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Brockett's Second Example:A FAS Approach Treatment

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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 ap-proach.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 char-acterized 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.

Brockett integratorcontinuous time-invariant controllersfully actuated system approachregion of attractionsub-stabilization

DUAN Guang-Ren

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Shenzhen Key Laboratory of Control Theory and Intelligent Systems,Southern University of Science and Tech-nology,Shenzhen 518055,China

Center for Control Theory and Guidance Technology,Harbin Institute of Technology,Harbin 150001,China

Shenzhen Key Laboratory of Control Theory and Intelligent SystemsScience Center Program of the National Natural Science Foundation of China国家自然科学基金重大项目国家自然科学基金重大项目

ZDSYS20220330161800001621881016169021061690212

2023

10.1007/s11424-023-2282-x

系统科学与复杂性学报(英文版)
中国科学院系统科学研究所

系统科学与复杂性学报(英文版)

CSCDEI
影响因子：0.181
ISSN：1009-6124
年,卷(期)：2023.36(5)
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