Containment control of multi-agent systems with measured noise based on the Kalman-Bucy filtering theory

Abstract

This paper investigates stochastic containment control problems of multi-agent systems with measured noise in mean square sense. First, based on the Kalman-Bucy filtering theory, we design a proposed protocol for stochastic containment control problems based on the neighbors' information, and give a proof to check that Kalman-Bucy filtering estimation is an asymptotically unbiased estimation. Second, by using the tools of stochastic theory and algebraic graph theory, for the networks with directed and undirected topologies, respectively, necessary and sufficient conditions that make the mean square containment problems of multi-agent systems with measured noise are proposed where the communicated graph G has a spanning forest. Third, if the G has a spanning forest, then the mean square of containment control error E(||δ(t)||2) is upper bounded by O(t−1) for directed graph, and is upper bounded and lower bounded by Θ(t−1) for undirected graph. Finally, an illustrative example with simulation is studied to support our results.