Brockett's Second Example:A FAS Approach Treatment  

作　　者：DUAN Guang-Ren 

机构地区：[1]Shenzhen Key Laboratory of Control Theory and Intelligent Systems,Southern University of Science and Technology,Shenzhen 518055,China [2]Center for Control Theory and Guidance Technology,Harbin Institute of Technology,Harbin 150001,China

出　　处：《Journal of Systems Science & Complexity》2023年第5期1789-1808,共20页系统科学与复杂性学报（英文版）

基　　金：partially supported by Shenzhen Key Laboratory of Control Theory and Intelligent Systems under Grant No.ZDSYS20220330161800001;the Science Center Program of the National Natural Science Foundation of China under Grant No.62188101;the Major Program of National Natural Science Foundation of China under Grant Nos.61690210 and 61690212。

摘　　要：In this paper,several equivalent forms of the well-known Brockett's second example system are firstly presented.The stabilization of the system is then treated in the fully actuated system approach.A simple continuous time-invariant sub-stabilizing controller is designed,and the corresponding region of attraction is characterized.As a result,all trajectories of the system starting from the characterized region of attraction are driven exponentially to the origin.Since the region of attraction is very large,the designed sub-stabilizing controller can be directly useful in many practical situations.In cases where the initial values are indeed needed to be chosen out of the region of attraction,extremely simple pre-controllers can be designed,which drive the system trajectories into the designed region of attraction.A simulation of the designed control system is carried out to show the effect of the proposed approach.

关 键 词：Brockett integrator continuous time-invariant controllers fully actuated system approach region of attraction sub-stabilization 

分 类 号：O231[理学—运筹学与控制论]