Approximate consensus in multi-agent stochastic systems with switched topology and noise

Abstract

In this paper the approximate consensus problem in multi-agent stochastic systems with noisy information about the current state of the nodes and randomly switched topology for agents with nonlinear dynamics is considered. The control is formed by the local voting protocol with step size not tending to zero. To analyze closed loop system we propose to use method of continuous models (ODE approach or Derevitskii-Fradkov-Ljung (DFL)-scheme). The usage of this method allows one to reduce the computation load. The bounds of the mean proximity of trajectories of the discrete stochastic system to its continuous deterministic model are obtained. Based on those bounds the conditions for achieving mean square ε-consensus are established. The method is applied to the load balancing problem in decentralized stochastic dynamic network with incomplete information about the current state of nodes and changing set of communication links is considered. The load balancing problem is reformulated as consensus problem in noisy model with switched topology. The conditions to achieve the optimal level of nodes load are obtained. The performance of the system is evaluated both analytically and by simulation. Obtained results are important for control of production networks, multiprocessor or multicomputer networks, etc.