Страница публикации

Numeric algorithm for optimal impulsive control based on feedback maximum principle

Тип публикации: Статья в журнале

Тип материала: Текст

Авторы: Sorokin S.P., Staritsyn M.V.

Журнал: Optimization Letters

Язык публикации: english

Том: 13

Номера страниц: 1953-1967

Количество страниц: 15

Номер: 8

Год публикации: 2019

Отчетный год: 2018

DOI: 10.1007/s11590-018-1344-9

Аннотация: In this short note, we present an approach for numeric analysis of a class of nonlinear optimal impulsive control problems with states of bounded variation. The approach is based on feedback necessary optimality condition laying in the formalism of the Pontryagin maximum principle (employing only the related standard constructions), but involving feedback control variations of an “extremal” structure. We make a “double reduction” of the impulsive control problem: first, we perform a well-known equivalent transform of the measure-driven system to an ordinary terminally-constrained control system and, second, pass to its discrete-time counterpart. For the resulted discrete control problem, we present a necessary condition of global optimality called the discrete feedback maximum principle. Based on this optimality condition, we elaborate a nonlocal numeric algorithm, which can, potentially, improve nonoptimal extrema of the discrete maximum principle. Due to a specific structure of the investigated model, the algorithm admits a deep specification. As an illustration of our approach, we present a numeric implementation of an academic example—a singular version of a generalized Sethi–Thompson investment problem from mathematical economics.

Индексируется WOS: Q2

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Да

Индексируется ВАК: Нет

Индексируется CORE: Нет