Brockett's First Example: An FAS Approach Treatment

Duan Guang-Ren1,2

2022-04-01

10.1007/s11424-022-2090-8

Journal of Systems Science & Complexity   影响因子和分区

1009-6124

1559-7067

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 z(0)-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 z(0)-axis also to go to the origin. The idea is to firstly move an initial point on the z(0)-axis away from the axis using a pre-controller, and then to take over by the designed exponentially sub-stabilizing controller.

Exponential sub-stabilization feedback stabilization fully actuated system approach region of attraction singularity sets

SCI ; EI

英语

第一 ; 通讯

Major Program of National Natural Science Foundation of China[61690210,61690212] ; National Natural Science Foundation of China[61333003] ; Science Center Program of the National Natural Science Foundation of China[62188101]

Mathematics

Mathematics, Interdisciplinary Applications

WOS:000786419800002

SPRINGER HEIDELBERG

20221611990820

Controllers ; Feedback

Control Systems:731.1 ; Control Equipment:732.1

Web of Science

1.Southern Univ Sci & Technol, Ctr Control Sci & Technol, Shenzhen 518055, Peoples R China
2.Harbin Inst Technol, Ctr Control Theory & Guidance Technol, Harbin 150001, Peoples R China

Duan Guang-Ren. Brockett's First Example: An FAS Approach Treatment[J]. Journal of Systems Science & Complexity,2022,35(2):441-456.

Duan Guang-Ren.(2022).Brockett's First Example: An FAS Approach Treatment.Journal of Systems Science & Complexity,35(2),441-456.

Duan Guang-Ren."Brockett's First Example: An FAS Approach Treatment".Journal of Systems Science & Complexity 35.2(2022):441-456.