Research On Consensus Of Fractional-Order Multi-Agent Systems Via Discontinuous Communication Control

The research on cooperative control of multi-agent systems is not only helpful to reveal the intrinsic mechanism of biological collective behaviors,but also helpful to solve some practical engineering applications,such as the multi-robot formation,smart grid,just to name a few.However,many phenomena in nature or practical systems cannot be described in the framework of the classical integer-order models,while they can be described by fractional-order(noninteger-order)models,which can show their physical and dynamic processes more scientifically and reflect the characteristics of their systems more accurately.Hence,the research on cooperative control of multi-agent systems depicted by fractionalorder models has gained an interest of some researchers.Due to the limitation of channel transmission bandwidth,the disturbance of external environment,and the device restriction of the controllers,etc,it is unrealistic to realize the continuous information communication between agents and the continuous updating of controllers.Therefore,we focus on the fractional-order multi-agent systems in this paper.Based on some diverse discontinuous communication control strategies which can reduce the updated rate of controllers and cut down the energy of systems,the consensus of fractional-order multi-agent systems is investigated.The main contents can be summarized as follows:Research on consensus of fractional-order multi-agent systems via periodical sampleddata control strategy.Under the periodical sampled-data control strategy,each agent transmits its information to its neighbors and updates its controller only at some period instants.Applying the Laplace transform,the mathematical induction,and the stability theory,some necessary and sufficient conditions are provided to ensure the consensus of fractional-order multi-agent systems.What's more,some detailed discussions are presented about how to select the sampling period for the determinate coupling strengths and a fixed network and how to design the coupling strengths for a certain sampling period and a fixed network,respectively,which provides a guidance for the selection of parameters.Research on consensus of fractional-order multi-agent systems via periodical intermittence sampled-data control strategy.Under the periodical intermittence sampleddata control strategy,for every given period,the controller only works for a fraction of the period and will rest in the remaining time.Combing the intermittence control technology and the sampled-data control technology,a periodical intermittence sampled-data control protocol is proposed,and some necessary and sufficient conditions are provided to ensure the consensus of fractional-order multi-agent systems,which reveal the relations among the sampling period,the communication width,the fractional order,the coupling strengths,and the network topology,explicitly.Research on consensus of fractional-order multi-agent systems subject to input time delay via periodical intermittence sampled-data control strategy.A distributed intermittence sampled-data control protocol with input time delay is proposed.Due to the relationship among the input time delay,the communication width,and the sampling period,four cases are carefully discussed and some necessary and sufficient conditions are provided to ensure the consensus of fractional-order multi-agent systems,which reveal the relations among the sampling period,the communication width,the input time delay,the fractional order,the coupling strengths,and the network topology,explicitly.Research on leader-following consensus of fractional-order multi-agent systems depicted by general linear dynamics via event-triggered control strategy.Under the eventtriggered control strategy,the triggered function for each agent only dependending on its only states is designed and each agent will not transmit its information to its neighbors and its controller will not be updated until the given events are triggered.Applying the properties of Mittag-Leffler function and improper integral,some sufficient conditions are provided to ensure the leader-following consensus of fractional-order multi-agent systems.What's more,it is proved that the designed event-triggered control strategy can avoid the Zeno behavior.Research on leader-following consensus of fractional-order multi-agent systems subject to input time delay via event-triggered control strategy.Through the combinational measurement method,the distributed control protocol is designed which only depends on the agent states at triggering instants.Applying the properties of Mittag-Leffler function and the method of proof by contradiction,some sufficient conditions are provided to ensure the leader-following consensus of fractional-order multi-agent systems for any bounded input time delay.Furthermore,it is proved that the designed event-triggered control strategy can avoid the Zeno behavior.