Controlled Invariant Hypersurfaces of Polynomial Control Systems
Controlled Invariant Hypersurfaces of Polynomial Control Systems
复制标题
多项式控制系统的受控不变超曲面
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Walcher
中科院分区：
文献类型：
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作者：
E. Zerz;S. Walcher
研究具有多项式非线性的输入仿射控制系统。如果存在一个多项式型的反馈律，使得闭环系统有V作为一个不变的变量，则称变量V是受控不变的。使用Gröbner基础理论，我们展示了如何建设性地决定给定变量是否为给定系统的受控不变量，如果是，如何确定实现任务的所有反馈律。我们还描述了一组“平凡的”向量场，其中V是不变的。如果V是一个光滑的超曲面，那么V只有在平凡的向量场中是不变的。我们讨论在哪些条件下逆命题也成立。
We study input-affine control systems with polynomial nonlinearity. A variety V is said to be controlled invariant if there exists a feedback law of polynomial type that causes the closed loop system to have V as an invariant variety. Using the theory of Gröbner bases, we show how to constructively decide whether a given variety is controlled invariant for a given system, and if so, how to determine all feedback laws achieving the task. We also describe a set of “trivial” vector fields for which V is invariant. If V is a smooth hypersurface, then V is only invariant for its trivial vector fields. We discuss conditions under which the converse is also true.