Stochastic Approximation in Unbalanced Time-Varying Networks for Robust Distributed Coordinated Control

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.