Stabilization via Fully Actuated System Approach:A Case Study  

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3期731-747,共17页系统科学与复杂性学报（英文版）

基　　金：partially supported by the Major Program of National Natural Science Foundation of China under Grant Nos.61690210 and 61690212;the National Natural Science Foundation of China under Grant No.61333003;the Science Center Program of the National Natural Science Foundation of China under Grant No.62188101。

摘　　要：In this note,a benchmark example system which is not stabilizable by a smooth state feedback controller is considered with the fully actuated system(FAS)approach.It is shown that a smooth controller exists which drives the trajectories starting from a large domain in the initial value space to the origin exponentially.Such a result brings about a generalization of Lyapunov asymptotical stability,which is termed as global exponential sub-stability.The region of attraction is allowed to be an unbounded open set of the initial values with closure containing the origin.This sub-stability result may be viewed to be superior to some local stability results in the Lyapunov sense because the region of attraction is much larger than any finite ball containing the origin and meanwhile the feasible trajectories are always driven to the origin exponentially.Based on this sub-stabilization result,globally asymptotically stabilizing controllers for the system can be provided in two general ways,one is through combination with existing globally stabilizing controllers,and the other is by using a pre-controller to first move an initial point which is not within the region of attraction into the region of attraction.

关 键 词：Feedback stabilization fully actuated system approach nonlinear systems region of attraction singularity sets 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]