Brockett’s Second Example: A FAS Approach Treatment

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 approach. A simple continuous time-invariant sub-stabilizing controller is designed, and the corresponding re...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of systems science and complexity 2023-10, Vol.36 (5), p.1789-1808
1. Verfasser: Duan, Guang-Ren
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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 approach. 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 characterized 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.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-023-2282-x