Estimation And Control Of Fractional-order Systems Based On Event-triggered Mechanism

Fractional-order differential systems(FODS)are a generalized form of integer-order differential systems(IODS).FODS have obvious advantages in portraying genetic and memory properties and are widely used in many fields such as biology,chemical engineering and automation.In addition,the event-triggered mechanism(ETM)is an intermittent mechanism which can be triggered as needed to reduce resource consumption while ensuring system performance.ETM has been used in the analysis and synthesis of IODS.Research on the estimation and control of FODS under ETM is in the initial stage.This paper investigates the state estimation and control problems for several classes of FODS by introducing ETM.The research is as follows.Firstly,the event-triggered state estimation(ETSE)for a class of fractional-order neural networks(FONN)is investigated.With the output signal,a static ETM has been designed to effectively reduce the transmission frequency of the measurement signal.Using Lyapunov stability theory and the properties of FODS,sufficient conditions for the global Mittag-Leffler stability of the error system are established,and the Zeno behavior in ETM is excluded.Combined with the linear matrix inequality(LMI),an algorithm is given for computing estimator gain matrices.Finally,the feasibility of the theoretical results are verified by two numerical examples and simulations.Secondly,the leader-following group consensus(LFGC)in fractional-order multiagent systems(FOMS)with intergroup balance conditions(IBC)is investigated under centralized dynamic event-triggered mechanism(CDETM).With IBC,the LFGC control protocol is designed by using the states between agent and neighbours.Using information on FOMS and an auxiliary internal dynamic variable,a CDETM is constructed that effectively reduces the frequency of controller updates while maintaining control performance.A sufficient condition for the stability of the error system is established by constructing Lyapunov function.The controller gain matrix is obtained by solving the LMI.Lastly,the validity of the theoretical results is verified by numerical examples.Thirdly,the LFGC in FOMS without IBC under distributed dynamic event-triggered mechanism(DDETM)is studied.Without IBC,the LFGC control protocol is established by adding connections between leaders and followers in the communication topology graph and combining the state of FOMS.DDETM has been designed using state from FOMS and auxiliary internal dynamic variables.Combining Lyapunov stability theory and knowledge of FODS,sufficient conditions are established for the error system to be stable and for the Zeno behavior to be excluded from DDETM.An algorithm for solving the controller gain matrix using a LMI is given.In the end,a numerical example illustrates the feasibility of the theoretical results.