Fully Distributed Fault-Tolerant Consensus Protocols for Lipschitz Nonlinear Multi-Agent Systems

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.

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 considers the consensus problem of multi-agent systems. It is pointed out that the existing consensus protocols decouple the effects of the agent and protocol dynamics of the consensus stability from that of the communication topology. In this paper, an integrated design approach is presented, under which a novel distributed adaptive consensus protocol is proposed to achieve consensus of multi-agent systems with undirected graphs. For the case there exist bounded external disturbances, by using the s modification technique, a distributed robust adaptive consensus protocol is presented to ensure the ultimate boundedness of the consensus error. Both of the proposed adaptive protocols are fully distributed, depending on only relative states of neighboring agents.

This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this paper, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.

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.

We consider several basic consensus problems in multi-agents systems with switching interconnection graphs, where the connections between any two agents are assumed bidirectional for notation simplicity. When the switching interconnection graphs are always connected, it has been shown in the literature that the Laplacian based algorithm always achieves the average consensus. We first extend the discussion to the case where disconnected interconnection graphs are involved, by showing that the average consensus is still achieved if the dwell time ratio between connected graphs and disconnected ones satisfies a specified condition. Next, we consider the case where there is no connected graph but the combination of a set of graphs is connected, and propose two switching strategies for achieving the average consensus. Several numerical examples are provided to show the algorithms.

In this paper, we study the consensus problem for multi-agent systems with external disturbances, and the leader has a bounded input. A state feedback control protocol is designed for each follower. Assuming that the communication graph between followers is directed and the leader has a directed path to each follower. The consensus was proved by using the Lyapunov stability theories. Numerical simulation is provided to demonstrate the theoretical results.

This technical note investigates the positive consensus problem of multiagent systems with directed communication topologies, where all the agents have identical continuous-time positive linear dynamics. Existing works of such a problem mainly focus on the case, where networked communication topologies are of either undirected and incomplete graphs, or strongly connected directed graphs. In contrast to them, we study this problem in which the communication topologies of the multiagent system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Based on the existing results in spectral graph theory and positive linear systems theory, several necessary, and sufficient conditions on positive consensus of the directed multiagent system are derived through using linear matrix inequality techniques. A primal-dual iterative algorithm is developed for the computation of solutions. Finally, several numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results.

This paper investigates the leaderless <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem of multi-agent systems with higher-order Lipschitz dynamics and external disturbance. The topology is assumed to be directed. Distributed controllers using only relative outputs information of the adjacent agents are constructed. In order to deal with the non-symmetric property of the associated Laplacian matrix of directed topology, some properties of Laplacian matrix are introduced. By introducing an appropriate state transformation, the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem is converted to a low-dimensional system stability problem which is solved using Lyapunov stability analysis method. The effectiveness of the proposed control design is demonstrated through simulation examples.

With the development of swarm intelligence in last decades, consensus problem of multi-agent systems has been attracting much attention. To reveal the inherent mechanism of leader-following consensus in multi-agent systems with stochastic dynamics, PI control protocols are designed in this paper. Owing to the stochastic analysis techniques, algebraic graph theory, and constructing appropriate Lyapunov function, it is proved that the leader-following consensus of nonlinear stochastic dynamical multi-agent systems can be reached in mean square. Sufficient condition are deduced to select the PI control protocol parameters. Finally, the theoretical results are demonstrated through a simulation example.

In this paper, the distributed leader-following consensus problem of multi-agent systems with uncertain topological graph is formulated from the viewpoint of two dimensional systems over a finite time interval. Combining with iterative learning control, the fully distributed consensus protocols with the adaptive updating laws of unknown time-varying coupling strengthes appeared in the communication topology are proposed for linear multi-agent systems. By choosing appropriate Lyapunov-Krasovskii functional, the leader-following consensus can be achieved on [0,T] for all undirected connected topology graph when the number of iterations tends to infinity. Finally, a simulation example is given to demonstrate the effectiveness of theoretical results.

This paper investigates the event-triggered consensus problem of multi-agent systems with uncertainties and input saturation. First, a fully distributed robust consensus low-gain feedback control strategy is proposed, in which some global information, such as the communication graph and the scale of network, is not needed. Then, by defining an internal dynamic variable to memory the past state, an adaptive dynamic event-triggering mechanism is proposed, which contributes to reducing the usage of communication resources and also does not rely on any global information. Furthermore, Lyapunov-based consensus analysis results are presented, and it is also formally shown that Zeno behavior can be excluded with the proposed consensus protocols. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.