Consensus seeking in multi-agent systems with noisy and delayed communication in digraphs having spanning tree

This paper studies the consensus problem of continuous-time single-integrator multi-agent systems with measurement noises and time delays under directed fixed topologies. Each agent in the team receives imprecise and delayed information from its neighbours. The noises are considered white noises, and time delays are assumed to be uniform for all the received information states. An analysis framework based on graph theory and stochastic tools is followed to derive conditions under which the asymptotic unbiased mean square linear χ-consensus is achieved in directed fixed topologies having a spanning tree. Then, conditions to achieve asymptotic unbiased mean square average consensus are deduced for fixed balanced digraphs having a spanning tree. The effectiveness of the proposed algorithms is proved through some simulations.     

Consensus of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises

This paper studies the consensus problem of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises. Directed switching topologies are considered. Firstly, for a kind of switching topology with each digraph containing a spanning tree, we give a weak consensus result on the basis of the mode‐dependent average dwell time method. Then, if all digraphs in a switching topology are strongly connected and the corresponding Laplacian matrices have a common left eigenvector for zero eigenvalue, we prove that the mean square and almost sure consensus can always be guaranteed for an arbitrary switching sequence with some constant distributed control gains, and we also give the statistic properties of the final consensus points. Numerical examples are presented to illustrate the effectiveness of our results. Copyright © 2017 John Wiley & Sons, Ltd.     

Bipartite Linear χ‐Consensus of Double‐Integrator Multi‐Agent Systems With Measurement Noise

The bipartite consensus problem is investigated for double‐integrator multi‐agent systems in the presence of measurement noise. A distributed protocol with time‐varying consensus gain is proposed. By using tools of state transition matrix and algebraic graph theory, necessary and sufficient conditions for the designed protocol to be a mean square bipartite linear χ‐consensus protocol are given. It is shown that the signed digraph being structurally balanced and having a spanning tree are not only sufficient, but also necessary for bipartite consensus. Furthermore, the protocol is proved to be a mean square bipartite average consensus protocol if the signed graph is weight balanced.     

Distributed consensus of discrete‐time multi‐agent systems with multiplicative noises

In this paper, we consider the consensus problem of discrete‐time multi‐agent systems with multiplicative communication noises. Each agent can only receive information corrupted by noises from its neighbors and/or a reference node. The intensities of these noises are dependent on the relative states of agents. Under some mild assumptions of the noises and the structure of network, consensus is analyzed under a fixed topology, dynamically switching topologies and randomly switching topologies, respectively. By combining algebraic graph theory and martingale convergence theorem, sufficient conditions for mean square and almost sure consensus are given. Further, when the consensus is achieved without a reference, it is shown that the consensus point is a random variable with its expectation being the average of the initial states of the agents and its variance being bounded. If the multi‐agent system has access to the state of the reference, the state of each agent can asymptotically converge to the reference. Numerical examples are given to illustrate the effectiveness of our results. Copyright © 2014 John Wiley & Sons, Ltd.     

Time‐varying output formation control for linear multi‐agent systems with switching topologies

Time‐varying output formation control problems for linear multi‐agent systems with switching topologies are studied, where two types of switching topologies are considered: (1) the topology is undirected and jointly connected, and 2) each topology is directed and has a spanning tree. An output formation protocol under switching topologies is constructed using the outputs of neighboring agents via dynamic output feedback. Two algorithms are proposed to design the dynamic protocols under both jointly connected topologies and switching directed topologies. Time‐varying output formation feasibility conditions are given to describe the compatible relationship among the desired time‐varying output formation, the dynamics of each agent, and the switching topologies. The stability of the closed‐loop multi‐agent systems under the proposed two algorithms is investigated based on the common Lyapunov functional theory and the piecewise Lyapunov functional theory, respectively. In the case where the topologies are jointly connected, time‐varying output formation can be achieved for multi‐agent systems using the designed protocol if the given time‐varying output formation satisfies the feasible constraint. For the case where the switching topologies are directed and have a spanning tree, the time‐varying output formation can be realized if the output formation feasibility constraint is satisfied and the dwell time is larger than a positive threshold. Moreover, approaches to determine the output formation references are provided to describe the macroscopic movement of the time‐varying output formation. Finally, numerical simulation results are presented to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed consensus for multi-agent systems with delays and noises in transmission channels

This paper studies the distributed consensus problem for linear discrete-time multi-agent systems with delays and noises in transmission channels. Due to the presence of noises and delays, existing techniques such as the lifting technique and the stochastic Lyapunov theory are no longer applicable to the analysis of consensus. In this paper, a novel technique is introduced to overcome the difficulties induced by the delays and noises. A consensus protocol with decaying gains satisfying persistence condition is adopted. Necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non-leader–follower and leader–follower cases under a fixed topology. Under dynamically switching topologies and randomly switching topologies, sufficient conditions for strong consensus and mean square consensus are also obtained. Numerical examples are given to demonstrate the effectiveness of the proposed protocols.     

Distributed consensus of multi‐agent systems with general linear node dynamics and intermittent communications

Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi‐agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi‐agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low‐dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi‐step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi‐agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Leader-following consensus of single-integrator multi-agent systems under noisy and delayed communication

This paper proposes a leader-following consensus control for continuous-time single-integrator multi-agent systems with multiplicative measurement noises and time-delays under directed fixed topologies. Each agent in the team receives imprecise information states corrupted by noises from its neighbours and from the leader; these noises are depending on the agents’ relative states information. Moreover, the information states received are also delayed by constant or time-varying delays. An analysis framework based on graph theory and stochastic tools is followed to derive conditions under which the tracking consensus of a constant reference is achieved in mean square. The effectiveness of the proposed algorithms is proved through some simulation examples.     

Synchronization of General Linear Multi‐Agent Systems With Measurement Noises

This paper studies the synchronization of general linear multi‐agent systems with measurement noises in mean square. It shows that the conventional consensus protocol is efficient and robust to the additive and multiplicative measurement noises in mean square. For the additive measurement noises which are independent of the relative‐states, it shows that the multi‐agent systems can achieve synchronization in practical mean square. For the multiplicative measurement noises which are dependent of the relative‐states, it shows that the multi‐agent systems can achieve synchronization in (strict) mean square. Furthermore, the new consensus protocol is better than the conventional one at some specific situations, i.e., the multi‐agent systems with additive measurement noises can also achieve synchronization in (strict) mean square. Numerical simulations are also provided and the results show highly consistent with the theoretical results.     

Leader-following consensus for single-integrator multi-agent systems with multiplicative noises in directed topologies

This paper proposes a leader-following consensus control for continuous-time single-integrator multi-agent systems with multiplicative measurement noises under directed fixed and switching topologies. The consensus controller is developed by combining the graph theory and stochastic tools. The control input for each agent relies on its own state and its neighbours’ states corrupted by noises, the noises are considered proportional to the relative distance between agents, both of the noisy case and the noise-free case are studied, and conditions to achieve mean square convergence under noisy measurement and asymptotic convergence in absence of noises are derived. Finally, in order to prove the validity of the consensus control, some simulations were carried out.     

Consensus problem of high‐order multi‐agent systems with external disturbances: An H∞ analysis approach

This paper is devoted to the output consensus problem of directed networks of multiple high‐order agents with external disturbances, and proposes a distributed protocol using the neighbors' measured outputs. By defining an appropriate controlled output and conducting a model transformation in two steps, consensus performance analysis of the multi‐agent system under the proposed protocol is transformed into a normal H_∞ problem. Then using H_∞ theory of linear systems, conditions are derived to ensure the consensus performance with a prescribed H_∞ index for networks with fixed and switching topologies, respectively. A numerical example of the formation control application is included to validate the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Consensus strategy for a class of multi‐agents with discrete second‐order dynamics

This paper investigates consensus strategies for a group of agents with discrete second‐order dynamics under directed communication topology. Consensus analysis for both the fixed topology and time‐varying topology cases is systematically performed by employing a novel graph theoretic methodology as well as the classical nonnegative matrix theory. Furthermore, it is shown that the necessary and sufficient condition for the agents under fixed communication topology to reach consensus is that the communication topology has a spanning tree; and sufficient conditions for the agents to reach consensus when allowing for the dynamically changing communication topologies are also given. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed results. Copyright © 2011 John Wiley & Sons, Ltd.     

Guaranteed‐performance consensus tracking of singular multiagent systems with Lipschitz nonlinear dynamics and switching topologies

In this paper, the problem of guaranteed‐performance consensus tracking of continuous‐time singular multiagent systems with Lipschitz nonlinearities and switching topologies is investigated. Consideration is that the interaction of the concerned agent network is described by a set of directed graphs with the union graph having a directed spanning tree rooted at the leader. To establish the guaranteed‐performance criterion, a quadratic performance function is constructed by utilizing the consensus errors among all agents. Then, a consensus protocol that collects the local information from neighboring agents is proposed to achieve consensus tracking and to guarantee the consensus regulation performance of the multiagent systems. On the basis of nonsingular transformation approach, singular systems theory, and Lyapunov stability analysis, the concerned guaranteed‐performance consensus tracking problem is cast into the admissibility analysis for an equivalent kind of switched singular consensus error system. Furthermore, sufficient conditions on the guaranteed‐performance consensus tracking protocol design are formulated in terms of linear matrix inequalities. Finally, numerical examples are employed to demonstrate the effectiveness of the theoretical results.     

A New Observer‐Type Consensus Protocol for Linear Multi‐Agent Dynamical Systems

The consensus problem is investigated in this paper for a class of multi‐agent systems with general linear node dynamics and directed communication topologies. A new distributed observer‐type consensus protocol is designed based only on the relative output measurements of neighboring agents. Compared with existing observer‐type protocols, the one presented here does not require information about the relative states of the observers. Tools from small gain theory and matrix analysis, some sufficient conditions are obtained for achieving consensus in such multi‐agent systems where the underlying network topology contains a directed spanning tree. Finally, some numerical examples including an application in low‐Earth‐orbit satellite formation flying are provided to illustrate the theoretical results.     

Consensus of linear multi‐agent systems with stochastic noises and binary‐valued communications

This article studies consensus problems of discrete‐time linear multi‐agent systems with stochastic noises and binary‐valued communications. Different from quantized consensus of first‐order systems with binary‐valued observations, the quantized consensus of linear multi‐agent systems requires that each agent observes its neighbors' states dynamically. Unlike the existing quantized consensus of linear multi‐agent systems, the information that each agent in this article gets from its neighbors is only binary‐valued. To estimate its neighbors' states dynamically by using the binary‐valued observations, we construct a two‐step estimation algorithm. Based on the estimates, a stochastic approximation‐based distributed control is proposed. The estimation and control are analyzed together in the closed‐loop system, since they are strongly coupled. Finally, it is proved that the estimates can converge to the true states in mean square sense and the states can achieve consensus at the same time by properly selecting the coefficient in the estimation algorithm. Moreover, the convergence rate of the estimation and the consensus speed are both given by O(1/t). The theoretical results are illustrated by simulations.     

Consensus of heterogeneous first‐ and second‐order multi‐agent systems with directed communication topologies

In this paper, we consider the consensus problem for heterogeneous multi‐agent systems composed of some first‐order and some second‐order dynamic agents in directed communication graphs. Consensus protocols are proposed for the second‐ and first‐order dynamic agents, respectively. Under certain assumptions on the control parameters, for fixed communication topologies, necessary and sufficient conditions for consensus are given, and the consensus values of all agents are established. For switching topologies, sufficient conditions are given for all agents to reach consensus. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Admissible consensus analysis for high‐order linear singular swarm systems with multiple time‐varying delays and topology variances

Admissible consensus analysis problems for high‐order linear time‐invariant singular swarm systems with multiple time delays and time‐varying interaction topologies are investigated. First, necessary and sufficient conditions for admissible consensus are presented, and admissible consensus problems are transformed into admissible problems of multiple lower dimensional singular systems. Then, on the basis of the first equivalent form, explicit expressions of consensus functions are given, where the impacts of initial states of agents and protocols, time delays and topology variances are determined, respectively. Moreover, it is shown that if interaction topologies are balanced, then swarm systems with the same initial states but different interaction topologies and different time delays have an identical consensus function. Finally, numerical simulations are given to demonstrate theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Consensus of second‐order multi‐agent systems with exogenous disturbances

In this paper, the consensus of second‐order multi‐agent dynamical systems with exogenous disturbances is studied. A pinning control strategy is designed for a part of agents of the multi‐agent systems without disturbances, and this pinning control can bring multiple agents' states to reaching an expected consensus track. Under the influence of the disturbances, disturbance observers‐based control (DOBC) is developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi‐agent systems with disturbances under the composite controller can be achieved for fixed and switching topologies. Finally, by applying an example of multi‐agent systems with switching topologies and exogenous disturbances, the consensus of multi‐agent systems is reached under the DOBC with the designed parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Consensus of double-integrator multi-agent systems without relative states derivative under relative-state dependent measurement noises*

This paper proposes a consensus protocol for continuous-time double-integrator multi-agent systems under noisy communication in directed topologies. Each agent’s control input relies on its own velocity and the relative positions with neighbours; it does not require the relative velocities. The agent receives its neighbours’ positions information corrupted by time-varying measurement noises whose intensities are proportional to the absolute relative distance that separates the agent from the neighbours. The consensus protocol is mainly based on the velocity damping gain to derive conditions under which the unbiased mean square χ-consensus is achieved in directed fixed topologies, and the unbiased mean square average consensus is achieved in directed switching topologies. The mean square state errors are quantified for both the positions and velocities. Finally, to illustrate the approach presented, some numerical simulations are performed.