Adjoint Orbits of lus-plus">sl(2, ℝ) on Real Simple Lie Algebras and Controllability

详细信息    查看全文

• 作者：Rachida El Assoudi-Baikari
• 关键词：Simple Lie groups ; Root systems ; Invariant vector fields ; Controllability
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：23
• 期：1
• 页码：33-54
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Vibration, Dynamical Systems, Control; Calculus of Variations and Optimal Control; Optimization; Analysis; Applications of Mathematics; Systems Theory, Control;
• 出版者：Springer US
• ISSN：1573-8698
• 卷排序：23

文摘

This paper shows that for any Lie group G whose Lie algebra L is the split real form of a complex simple Lie algebra, and for any arbitrary root α, there exists a Cartan decomposition of L, related to α, which characterizes some controllability properties by using the adjoint orbits of sl(2, ℝ). For a class of invariant control systems evolving on G, it is proved that the necessary full rank condition for controllability is also sufficient.