Quantified inequalities and robust control
Quantified inequalities and robust control
复制标题
量化的不平等和稳健的控制
DOI：
--
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
V. Koltchinskii
中科院分区：
文献类型：
--
作者：
C. Abdallah;M. Ariola;P. Dorato;V. Koltchinskii
研究了量化的多变量多项式不等式与鲁棒控制问题的关系。我们证明了用多项式不等式表示的控制问题的难度有一个层次，并且与用来解决它们的方法类似。一方面，我们有精确的量词消去法，但其计算复杂性是双指数的，因此只能用于解决小尺寸问题。分支定界法牺牲了量词剔除的精确度来近似解决更大类的问题，而蒙特卡洛和统计学习方法解决了非常大的问题，但只能概率地解决。我们还提出了新的顺序学习方法来说明统计方法的有效性。
This paper studies the relationship between quantified multivariable polynomial inequalities and robust control problems. We show that there is a hierarchy to the difficulty of control problems expressed as polynomial inequalities and a similar hierarchy to the methods used to solve them. At one end, we have quantifier elimination methods which are exact, but doubly exponential in their computational complexity and thus may only be used to solve small size problems. The Branch-and-Bound methods sacrifice the exactness of quantifier elimination to approximately solve a larger class of problems, while Monte Carlo and statistical learning methods solve very large problems, but only probabilistically. We also present novel sequential learning methods to illustrate the power of the statistical methods.