Analysis of nonlinear local voting protocol for stochastic dynamical networks

The consensus problem for nonlinear stochastic networks with switched topology and noise in measurements is considered. A modification of known local voting protocol with non-decreasing step-size is analyzed for the case when inputs appear nonlinearly in the network model. The analysis is based on introduction of an averaged continuous-time model of the initial discrete-time stochastic system. It is shown that the trajectories of the initial system are close in mean-square sense to the trajectories of the averaged model. Such an approximation result is used for analysis of the initial system. To demonstrate the performance of the system with new protocol, an example for the load balancing problem is given. Corresponding simulation results show a reasonable quality of the control strategy.