Basic consensus problems in multi-agent systems with switching interconnection graphs

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

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.

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 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.

This paper proposes a class of distributed event-triggered algorithms that solve the average consensus problem in multi-agent systems. By designing events such that a specifically chosen Lyapunov function is monotonically decreasing, event-triggered algorithms succeed in reducing communications among agents while still ensuring that the entire system converges to the desired state. However, depending on the chosen Lyapunov function the transient behaviours can be very different. Moreover, performance requirements also vary from application to application. Consequently, we are instead interested in considering a class of Lyapunov functions such that each Lyapunov function produces a different event-triggered coordination algorithm to solve the multi-agent average consensus problem. The proposed class of algorithms all guarantee exponential convergence of the resulting system and exclusion of Zeno behaviours. This allows us to easily implement different algorithms that all guarantee correctness to meet varying performance needs. We show that our findings can be applied to the practical clock synchronisation problem in wireless sensor networks (WSNs) and further corroborate their effectiveness with simulation results.

Distributed Average Consensus under Quantized Communication via Event-Triggered Mass Splitting

Due to the unbalance distribution of network resources and network traffic, congestion is an inherent property of the Internet. The consensus congestion controller based on the multiagent system theory is designed for the multirouter topology, which improves the performance of the whole networks. Based on the analysis of the causes of congestion, the topology of multirouter networks is modeled based on the graph theory and the network congestion control problem is described as a consensus problem in multiagent systems. Simulation results by MATLAB and Ns2 indicate that the proposed algorithm maintains a high throughput and a low packet drip ratio and improves the quality of the service in the complex network environment.

This paper investigates semistability of discrete-time, switched linear systems under both deterministic and random switching policies. The notion of semistability pertains to a continuum of initial state dependent equilibria and has found wide applications such as consensus problems in multi-agent systems. The main contributions of the paper are three folds. First, we show that exponential semistability on a common equilibrium space is equivalent to output exponential stability of the switched linear system with a suitably defined output, under both arbitrary and random switchings. Further, their convergence rates are shown to be identical. Second, it is shown that output stability and its convergence rates can be efficiently characterized via the recently developed generating function approach. Third, we consider algorithm development and analysis of resource allocation schemes for topologically changing, distributed sensor networks. We formulate an iteration process of such an algorithm as a switched linear system, and characterize its convergence using the obtained semistability results.

This paper addresses the average consensus problem of multi-agent systems with neutral dynamics for the first time. By decoupling the neutral multi-agent system in terms of the eigenvalues of the Laplacian matrix, we establish necessary and sufficient conditions for average consensus of neutral multi-agent systems in undirected networks. For the particular case of constant delay, a least upper bound of the allowable time delay for consensus is given.

This paper investigate the event-triggered consensus problem for multi-agent systems in the average consensus case. An event of each agent is triggered only when certain measurement error reaches some prescribed threshold. Then at each event time instant, each agent communicates with its neighbors, sends information to them and then updates its controller. In the event design in this work, we use discontinuous threshold and as a result, the continuous communication among agents is avoided. This may reduce energy consumption in practice. To exclude the Zeno behavior, we propose an event/time hybrid triggering scheme. Then asymptotic consensus can be guaranteed while the Zeno behavior can be avoided. Moreover, the proposed algorithm is then extended to a self-triggered case and thus continuous self-state monitoring can be further avoided. The effectiveness of the proposed approach is illustrated by simulation examples.

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.

This study addresses the consensus problem of multi-agent systems (MAS) subject to external disturbance. Considering the presence of external disturbance factors, a theoretical analysis of consensus for distributed MAS is conducted. First, a state observer and an adaptive disturbance observer are designed to estimate both the node states and disturbance states of each agent in the system. Subsequently, a dynamic event-triggered control strategy is formulated based on the estimated values from the observers. Notably, the dynamic event-triggered strategy incorporates dynamically adjustable parameters, offering enhanced flexibility compared to conventional static event-triggered strategies. Using Lyapunov stability theory and inequality techniques, sufficient conditions for achieving consensus in disturbed MAS are derived. Finally, a numerical example is provided to demonstrate the effectiveness of the observers, control strategies, and theoretical results. This work provides new solutions for the consensus control of heterogeneous MAS with external disturbance, where both the obsever and the dynamic event-triggered controller are equipped with adjustable parameters, rendering the approach more practical for real-world applications.

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.

In this paper, the average consensus problem of multi-agent systems under logarithm quantized communication is investigated. The logarithm quantizer with finite quantization levels is considered. A sufficient condition is derived to ensure the convergence of the multi-agent system. Finally, a numerical example is given to show the effectiveness of the result obtained in this paper.

This paper studies the event-triggered consensus problem of multi-agent systems with general linear dynamics. To be specific, an observer-based event-triggered control protocol is proposed using the local output feedback information. It is proved that the multi-agent system reaches consensus under the proposed protocol, and the gain matrices of the protocol can be determined by solving a group of LMIs. In the end, a simulation example is given to verify the theoretical results.