О некоторых классах задач управления с фазовыми ограничениями

A Borel measure Lagrange multiplier appears in the maximum principle for state constrained problems. The question of continuity or absolute continuity of the measure-multiplier is highly relevant for various applications in particular for some problems of kinematic control. The velocity in such problems is considered as a state variable. As soon as the magnitude of the velocity is bounded, for instance above, (which is quite natural in problems of kinematic control), this leads to the state constraints and to a measure Lagrange multiplier in the necessary optimality conditions. In Control Theory, the methods that are use to solve these conditions often require the continuity of the measure. In this paper, we consider some examples of optimal control problems with state constraints for which one can ensure that this measure is continuous, without a calculation of extremal process.В принципе максимума для задач оптимального управления с фазовыми ограничениями возникает борелевская мера-множитель Лагранжаμ. В различных инженерных приложениях, в частности, в некоторых задачах кинематического управления одним из важных вопросов является вопрос о непрерывности или абсолютной непрерывности такой меры. Скорость в подобного рода задачах имеет смысл фазовой переменной. Если модуль скорости ограничен, например, сверху (что вполне естественно в задачах кинематического управления), то это приводит к фазовым ограничениями, и, следовательно, к упомянутой выше мере-множителю Лагранжа μ в необходимых условиях оптимальности. Методы, которые используются для решения таких задач, как правило, подразумевают непрерывность меры. В этой работе рассматриваются примеры задач управления с фазовыми ограничениями, для которых можно гарантировать a priori (то есть без вычисления экстремального процесса), что соответствующая мера непрерывна

Necessary optimality conditions for abnormal problems with geometric constraints

The abnormal minimization problem with a finite-dimensional image and geometric constraints is examined. In particular, inequality constraints are included. Second-order necessary conditions for this problem are established that strengthen previously known results. © Nauka/Interperiodica 2007

Necessary optimality conditions in an abnormal optimization problem with equality constraints

An abnormal minimization problem with equality constraints and a finite-dimensional image is examined. Second-order necessary conditions for this problem are given that strengthen previously known results. © MAIK "Nauka/Interperiodica"

Necessary optimality conditions in an abnormal optimization problem with equality constraints

An abnormal minimization problem with equality constraints and a finite-dimensional image is examined. Second-order necessary conditions for this problem are given that strengthen previously known results. © MAIK "Nauka/Interperiodica"

Regular zeros of quadratic maps and their application

Sufficient conditions for the existence of regular zeros of quadratic maps are obtained. Their applications are indicated to certain problems of analysis related to the inverse function theorem in a neighbourhood of an abnormal point. © 2011 RAS(DoM) and LMS

Necessary optimality conditions for abnormal problems with geometric constraints

The abnormal minimization problem with a finite-dimensional image and geometric constraints is examined. In particular, inequality constraints are included. Second-order necessary conditions for this problem are established that strengthen previously known results. © Nauka/Interperiodica 2007

Regular zeros of quadratic maps and their application

Sufficient conditions for the existence of regular zeros of quadratic maps are obtained. Their applications are indicated to certain problems of analysis related to the inverse function theorem in a neighbourhood of an abnormal point. © 2011 RAS(DoM) and LMS

Pontryagin's maximum principle for constrained impulsive control problems

Necessary conditions in the form of Pontryagin's maximum principle are derived for impulsive control problems with mixed constraints. A new mathematical concept of impulsive control is introduced as a requirement for the consistency of the impulsive framework. Additionally, this control concept enables the incorporation of the engineering needs to consider conventional control action while the impulse develops. The regularity assumptions under which the maximum principle is proved are weaker than those in the known literature. Ekeland's variational principle and Lebesgue's discontinuous time variable change are used in the proof. The article also contains an example showing how such impulsive controls could be relevant in actual applications. © 2011 Elsevier Ltd. All rights reserved

On second-order necessary optimality conditions in finite-dimensional abnormal optimization problems

[No abstract available

Inverse function in the neighborhood of an abnormal point of a smooth map

[No abstract available