Stochastic Approximation in Unbalanced Time-Varying Networks for Robust
Distributed Coordinated Control
Abstract
The stochastic approximation based control law has been proved to be a
powerful tool to achieve the robust distributed coordinated control for
multi-agent systems (MASs) with uncertain disturbances in fixed or
balanced time-varying network. However, its effectiveness proof in
unbalanced time-varying networks is not well solved. The main
contribution of this paper is solving this problem in two typical
coordinated control problems based on a time-varying quadratic Lyapunov
function. Firstly, the stochastic approximation for consensus problem of
discrete-time single-integrator MASs with additive noises is studied. We
build the weak consensus, mean square and almost sure consensus
conclusion under the assumption that the time-varying network is
uniformly strongly connected (USC) by adopting the stochastic
approximation based consensus protocol. The convergence rate of the weak
consensus is also quantified. Secondly, the stochastic approximation for
formation control problem of MASs with relative-position information in
the plane as an application of the built consensus conclusion is
studied. We show that the stochastic approximation based formation
control law can be used to achieve the desired formation for MASs if the
network is USC. We finally give numerical simulations to verify the
correctness of the conclusion.