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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.

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.

Information exchange between agents in multi-agents systems is often inexact and delayed. This paper proposes a distributed leader-following consensus algorithm for continuous-time single-integrator multi-agent systems under measurement noises and time-delays in directed topologies. The information states received by an agent from its neighbors are delayed by uniform time-delays. In the meantime, they are corrupted by additive white noises. Based on graph theory and stochastic tools, conditions to ensure the tracking consensus in mean square for both directed fixed and switching topologies are derived. The effectiveness of the proposed algorithms is proved through some simulations.

This paper presents a consensus algorithm for continuous-time double-integrator multi-agent systems with measurement/communication noises under directed fixed and switching topologies. The paper employs the algebraic graph theory and the stochastic tools to develop a consensus protocol in which a time-varying consensus gain is introduced to attenuate the additive white noises corrupting the information exchange between agents. Each agent׳s control input relies on its own information state and its neighbors׳ inaccurate information states and does not need the neighbors׳ information state derivatives. Conditions to guarantee mean square asymptotic convergence under noisy measurement for both fixed and switching topologies are derived. The consensus protocols developed in the noisy measurement case are proved to be still valid in the noise-free case, and they can ensure asymptotic mean square convergence. Finally, to illustrate the approach presented, some numerical simulations are carried out.

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.

Stochastic consensus of multi-agent systems is a main and an important research subject in distributed cooperative control. This is because the information shared in a network is always prone to some uncertainties, which can destroy the performances and the behavior of the entire system. One of these uncertainties is the measurement/communication noises. In this paper, we present an overview of the main contributions done in this field. A classification of these contributions depending on the agents' models and the noises' models is given. Other studies that investigate both the measurement/communication noises and other constraints simultaneously have been also reviewed.

In this paper, we present a distributed leaderless consensus protocol for continuous time single-integrator multi-agent systems with multiplicative measurement noises in time-varying topologies. The consensus has been proved to achieve mean square convergence under restricted conditions on the network topology than those established in the literature for the same problem. That is in our study, the topology is required to have a spanning tree between any two consecutive switching times and no need to be balanced. The analysis followed here is based mainly on graph theory, stochastic tools, and some results about the stability of switching systems. At the end of the paper, some numerical simulations have been derived to demonstrate the effectiveness of our approach.