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

Авторы: Dykhta V., Sorokin S.

Журнал: Lecture Notes in Computer Science, 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019; Ekaterinburg

Том: 11548

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Год: 2019

Отчётный год: 2019

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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.

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