Consensus of double-integrator multi-agent systems without relative state derivatives under communication noises and directed topologies

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.