Conditions For Mean-square Consensus Research Articles

Event-triggered consensus control for stochastic multi-agent systems under state-dependent topology

In this study, the mean square consensus problem for stochastic multi-agent systems with nonlinear protocols is concerned. In particular, the topological structure of the system is characterised by state-dependent directed graph, in which the edges are described by nonlinear function related to the states and possess much better performance than before. A novel proposition based on matrix theory is proposed to conquer the challenges of time-invariant asymmetric matrix. In view of the communication burden and practically, a time-dependent event-triggered strategies are explored, where the control input on each agent is updated only when a certain triggering condition is violated. Then, some sufficient conditions for mean square consensus of stochastic multi-agent with state-dependent topology are established. Furthermore, a positive lower bound for inter-event times can be found such that the Zeno phenomenon is eliminated. Finally, a simulation example is utilised to illustrate the validly of developed theoretical results and the effectiveness of the control protocol.

Consensus Control of Second-Order Time-Delayed Multiagent Systems in Noisy Environments Using Absolute Velocity and Relative Position Measurements.

This article designs an effective consensus control protocol for continuous-time second-order time-delayed multiagent systems in a multiplicative noisy environment, using absolute velocity and relative position measurements. The nonlinear case and double-integrator case are studied, respectively. Due to the time delay and multiplicative noise in such models, the conventional methods for consensus analysis are not applicable. In this article, therefore, a degenerated Lyapunov functional is used to derive the conditions for mean-square consensus and almost-sure consensus, related to the Lipschitz constants of the nonlinear term, time delay, and noise intensity. In particular, for the double-integrator setting, it is shown that the mean-square consensus and the almost-sure consensus can be achieved by choosing appropriate control gains for any given time delay and noise intensity. To show the effectiveness of the proposed control protocol, some numerical simulations are demonstrated.

Consensus control of second‐order delayed multiagent systems with intrinsic dynamics and measurement noises

SummaryThis paper studies the consensus control of second‐order multiagent systems with intrinsic dynamics based on delayed and noisy measurements, where the delays in the position and velocity measurements are allowed to be different. The nonlinear and linear intrinsic dynamics are considered, respectively. For the case with nonlinear dynamics, mean square and almost sure consensus conditions are established by applying the degenerate Lyapunov functional and stochastic stability theorems. For the delay‐free case with linear dynamics, appropriate Lyapunov functions are established to get some simple sufficient conditions for mean square and almost sure consensus, and necessary conditions for mean square consensus. It is shown that, with respect to the weighted average type control protocols, second‐order multiagent systems are kept mean square consentable under multiplicative measurement noises alone or intrinsic dynamics alone, but may become unconsentable due to the coexistence of multiplicative noises and intrinsic dynamics. These results are further extended to leader‐following multiagent systems.

Mean-square consensus of discrete-time multi-agent systems with Markovian switching topologies and persistent disturbances

This article deals with the leader-following mean-square consensus problem of discrete-time general linear multi-agent systems with Markovian switching topologies and persistent disturbances. Assume that the communication topology is not connected at any time but the union topology is connected. First, the estimators are designed to calculate the states of agents when external disturbance not exists. Based on the error information between the truth-values and estimated-values of states, the compensators are proposed to subject to the effect of persistent disturbances. And then, a new mean-square consensus control protocol is proposed for each agent. Second, by using the property of permutation matrix, the original closed-loop system is transferred into an equivalent system. Third, sufficient conditions for mean-square consensus are obtained in the form of matrix inequalities. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results.

Consensus Control of Second-Order Stochastic Delayed Multi-Agent Systems with Intrinsic Dynamics and Undirected Topologies

In this paper, we address the consensus control of stochastic multi-agent systems with intrinsic dynamics based on measurements with time-delay and multiplicative noises under undirected graphs. By developing degenerate Lyapunov functional and stochastic stability theorem, we establish mean square and almost sure consensus conditions explicitly related to the nonlinearity of agent dynamics, control gains, noise intensities and parameters of network graphs. Especially, for the case with linear dynamics, we get necessary conditions for mean square consensus. It is shown that with respect to the weighted-average type control protocols, second-order multi-agent systems are kept mean square consentable with multiplicative measurement noises alone or intrinsic dynamics alone, but may become unconsentable due to the co-existence of multiplicative noises and intrinsic dynamics.

Sampled-Data Consensus Over Random Networks

This paper considers the consensus problem for a network of nodes with random interactions and sampled-data control actions. We first show that consensus in expectation, in mean square, and almost surely are equivalent for a general random network model when the inter-sampling interval and network size satisfy a simple relation. The three types of consensus are shown to be simultaneously achieved over an independent or a Markovian random network defined on an underlying graph with a directed spanning tree. For both independent and Markovian random network models, necessary and sufficient conditions for mean-square consensus are derived in terms of the spectral radius of the corresponding state transition matrix. These conditions are then interpreted as the existence of critical value on the inter-sampling interval, below which global mean-square consensus is achieved and above which the system diverges in mean-square sense for some initial states. Finally, we establish an upper bound on the inter-sampling interval below which almost sure consensus is reached, and a lower bound on the inter-sampling interval above which almost sure divergence is reached. Some numerical simulations are given to validate the theoretical results and some discussions on the critical value of the inter-sampling intervals for the mean-square consensus are provided.

Tracking consensus of nonlinear MASs with asymmetric communication delays in noisy environments

This paper investigates the tracking consensus problem of nonlinear multi-agent systems (MASs) with asymmetric time-varying communication delays in noisy environments under the conditions of fixed and switching directed topologies. A novel stochastic analysis approach is proposed, which guarantees that the designed two distributed tracking protocols can guide the controlled systems to achieve tracking consensus in the sense of mean square. In order to further reveal the influence of asymmetric communication delays on the tracking consensus ability for MASs, some new delay-dependent sufficient conditions for mean-square consensus are also developed. A simple example is finally given to illustrate the effectiveness of the proposed theoretical results.

Mean square consensus of second-order multi-agent systems under Markov switching topologies

This paper studies the mean square consensus problems of second-order continuous-time multi-agent systems with and without non-linear dynamics under the Markov switching topologies, respectively. Under the proposed consensus protocols, sufficient conditions for mean square consensus of multi-agent systems with noises are derived under Markov switching directed topologies, while necessary and sufficient conditions for mean square consensus of multi-agent systems without non-linear dynamics and noises are obtained under Markov switching directed topologies. Finally, simulation examples are given to show the effectiveness of the proposed methods.

Multi-Agent Consensus Control under Markovian Switching Topology and Time-Delay

In this note, the consensus problem of linear multi-agent systems with Markovian communication topology and time-varying delay is investigated. The topology of network is switched by Markovian process and the time-delay is considered to be time-varying and has a lower and upper bounds. A sufficient condition of mean square consensus is obtained in terms of linear matrix inequalities, and based on the condition, a controller design method is presented such that the multi-agent systems reaches to mean square consensus.

Necessary and sufficient conditions for mean square consensus under Markov switching topologies

This article deals with the mean square consensus problem for second-order discrete-time multi-agent systems. Both cases of systems with and without time delays in Markov switching topologies are considered. With the introduced control protocols, necessary and sufficient conditions for mean square consensus of second-order multi-agent systems are derived. Under the given control protocols in Markov switching topologies, the second-order multi-agent systems can reach mean square consensus if and only if each union of the graphs corresponding to all the nodes in closed sets has a spanning tree. Finally, a simulation example is provided to illustrate the effectiveness of our theoretical results.

Multiagent Consensus Control under Network-Induced Constraints

Mean consensus problem is studied using a class of discrete time multiagent systems in which information exchange is subjected to some network-induced constraints. These constraints include package dropout, time delay, and package disorder. Using Markov jump system method, the necessary and sufficient condition of mean square consensus is obtained and a design procedure is presented such that multiagent systems reach mean square consensus.

Observer‐based consensus of second‐order multi‐agent system with fixed and stochastically switching topology via sampled data

SUMMARYThis paper addresses the distributed observer‐based consensus problem of second‐order multi‐agent systems via sampled data. Firstly, for the case of fixed topology, a velocity‐independent distributed control law is proposed by designing a distributed observer to estimate the unavailable velocity, then a sufficient and necessary condition of consensus on design parameters and sampling period is obtained by using the matrix analysis method. Secondly, for the case of stochastically switching topology, a sufficient and necessary condition of mean square consensus is also proposed and proven, and an algorithm is provided to design the parameters in the consensus protocol. Two simulation examples are given to illustrate the effectiveness of the proposed consensus algorithms. Copyright © 2012 John Wiley & Sons, Ltd.

Consensus Conditions of Multi-Agent Systems with Unbalanced Topology and Stochastic Disturbances

Consensus conditions of multi-agent systems with general directed communication topology and Guassian communication noises are investigated.Here the topology includes not only the balanced graphes but also unbalanced graphes,and the latter is the main concern of this paper.By using the results of Markov chains,a communication class of network nodes is given.By considering the influence of the noises,the consensus conditions are provided:(1) for the case where the information received by some agents in the communication class corrupted by noises,a sufficient and necessary condition of mean square consensus is given.It is shown that this condition can also ensure almost sure consensus.(2) For the case where no information received by the agents in the communication class is corrupted,but the information received by some agents outside of the communication class is corrupted,a sufficient condition of mean square consensus is obtained,which is shown to be necessary in some sense.(3) For the case without noise,a sufficient and necessary condition of consensus is presented.