Discrete-time stochastic consensus: A Kalman-filter-based two-time-scale protocol

This paper investigates the discrete-time multi-agent consensus with stochastic communication noises. A Kalman-filter-based two-time-scale protocol that alternates between estimation and control is proposed. Compared with the classical case of the Kalman-filter-based consensus algorithm, we have relaxed the condition on the communication environment by dropping the assumption that each agent can receive its neighbors' control input information. In absence of the information of the noises and initial states, the Kalman-filter-based estimator is shown to be asymptotically unbiased. The stability property of the proposed protocol is also given by analyzing the convergence of the explicit closed-loop solution in mean square. Some numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.(c) 2023 Elsevier B.V. All rights reserved.