Preview Repetitive Control For Several Classes Of Linear Discrete Multi-Agent Systems

In the actual system,there are a lot of periodic work.Repetitive control is an effective method to solve this kind of control system for high-precision tracking of periodic signals.Preview control is a control method that uses known future information to improve the dynamic response of the system,suppress external disturbances and improve the tracking performance of the system.Therefore,the repetitive control based on preview compensation,that is,preview repetitive control,can combine the characteristics of the two control methods to improve the tracking performance of the control object.The consistency of multi-agent system is one of the hotspots in the research of multi-agent system.The research focus of consistency problem is to design a distributed controller to make the output of multi-agent system consistent.Based on the existing research results of preview repetitive control,this paper extends the preview repetitive control method to linear discrete multi-agent systems,and puts forward the optimal preview repetitive control for linear discrete multi-agent systems based on virtual equation,Preview repetitive control of uncertain linear discrete multi-intelligent systems based on two-dimensional model and preview repetitive control of uncertain linear discrete multi-intelligent systems based on equivalent input interference compensation.The specific research contents are as follows:(1)Optimal preview repetitive control for linear discrete multi-agent systems based on virtual equation.An optimal preview repetitive controller based on virtual equation is designed for a class of linear discrete-time multi-agent systems.Firstly,using the known future reference signals,a linear discrete-time multi-agent system corresponding to the linear discrete-time multi-agent system based on virtual equation is constructed.Then,using the T-order difference operator,the augmented error system including the preview information of the reference signal and the output of the repetitive controller is obtained,so the design problem of the optimal preview repetitive controller is transformed into the optimal regulation problem of the augmented error system.On this basis,the controller which makes the augmented error system asymptotically stable is obtained by using the relevant results of discrete-time linear quadratic regulation theory.In order to ensure the existence of the controller of the augmented error system,the PBH rank criterion is used to verify the stability and observability of the augmented error system.Furthermore,an optimal preview repetitive controller is obtained to make the original system achieve tracking consistency.Finally,numerical simulation shows the effectiveness of the controller.(2)Preview repetitive control of uncertain linear discrete multi-agent systems based on two-dimensional model.For a class of linear uncertain discrete-time multi-agent systems,a preview repetitive controller based on virtual equation is designed.Firstly,a virtual equation is constructed by using the known future reference signal and repetitive controller.Then,a two-dimensional discrete system including target signal preview information and repetitive controller output is obtained by using T-order difference operator.Therefore,the design problem of preview repetitive controller is transformed into the stability problem of two-dimensional discrete system.The stability conditions and parameters of the preview repetitive controller are obtained by LMI technique and the stability theory of two-dimensional model.Finally,numerical simulation shows the effectiveness of the controller.(3)Preview repetitive control for uncertain linear discrete multi-agent systems based on equivalent input disturbance compensation.For a class of uncertain linear discrete-time multi-agent systems with external disturbances,a preview repetitive control based on equivalent input disturbance(EID)compensation is designed.By introducing a repetitive controller into the forward channel to form a high-precision feedback control system,the T-order difference operator is used to make the augmented error system integrate preview information,and the design problem of preview repetitive controller is transformed into the regulation problem of output feedback.The stability conditions of the system are obtained by LMI method.Considering the external disturbance of uncertain linear discrete multi-agent system,by reconstructing the state variables,a multi degree of freedom system structure including EID compensation is introduced into the feedback channel,and a preview repetitive control based on equivalent input disturbance(EID)compensation is designed.Finally,numerical simulation shows the effectiveness of the controller.