Stochastic bounded consensus for multi-agent systems with fractional Brownian motions via sliding mode control.

Utilizing the sliding mode control method, the analysis of the finite-time stochastic bounded consensus for multi-agent systems under the disturbance of fractional Brown-ian motions with semi-Markovian jumping topologies is investigated. Semi-Markov jump-ing topologies are introduced to describe the information interaction between agents. In order to obtain the sliding mode error dynamics between leader and followers, an inte-gral sliding mode surface based on neighbor information of agents is designed consider-ing semi-Markovian jumping topologies. Different from the normal Lyapunov functional, a double-integral-type Lyapunov functional based on the Hurst index is constructed to deal with fractional Brownian motions, then the finite-time stochastic bounded consensus of sliding mode dynamics are studied. Then the finite-time reachability of the error system state to the proposed sliding mode surface is analyzed. Last a distributed microgrid model and a numerical example are given and simulated to verify the effectiveness of the pro-posed method.(c) 2023 Elsevier Inc. All rights reserved.