multi-agent systems with actuator faults. Based on the relative state information, fully distributed adaptive protocols are designed for these agents described by Lipschitz nonlinear dynamics under leaderless and leader-follower communication structures. As the special case, for linear multi-agent systems, fault-tolerant consensus problems are also solved with the proposed protocols. First, for the leaderless multi-agent systems, all agents reach an agreement on a common value with undirected connected communication graphs. Second, for the leader-follower multi-agent systems, in which the state of the leader is only available to a subset of the followers, the state of each follower converges to the state of the leader, asymptotically. A distinctive feature of this paper is that the adaptive protocols here are independent of the eigenvalues of the Laplacian matrix associated with the whole communication graph, which means the protocols can be implemented by each agent in a fully distributed fashion. Simulation examples are provided to illustrate the theoretical results.

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

Event-triggered formation control of linear continuous-time multiagent systems is studied in this article. A complex-valued Laplacian is adopted by the local information of desired formation. For each agent, an event-triggering mechanism based on the neighboring information at event-triggering time instants is presented and continuous communications between neighboring agents are avoided. Furthermore, an event-triggered control strategy using the idea of dynamic state observer is designed. It is shown that any desired formation shape can be achieved. Moreover, the Zeno-behavior is strictly excluded. Finally, effectiveness of the obtained theoretical results is validated by two simulation examples.