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.     

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.     

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.     

Leader-following consensus of double-integrator multi-agent systems with noisy measurements

This paper proposes a leader-following consensus control for continuous-time double-integrator multi-agent systems in noisy communication environment with a constant velocity reference state. Each follower in the team inaccurately measures its neighbors’ positions and the leader’s position if this follower has access to the leader, that the measured positions are corrupted by noises. The constant velocity of the leader is a priori well known. The consensus protocol is constructed based on algebraic graph theory and some stochastic tools. Conditions to ensure the tracking consensus in mean square are derived for both fixed and switching directed topologies. Finally, to illustrate the approach presented, some numerical simulations are carried out.     

Mean square average-consensus under measurement noises and fixed topologies: Necessary and sufficient conditions

In this paper, average-consensus control is considered for networks of continuous-time integrator agents under fixed and directed topologies. The control input of each agent can only use its local state and the states of its neighbors corrupted by white noises. To attenuate the measurement noises, time-varying consensus gains are introduced in the consensus protocol. By combining the tools of algebraic graph theory and stochastic analysis, the convergence of these kinds of protocols is analyzed. Firstly, for noise-free cases, necessary and sufficient conditions are given on the network topology and consensus gains to achieve average-consensus. Secondly, for the cases with measurement noises, necessary and sufficient conditions are given on the consensus gains to achieve asymptotic unbiased mean square average-consensus. It is shown that under the protocol designed, all agents’ states converge to a common Gaussian random variable, whose mathematical expectation is just the average of the initial states.     

Finite-time consensus of multiple second-order dynamic agents without velocity measurements

This article considers the finite-time consensus of multiple second-order dynamic agents without velocity measurements. A feasible protocol under which each agent can only obtain the measurements of its position relative to its neighbours is proposed. By applying the graph theory, Lyapunov theory and the homogeneous domination method, some sufficient conditions for finite-time consensus of second-order multi-agent systems are established under the different kinds of communication topologies. Some examples are presented to illustrate the effectiveness of the theoretical results.     

Leader-following scaled consensus of second-order multi-agent systems under directed topologies

ABSTRACT

This paper investigates the leader-following scaled consensus problem of second-order multi-agent systems under directed topologies. Three novel leader-following scaled consensus protocols are designed. First, a novel scaled consensus protocol is proposed. It can guarantee the velocity of each agent in one sub-group exactly follow that of a leader, and the follower agents achieve scaled consensus. Second, another proposed protocol enables the agents' positions and velocities of one sub-group accurately track those of a leader, and the follower agents achieve scaled consensus. Third, consider the case where the leader's states available to one or multiple followers and the leader travels with a varying velocity, a novel scaled consensus tracking protocol is proposed. Sufficient and necessary conditions are obtained to guarantee scaled consensus tracking for the three cases,respectively. Finally, simulation examples are made to verify the effectiveness of the theoretical results.     

Asynchronous consensus of multiple second-order agents with partial state information

This article studies the asynchronous consensus problem of multiple second-order agents in a sampled-data setting, where asynchrony means that the sampling period of each agent is independent of the others. It is assumed that each agent can only obtain the information of its positions relative to its neighbours at sampling instants. First, a discrete-time protocol is provided based on velocity estimation, and a sufficient and necessary condition for consensus under this protocol is established in virtue of properties of periodic systems. Second, a continuous-time protocol is presented by the theory of dynamic output feedback control, and a sufficient condition for consensus under this protocol is obtained by applying an input delay approach. Simulations are performed to illustrate the effectiveness of the theoretical results.     

Stochastic consensus of single‐integrator multi‐agent systems under relative state‐dependent measurement noises and time delays

This paper proposes a consensus algorithm for continuous‐time single‐integrator multi‐agent systems with relative state‐dependent measurement noises and time delays in directed fixed and switching topologies. Each agent's control input relies on its own information state and its neighbors' information states, which are delayed and corrupted by measurement noises whose intensities are considered a function of the agents' relative states. The time delays are considered time‐varying and uniform. For directed fixed topologies, condition to ensure mean square linear χ‐consensus (average consensus, respectively) are derived for digraphs having spanning tree (balanced digraphs having spanning tree, respectively). For directed switching topologies, conditions on both time delays and dwell time have been given to extend the mean square linear χ‐consensus (average consensus, respectively) of fixed topologies to switching topologies. Copyright © 2016 John Wiley & Sons, Ltd.     

Consensus of multi-agent systems based on sampled-data control

This article studies the consensus problem in directed networks, assuming that each agent is with double-integrator dynamics and only obtains the measurements of its positions relative to its neighbours at sampling instants. We propose a protocol based on sampled-data control and derive an equivalent characterisation of the solvability of the consensus problem under this protocol. In virtue of this equivalent characterisation, we further consider two cases: fixed topology and switching topology. For the first case, we present a set of sampling periods and feedback coefficients which ensure that the protocol can solve a consensus problem. For the second case, we derive sufficient conditions for the protocol to solve a consensus problem under arbitrary switching signals and under a class of switching signals, respectively. Finally, simulations are provided to illustrate the effectiveness of the theoretical results.     

Consensus seeking in a network of discrete-time linear agents with communication noises

This paper studies the mean square consensus of discrete-time linear time-invariant multi-agent systems with communication noises. A distributed consensus protocol, which is composed of the agent's own state feedback and the relative states between the agent and its neighbours, is proposed. A time-varying consensus gain a[k] is applied to attenuate the effect of noises which inherits in the inaccurate measurement of relative states with neighbours. A polynomial, namely ‘parameter polynomial’, is constructed. And its coefficients are the parameters in the feedback gain vector of the proposed protocol. It turns out that the parameter polynomial plays an important role in guaranteeing the consensus of linear multi-agent systems. By the proposed protocol, necessary and sufficient conditions for mean square consensus are presented under different topology conditions: (1) if the communication topology graph has a spanning tree and every node in the graph has at least one parent node, then the mean square consensus can be achieved if and only if ∑^∞_{k = 0}a[k] = ∞, ∑^∞_{k = 0}a²[k] < ∞ and all roots of the parameter polynomial are in the unit circle; (2) if the communication topology graph has a spanning tree and there exits one node without any parent node (the leader–follower case), then the mean square consensus can be achieved if and only if ∑^∞_{k = 0}a[k] = ∞, lim_{k → ∞}a[k] = 0 and all roots of the parameter polynomial are in the unit circle; (3) if the communication topology graph does not have a spanning tree, then the mean square consensus can never be achieved. Finally, one simulation example on the multiple aircrafts system is provided to validate the theoretical analysis.     

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.     

Distributed δ-consensus in directed delayed networks of multi-agent systems

In this article, we propose a distributed δ-consensus protocol in directed networks of dynamic agents having communication delays. The δ-consensus protocol is an average consensus protocol where agents exchange the information with their neighbours at some discontinuous moments. We provide convergence analysis for such consensus algorithm under stochastic switching communication graphs, and then present some generic criteria for solving the average consensus problem. We also show that directed delayed networks of dynamic agents can achieve average consensus even when each agent in the networks intermittently exchanges the information with its neighbours only at some discrete moments. Subsequently, a typical numerical example illustrates and visualises the effectiveness and feasibility of the theoretical results.     

Mean square consensus of multi-agent systems with multiplicative noises and time delays under directed fixed topologies

This paper investigates the mean square consensus problem of multi-agent systems impacted by the combined uncertainty of multiplicative noises and time delays. Considering general network under directed fixed topologies, we propose consensus protocol that take into account both the multiplicative noises and time delays. Using tools from stochastic differential delay equation (SDDE), martingale theory and stochastic inequality, we establish sufficient conditions and obtain the explicit consensus gain and delay upper bounds under which the proposed protocol leads to mean square consensus. In addition, we compare the impact of multiplicative and additive noise and reach the conclusion that multiplicative noises have the property of stabilizing effect. Simulations demonstrate the theoretical results.     

Stochastic consensus of double-integrator leader-following multi-agent systems with measurement noises and time delays

This paper studies a leader-following consensus problem of continuous-time double-integrator multi-agent systems with measurement noises and time-varying communication delays under directed topology. By utilising the neighbour position and velocity information, which are delayed and disturbed by measurement noises whose intensities are considered a function related to the neighbour position and velocity of agents, a distributed consensus protocol is presented, sufficient conditions of the tracking consensus in the sense of mean square are derived. Finally, the effectiveness of the proposed consensus protocol is proved by some simulations.     

Second-order consensus of multi-agent systems with unknown but bounded disturbance

This paper addresses a consensus problem for second-order agents with unknown but bounded (UBB for short) disturbance which may affect the measure of neighbors’ velocities. In this study, the communication topology of the multi-agent system is supposed to be connected. In order to solve this consensus problem, a new velocity estimation called distributed lazy rule is firstly proposed, where each agent can estimate its neighbors’ velocities one by one. Then, a group of sufficient conditions for this second-order consensus problem are presented by adopting graph theory and the well-known Barbalat lemma, and the bounded consensus protocol is taken into account due to actuator saturation. Theoretically, the group of agents can reach consensus under the proposed control protocol, which is also validated by some numerical experiments.     

Group consensus control for double‐integrator dynamic multiagent systems with fixed communication topology

The problem of group consensus is investigated in this paper, where all agents possess double‐integrator dynamics. Two different kinds of consensus protocols are proposed for networks with fixed communication topology to reach group consensus for the agents’ positions and velocities. Convergence analysis is discussed, and necessary and/or sufficient conditions are presented for multiagent systems to achieve group consensus. The first protocol leads to dynamic consensus where positions of all agents reach time‐varying consensus values. By applying the second protocol, both the agents’ positions and their velocities reach constant consensus values. That is, static consensus is achieved. Simulation examples are given to show the effectiveness of the theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.     

Consentability and protocol design of multi-agent systems with stochastic switching topology

This paper studies the mean square consentability problem for a network of double-integrator agents with stochastic switching topology. It is proved that in Markov-switching topologies, the network is mean square consentable under linear consensus protocol if and only if the union of graphs in the switching topology set has globally reachable nodes. A necessary and sufficient condition of the mean square consensus is obtained. Finally, an LMI approach to the design of the consensus protocol is presented. Numerical simulations are given to illustrate the results.     

Accelerating average consensus by using the information of second-order neighbours with communication delays

This article investigates the problem of accelerating average consensus in undirected and connected networks. The protocol using the information of second-order neighbours with communication delays is proposed and the delay effects on stability and the convergence speed are analysed, respectively, under an assumption about the network topologies. It is proved that, for appropriate communication delays, networks reach average consensus faster under the proposed protocol than the standard protocol using only the information of first-order neighbours. Finally, a simulation example is presented to illustrate the proposed results.     

Distributed node‐to‐node consensus of multi‐agent systems with stochastic sampling

This paper is concerned with the mean square node‐to‐node consensus tracking problem for multi‐agent systems with nonidentical nonlinear dynamics and directed topologies. The randomly occurred uncertainties in the sampling devices may result in stochastically varied sampling periods, which lead to the investigation of node‐to‐node consensus problem under stochastic sampling. By employing the input‐delay method and discontinuous Lyapunov functional approach, it arrives at some sufficient conditions under which the state of each follower can track that of the corresponding leader asymptotically in the mean square sense. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.