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On the Construction of Nonconvex Approximations to Reach Sets of Piecewise Linear Systemsстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 11 января 2016 г.
- Автор: Tochilin P.A.
- Журнал: Differential Equations
- Том: 51
- Номер: 11
- Год издания: 2015
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 1503
- Последняя страница: 1515
- DOI: 10.1134/S0012266115110117
- Аннотация: We solve the problem of constructing external and internal approximations to reach sets for hybrid systems with piecewise linear dynamics. As a rule, such sets are not convex and have complicated structure. For their estimation, we suggest to use the comparison principle and piecewise quadratic value functions of special form. To define the parameters of such functions, we use solutions of a family of systems of Riccati matrix differential equations and some additional ordinary differential equations. On the basis of the obtained theoretical results, one can develop efficient numerical methods for the reachability problem for the considered class of control systems. Two examples are presented. In particular, we solve the problem of the approximate construction of the reach set for a linear system of ordinary differential equations with noise in the case of nonconvex initial set.
- Добавил в систему: Точилин Павел Александрович