Continuous-time multi-agent averaging with relative-state-dependent measurement noises: matrix intensity functions

In this study, the distributed averaging of high-dimensional first-order agents is investigated with relative-state-dependent measurement noises. Each agent can measure or receive its neighbours’ state information with random noises, whose intensity is a non-linear matrix function of agents’ relative states. By the tools of stochastic differential equations and algebraic graph theory, the authors give sufficient conditions to ensure mean square and almost sure average consensus and the convergence rate and the steady-state error for average consensus are quantified. Especially, if the noise intensity function depends linearly on the relative distance of agents’ states, then a sufficient condition is given in terms of the control gain, the noise intensity coefficient constant, the number of agents and the dimension of agents’ dynamics.