Stochastic consentability of continuous-time multi-agent systems with relative-state-dependent measurement noises

In this paper, we consider the distributed consensus of high-dimensional first-order agents with relative-state-dependent measurement noises. Each agent can measure or receive its neighbors' state information with random noises, whose intensity is a nonlinear vector function of agents' relative states. For this kind of multi-agent networks, it is a prominent feature that the dynamics associated with the network uncertainties interact with the dynamics of agents' states in a distributed information architecture. By investigating the structure of this interaction and the tools of stochastic differential equations, we develop some small consensus gain theorems to give sufficient conditions to ensure mean square and almost sure consensus, based on which we prove that the connectivity of the network is the necessary and sufficient condition for the existence of control gain matrices to achieve asymptotically unbiased mean square average-consensus.