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On One Method of Optimization of Quantum Systems Based on the Search for Fixed Pointsстатья
- Авторы: Buldaev Alexander, Kazmin Ivan
- Сборник: Communications in Computer and Information Science
- Том: 1514
- Год издания: 2021
- Издательство: Springer International Publishing AG
- Местоположение издательства: Cham, Switzerland
- Первая страница: 67
- Последняя страница: 81
- DOI: 10.1007/978-3-030-92711-0_5
- Аннотация: A class of optimal control problems for quantum systems is considered, which is described by bilinear differential equations with a quadratic optimality criterion. A method for non-local improvement of control is proposed, which, in contrast to gradient and other local methods, does not require the operation of calculating the target functional to achieve the improvement goal. The method is based on the construction of a control improvement condition in the form of a fixed point problem in the control space. The obtained condition allows us to apply and modify the well-known theory and methods of fixed points for constructing an iterative algorithm for solving the optimal control problems under consideration. Based on the proposed fixed-point approach, the well-known maximum principle and a strengthened necessary condition for optimality of control are described. Conditions for the convergence of iterative control sequences are given. A comparative analysis of the proposed optimization method with known methods is carried out using model examples.
- Добавил в систему: Булдаев Александр Сергеевич