A proven method for an optimal control problem with linear dynamics, phase constraints, and boundary value problems

Antipin, A.S.; Khoroshilova, E.V.

Авторы: Antipin A.S., Khoroshilova E.V.
Сборник: XXII International Conference “Mathematical Optimization Theory and Operations Research” (MOTOR 2023). Abstracts / M. Khachay, Y. Kochetov, A. Eremeev, O. Khamisov, V. Mazalov, and P. Pardalos (Eds.)
Серия: The Conference is devoted to 90th anniversary of academician I.I. Eremin
Том: 1
Тезисы
Год издания: 2023
Место издания: UMC UrFU Ekaterinburg, Russia
Первая страница: 101
Последняя страница: 101
Аннотация: On a finite time interval, we consider an optimal control problem with linear dynamics and a tube of phase constraints. Constraints are a continuous system of linear inequalities depending on time. At each moment of time we have in section a polyhedron in a finite-dimensional space R^n. At the ends of the time interval, in n-dimensional spaces, objective functions are set. These functions, together with constraint polytopes, generate two boundary value problems of linear programming. The dynamics includes two time-dependent functional variables (control and phase variables), as well as finite-dimensional variables of boundary value problems. Dynamics develops on a time interval in Hilbert space. For each control taken from the convex closed set of the Hilbert space, there is a unique phase trajectory. This correspondence is guaranteed by the existence and uniqueness theorem for the solution of a differential equation.The statement of the problem involves choosing a control so that the corresponding phase trajectory is to be inside the phase tube (perhaps, touching its walls), and at the ends of the segment, the phase trajectory takes values that coincide with the solutions of boundary-value problems of linear programming.To solve the problem, an evidential method of the saddle type is proposed. This method (computing technology) generates a sequence of asymptotic approximations to the solution of the problem. This sequence has limit points, which are guaranteed to be solutions to the source problem. The proof of the method convergence to the solution is based on the theory of duality, the Lagrange function, and the convexity of the problem. Only evidence-based calculations transform mathematical models into a tool for obtaining reasonable estimates for making guaranteed solutions.
Добавил в систему: Хорошилова Елена Владимировна

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