Containment control for multi-agent systems with fractional Brownian motion

The coordination control of multi-agent systems (MASs) with stochastic noise has been widely studied. But it is still unclear when the stochastic noise is the fractional Brownian motion (fBm), which has the character of memorability. In this paper, we investigate the containment control problem of MASs with fBm over a directed communication network. Firstly, we design several state observers to estimate the states of the followers. Then, based on the estimation information, we design a novel control function for each follower. With the aid of the properties of analytic semigroup and fixed point theorem, we prove that the MASs can achieve the mean-square containment control or quasi-containment control. Finally, we provide simulation examples to demonstrate the effectiveness of the obtained theoretical results. (C) 2021 Elsevier Inc. All rights reserved.