Brockett's First Example:An FAS Approach Treatment

• 作者: DUAN Guang-Ren
• 来源期刊: 系统科学与复杂性学报（英文版）
• 年，卷（期）: 2022,（2）
• 页码范围: 441-456
• 页数: 16页
• 语种: 英文
• DOI: 10.1007/s11424-022-2090-8

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 sub-stabilized 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.