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.