68159

Автор(ы): 

Автор(ов): 

3

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Random Sampling Many-Dimensional Sets Arising in Control

DOI: 

10.3390/math9050580

Наименование источника: 

  • Mathematics

Обозначение и номер тома: 

Т. 9, № 5

Город: 

  • Bazel, Switzerland

Издательство: 

  • MDPI

Год издания: 

2021

Страницы: 

580 (1-16)
Аннотация
Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas of computational mathematics, optimization, data processing, etc. Whereas for regularly shaped sets such sampling is immediate to arrange, for nontrivial, implicitly specified domains these techniques are not easy to implement. We consider the so-called Hit-and-Run algorithm, a representative of the class of Markov chain Monte Carlo methods, which became popular in recent years. To perform random sampling over a set, this method requires only the knowledge of the intersection of a line through a point inside the set with the boundary of this set. This component of the Hit-and-Run procedure, known as boundary oracle, has to be performed quickly when applied to economy point representation of many-dimensional sets within the randomized approach to data mining, image reconstruction, control, optimization, etc. In this paper, we consider several vector and matrix sets typically encountered in control and specified by linear matrix inequalities. Closed-form solutions are proposed for finding the respective points of intersection, leading to efficient boundary oracles; they are generalized to robust formulations where the system matrices contain norm-bounded uncertainty.

Библиографическая ссылка: 

Щербаков П.С., Ding M.S., Yuchi M.A. Random Sampling Many-Dimensional Sets Arising in Control // Mathematics. 2021. Т. 9, № 5. С. 580 (1-16).