Investigation of second-order optimality conditions for impulsive control problems under the Frobenius condition

In this work impulsive control problems are investigated in that case in which matrix G that appears in the dynamics multiplying vector-valued control measure μ depends on the state variable, that is, G = G(x, t). The solution concept and the extension procedure in this non-linear case are not as trivial as in the case G = G (t). The key-point is to ensure robustness of the impulsive control system w.r.t. the control measure and regarding the approximations in the weak-∗ topology ('w.r.t.' stands for 'with respect to' here and further). Note that such approximations are required by applications. But this type of robustness is generally lost unless some extra assumptions on the matrix G w.r.t. the x-variable are imposed. It turns out that the weakest possible assumption, that still meets the robustness property, is the so-called Frobenius condition presented and discussed below. Under the Frobenius condition and without a priori regularity assumptions, we derive second-order necessary optimality conditions in a new form. This form and relations with previous results are discussed. © 2017 IEEE.

Авторы
Редакторы
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Сборник материалов конференции
Издательство
Institute of Electrical and Electronics Engineers Inc.
Номер выпуска
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Язык
Английский
Страницы
126-132
Статус
Опубликовано
Подразделение
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Ссылка
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Номер
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Том
2018-January
Год
2018
Организации
  • 1 RUDN University, Miklukho-Maklaya Str. 6, Moscow, 117198, Russian Federation
  • 2 Federal Research Center 'Computer Science and Control' of the Russian Academy of Sciences, Vav-ilova street, 44, Moscow, 119333, Russian Federation
  • 3 SYSTEC/Faculdade de Engenharia, Universidade Do Porto, Rua Dr. Roberto Frias, s/n, Porto, 4200-465, Portugal
Ключевые слова
Robust control; Control measures; Impulsive control systems; Impulsive controls; Necessary optimality condition; Regularity assumption; Robustness properties; Second-order optimality conditions; Solution concepts; Robustness (control systems)
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6901/