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On One Approach to the Optimization of Discrete-Continuous Controlled Systemsстатья
- Автор: Buldaev Alexander
- Сборник: Communications in Computer and Information Science
- Том: 1476
- Год издания: 2021
- Издательство: Springer International Publishing AG
- Местоположение издательства: Cham, Switzerland
- Первая страница: 463
- Последняя страница: 477
- DOI: 10.1007/978-3-030-86433-0_32
- Аннотация: A class of discrete-continuous control systems described by differential equations with piecewise constant controls is considered. Conditions for nonlocal improvement and control optimality are constructed in the form of fixed point problems in the control space. This representation of conditions makes it possible to apply and modify the well-known theory and methods of fixed points for constructing iterative algorithms for solving the considered discrete-continuous optimal control problems. The proposed iterative algorithms have the property of nonlocality of successive control approximations and the absence of a procedure for the parametric search for an improving approximation at each iteration, which is characteristic of known standard gradient-type methods. Based on the proposed approach, new necessary conditions for control optimality are constructed, which strengthen the known conditions of optimality. Conditions for the convergence of relaxation sequences of controls obtained based on the constructed sufficient conditions for nonlocal improvement of control are derived. Illustrative examples of improving admissible controls and obtaining optimal controls by fixed-point methods are given.
- Добавил в систему: Булдаев Александр Сергеевич