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

This work addresses the leader-following consensus control of continuous-time single-integrator multi-agents systems with measurement noises and time-delays. As often happened in practical applications, the states information received by an agent from its neighbors are assumed with time-delays and contaminated by additive or multiplicative noises. Using stochastic analysis tools and algebraic graph theory, the mean square leader-following consensus and the almost sure leader-following consensus are proposed for multi-agent systems under additive and multiplicative noises, respectively. For the case with additive noises, the sufficient conditions of the mean square and the almost sure leader-following consensus are obtained by employing the variation of constants formula. As to the case with multiplicative noises, Lyapunov functional is constructed to get the sufficient conditions for the leader-following consensus, where the agents converge to the leader with an exponential rate. These results show that for any given time-delay and noise intensity, the two consensus can be achieved under the appropriate control gains. Numerical simulations are conducted to justify the effectiveness of the proposed consensus protocols. (C) 2017 Elsevier B.V. All rights reserved.