Brockett’s First Example: An FAS Approach Treatment  

作　　者：DUAN Guang-Ren 

机构地区：[1]Center for Control Science and Technology,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》2022年第2期441-456,共16页系统科学与复杂性学报（英文版）

基　　金：This paper has been partially supported by the Major Program of National Natural Science Foundation of China under Grant Nos.61690210,61690212;National Natural Science Foundation of China under Grant No.61333003;also by the Science Center Program of the National Natural Science Foundation of China under Grant No.62188101.

摘　　要：In this note,the well-known Brockett’s first example system is treated with the fully actuated system(FAS)approach.Firstly,it is shown that the system can be exponentially substabilized by a smooth controller in the sense that,except those starting from initial values on the z0-axis of the initial value space,all trajectories of the designed system as well as the control signals decay to zero exponentially.Secondly,global stabilization is realized through a way of enabling the trajectories starting from initial values on the z0-axis also to go to the origin.The idea is to firstly move an initial point on the z0-axis away from the axis using a pre-controller,and then to take over by the designed exponentially sub-stabilizing controller.

关 键 词：Exponential sub-stabilization feedback stabilization fully actuated system approach region of attraction singularity sets 

分 类 号：V448[航空宇航科学与技术—飞行器设计] TP273[自动化与计算机技术—检测技术与自动化装置]