Cooperative Preview Tracking Control Of Multi-Agent Systems

Preview control has attracted considerable attention due to its extensive applications in various fields.Many novel methods have also been developed in recent years to handle the preview control problems of different systems.Based on the theory of preview control and cooperative control of multi-agent systems,this thesis presents a systematic study on the cooperative preview tracking control problems of multi-agent systems.The detailed results are as follows:(1)The cooperative preview control method is presented for continuous-time multi-agent systems with a time-invariant directed communication topology.First,the cooperative tracking preview control problem is transformed into the optimal regulation problem of an augmented system.Next,by applying the results of the standard optimal preview control of continuous-time linear systems,a controller of the augmented system is obtained.Furthermore,the stabilizability and detectability of the augmented system are studied under the fixed digraph and the prescribed leader.Then the controller of multi-agent systems with global output error integral and preview action is derived,which can guarantee the achievement of cooperative optimal preview tracking.(2)The cooperative optimal preview tracking problem of discrete-time multi-agent systems is studied under the assumption of the communication topology containing a directed spanning tree.Firstly,a state augmentation technique is used to convert the cooperative preview tracking problem into a global optimal regulation problem of an augmented system.Secondly,by resorting to relative conclusions about the discrete-time linear quadratic regulation theory,an optimal controller is obtained,which can guarantee the asymptotic stability of the closed-loop augmented system.Moreover,a global optimal preview controller is provided in order for the original system to achieve the tracking consensus.(3)The cooperative global optimal preview tracking problem of linear multi-agent systems is investigated under the assumption that the output of a leader is a previewable signal with non-decreased amplitude and the topology graph contains a directed spanning tree.Firstly,a type of distributed internal model is introduced,and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system.Secondly,an optimal controller,which can guarantee the asymptotic stability of the augmented system,is obtained by means of the standard linear quadratic optimal preview control theory.Thirdly,on the basis of proving the existence conditions of the controller,sufficient conditions are given for the original problem to be solvable,meanwhile a cooperative global optimal controller with error integral and preview compensation is derived.(4)A discrete-time counterpart of the above problem is considered.An auxiliary system based on preview information,together with a type of distributed internal model,is introduced to establish an augmented system for each follower.This procedure successfully assists in formulating the cooperative preview tracking problem as a DOR problem.After proving the solvability of the DOR problem and the stabilizability of the augmented system under some standard assumptions,the sufficient conditions are derived that ensure the outputs of the identical followers tracking the previewable output of the leader.Meanwhile,with the help of a discrete algebraic Riccati equation(DARE),a distributed dynamic feedback control law with virtual regulated output integral and preview feedforward compensation is proposed.(5)The cooperative optimal preview tracking problem is considered for continuous-time descriptor multi-agent systems with a directed topology containing a spanning tree.By the acyclic assumption and state augmentation technique,it is shown that the cooperative tracking problem is equivalent to local optimal regulation problems of a set of low-dimensional descriptor augmented subsystems.To design distributed optimal preview controllers,restricted system equivalent and preview control theory are first exploited to obtain optimal preview controllers for reduced-order normal subsystems.Then,by using the invertibility of restricted equivalent relations,a constructive method for designing distributed controller is presented which also yields an explicit admissible solution for the generalized algebraic Riccati equation.Sufficient conditions for achieving global cooperative preview tracking are proposed proving that the distributed controllers are able to stabilize the descriptor augmented subsystems asymptotically.