Approximate Consensus in Multi-agent Nonlinear Stochastic Systems

The paper is devoted to the approximate consensus problem for networks of nonlinear agents with switching topology, noisy and delayed measurements. In contrast to the existing stochastic approximation-based control algorithms (protocols), local voting protocols with nonvanishing step size are proposed. Nonvanishing (e.g., constant) step size allows to achieve better convergence rate and copes with time-varying loads and agent states. The price to pay is replacement of the mean square convergence with an approximate one. To analyze dynamics of the closed loop system, the so-called the method of the averaged models is used. It allows to reduce complexity of the closed loop system analysis. In this paper new upper bounds for mean square distance between the initial system and its approximate average model are proposed. The proposed upper bounds are used to obtain conditions for approximate consensus achievement. The method is applied to the balancing problem of information capabilities in stochastic dynamic network with incomplete information about the current state of nodes and changing set of communication links. This problem is reformulated as consensus problem in noisy model with switched topology. The conditions to achieve the optimal level of agents load are obtained. The performance of the system is evaluated analytically and by simulations.