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Nonstandard duality and nonlocal necessary optimality conditions in nonconvex optimal control problems

Авторы: Dykhta V.A.

Журнал: Automation and Remote Control

Том: 75

Номер: 11

Год: 2014

Отчётный год: 2014

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Местоположение издательства:

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DOI: 10.1134/S0005117914110022

Аннотация: To partially implement the idea of considering nonlinear optimal control problems immediately on the set of Pontryagin extremals (or on quasiextremals if the optimal solution does not exist), we introduce auxiliary functions of canonical variables, which we call bipositional, and the corresponding modified Lagrangian for the problem. The Lagrangian is subject to minimization on the trajectories of the canonical system from the Maximum Principle. This general approach is further specialized for nonconvex problems that are linear in state, leading to a nonstandard dual optimal control problem on the trajectories of the adjoint system. Applying the feedback minimum principle to both original and dual problems, we have obtained a pair of necessary optimality conditions that significantly strengthen the Maximum Principle and admit a constructive realization in the form of an iterative problem solving procedure. The general approach, optimality features, and the iterative solution procedure are illustrated by a series of examples.

Индексируется WOS: Q4

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Нет

Индексируется ВАК: Нет

Индексируется CORE: Нет

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