Containment control of fractional complex networks with stochastic communication noises

This paper aims to investigate the containment control for fractional complex networks (FCNs) with double-integrator fractional-order dynamics under stochastic communication noises. It is assumed that the agents’ communication channels are affected by stochastic noises, which depend on their relative positions. Then, a distributed containment protocol is designed for each follower to counteract the impact of stochastic communication noises. Next, by directly utilizing the properties of the integral mild solution, sufficient conditions are deduced for achieving containment control of the FCNs. The theoretical analysis shows that under the proposed protocol and given sufficient conditions, all followers converge towards into the convex hull spanned by the leaders in the mean square sense. Finally, several numerical examples are provided to validate the effectiveness of the proposed protocol.