Страница публикации

Feedback minimum principle for optimal control problems in discrete-time systems and its applications

Тип публикации: Статья в журнале

Тип материала: Текст

Авторы: Dykhta V., Sorokin S.

Журнал: Lecture Notes in Computer Science: Proc. of the 18th Intern. Conf. on Mathematical Optimization Theory and Operations Research (MOTOR'2019; Ekaterinburg)

Язык публикации: english

Серия книг: Lecture Notes in Computer Science

Том: 11548

Номера страниц: 449-460

Количество страниц: 12

Год публикации: 2019

Отчетный год: 2019

DOI: 10.1007/978-3-030-22629-9_31

Аннотация: The paper is devoted to a generalization of a necessary optimality condition in the form of the Feedback Minimum Principle for a nonconvex discrete-time free-endpoint control problem. The approach is based on an exact formula for the increment of the cost functional. This formula is completely defined through a solution of the adjoint system corresponding to a reference process. By minimizing that increment in control variable for a fixed adjoint state, we define a multivalued map, whose selections are feedback controls with the property of potential “improvement” of the reference process. As a result, we derive a necessary optimality condition (optimal process does not admit feedback controls of a “potential descent” in the cost functional). In the case when the well-known Discrete Maximum Principle holds, our condition can be further strengthened. Note that obtained optimality condition is quite constructive and may lead to an iterative algorithm for discrete-time optimal control problems. Finally, we present sufficient optimality conditions for problems, where Discrete Maximum Principle does not make sense.

Индексируется WOS: Q4

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Нет

Индексируется ВАК: Нет

Индексируется CORE: Нет