Controlled invariant varieties of polynomial control systems

Controlled invariant varieties of polynomial control systems
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多项式控制系统的受控不变簇

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发表时间：
2010
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通讯作者：
Fadime Güçlü
Fadime Güçlü
中科院分区：
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文献类型：
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作者：
E. Zerz;S. Walcher;Fadime Güçlü

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研究了具有多项式非线性的输入仿射控制系统。如果存在多项式类型的反馈律，使得闭环系统具有V作为不变变量，则称变量V是受控不变的，这意味着从V开始的任何轨迹将始终保持在那里。使用理论的Gröbner基地，我们显示（在一定条件下的V的表示）如何建设性地决定是否一个给定的品种是控制不变的一个给定的系统，如果是这样，如何确定所有的反馈法实现的任务。
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, which means that any trajectory starting in V will remain there for all times. Using the theory of Gröbner bases, we show (under certain conditions on the given representation of V ) 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.