Sliding Mode Consensus Control For Multi-agent Systems With Fractional Brownian Motions

Fractional Brownian motion has the properties of stationary increment,long-range correlation and self-similarity,which can better describe stochastic disturbance than Brownian motion.Therefore,fractional Brownian motion is more reasonable and effective as stochastic noises in stochastic models such as mathematical,financial,population dynamic systems and communication networks.In practice,due to the influence of external disturbances,space obstacles and communication obstacles,the communication topology between agents often cannot remain fixed.In order to describe this time-varying topology in multi-agent systems,the time-varying topology is usually assumed to be a switch between several known topologies,and the switching process between topologies is modeled as a Markov process.However,if Markov jump topology is used to describe the topology change of multi-agent systems,the transition probability of topology needs to be assumed to be constant,which is difficult to achieve in many practical problems.Semi-Markov processes have attracted more and more attention because their functional distribution of sojourn-time can be relaxed to a more general probability distribution.Therefore,this paper studies the leader-follower consensus of sliding mode control for multi-agent systems under the disturbance of fractional Brownian motion.The specific contents are as follows:(1)The stochastic bounded consensus for multi-agent systems with fractional Brownian motions via sliding mode control is studied.Utilizing the sliding mode control method,the analysis of the finite-time stochastic bounded consensus for multi-agent systems under the disturbance of fractional Brownian motions with semi-Markovian jumping topologies is investigated.Semi-Markov jumping topologies are introduced to describe the information interaction between agents.In order to obtain the sliding mode error dynamics between leader and followers,an integral sliding mode surface based on neighbor information of agents is designed considering 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 is studied.Then the finite-time reachability of the error system state to the proposed sliding mode surface is analyzed.Last a simulation example of distributed microgrid model is given to verify the effectiveness of the proposed method.(2)The consensus for semi-Markov switched topology multi-agent systems with partially unknown transfer rates with fractional Brownian motion via sliding mode control is studied.Considering that the transfer rates of the semi-Markov switching topology is partially unknown,an integral sliding mode surface is designed and the state error model between the leader and the follower is established.Then the stochastic boundedness of the sliding mode dynamics is studied by using a new Lyapunov function related to Hurst exponent.Then a sliding mode controller is designed to make the state trajectory reach and maintain on the desired sliding surface.Finally,the validity of the results is verified by numerical simulation.(3)The consensus of event-triggered sliding mode control for multi-agent systems with fractional Brownian motion is studied.Firstly,a linear multi-agent system model with fractional Brownian motion is established,the event triggering strategy based on sampled data and sliding surface function are designed.Then,the stochastic boundedness of the closed-loop system is analyzed and the sufficient conditions for the joint design of sliding surface and event triggering parameters are given.Finally,a sliding mode controller based on event triggering strategy and sliding surface function is designed to drive the state trajectory to the desired sliding surface and keep it there in the following time.Finally,the simulation results show the effectiveness of the proposed design method.