Brockett’s First Example: An FAS Approach Treatment

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...

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Bibliographic Details
Published inJournal of systems science and complexity Vol. 35; no. 2; pp. 441 - 456
Main Author Duan, Guang-Ren
Format Journal Article
LanguageEnglish
Published Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.04.2022
Springer Nature B.V
Subjects
Complex Systems
Control
Control systems design
Controllers
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Statistics
Systems Theory
fully actuated system approach
feedback stabilization
Exponential sub-stabilization
region of attraction
singularity sets
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-022-2090-8