Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

Abstract

This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, 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. Second, 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. Third, 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. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

Observer‐based preview repetitive control for uncertain discrete‐time systems

“…Compared with other control methods, the main advantages of PC theory consist of enhancing the transient response of the closed‐loop system and reducing energy consumption 14 . In the past few years, the PC theory has been extensively considered in many fields, such as singular systems, 15,16 time delay systems, 17 stochastic systems, 18,19 and multi‐agent systems, 20 and so on. In order to guarantee the robustness for the unknown disturbance in the sense of L 2 gain, the H ∞ criterion has been introduced into the PC problems 21‐23 .…”

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

“…In preview control, most control methods are based on linear quadratic control theory . These methods, however, do not consider the unknown disturbances effect on the system when designing a preview controller.…”

“…The monograph of Tsuchiya and Egamis 23 summarized the chief research results at that time. Subsequently, the study of preview control theory and its application have also continued to draw research interest (see other works [24][25][26][27][28] ).…”

“…In preview control, most control methods are based on linear quadratic control theory. [18][19][20][21][22][23][24][25][26][27][28] These methods, however, do not consider the unknown disturbances effect on the system when designing a preview controller. However, a number of preview control methods have been reported based on H 2 and H ∞ criteria that consider the unknown disturbances in order to design control systems with better performance measures.…”

Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems

“…Firstly, the error system is constructed based on the preview control theory [19,20], and the problem is turned into a FTB problem of the output vector of the error system. Then a state feedback controller is designed for the error system via the LMI approach.…”