Adaptive methods for solvings minimax problems<sup>∗</sup>

Габасов, Р.; Кириллова, Ф. М.; Kostina, Ekaterina

doi:10.1080/02331930108844554

Cited by 6 publications

(9 citation statements)

References 13 publications

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“…В рассматриваемой задаче в предположении существования оптимального управления установлен ряд необходимых условий оптимальности первого порядка (дискретный принцип максимума, линеаризованное условие максимума, аналог уравнения Эйлера) при различных предположениях [7][8][9][10][11][12][13][14][15].…”

Section: постановка задачиunclassified

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Investigation of discrete analogue of one boundary problem of optimal control

Agamaliyeva

2022

Applied Mathematics and Control Sciences

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In the paper, one boundary value problem of optimal control for discrete two-parameter systems with discrete time is investigated. Such problems are discrete analogues of optimal control problems described by integro-differential partial differential equations of the first order. The initial function is controllable and is defined as the solution of the Cauchy problem for nonlinear ordinary difference equation, the right part of which includes concentrated control. The quality functional presents the sum of two different terms and is a Boltz type functional for the optimal control problem under consideration. The cases of arbitrary, convex and open control area defining the corresponding class of admissible controls are studied. Imposing various natural smoothness conditions on the right-hand sides of the two-dimensional and one-dimensional difference equations under consideration, assuming the convexity of the analogue of the set of admissible velocities of the system under consideration, a special increment of the quality criterion is calculated using a modified functional increment method and, based on its non-negativity along the optimal control, an analogue of the discrete Pontryagin maximum principle is proved. Assuming the convexity of the control area, by linearizing the terms in the functional increment formula and introducing a special variation of the admissible control, an analogue of the linearized maximum condition is proved. In contrast to the continuous case, the linearized maximum principle is not a consequence of the discrete maximum principle and has an independent value as a necessary condition for optimality. In the case of open control area, by introducing a classical variation of the control, the first variation (in the classical sense) of the functional is calculated and established that in the case of open control area, the first variation of the quality criterion equals zero, with its help, an analogue of the Euler equation for the optimal control problem under consideration is obtained. The scheme used in the work also makes it possible to further investigate some cases of degeneration of the obtained necessary conditions of optimality of the first order and to deduce new, constructive necessary conditions of optimality of the second order, allowing to narrow down the set of permissible controls suspicious of optimality.

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Section: постановка задачиunclassified

“…Далее, делая замену переменных 1, ts += с помощью рассуждений, аналогичных приведенным в [9][10][11], получим ( ) ( ) ( ) ( )…”

Section: T X X T T X X X X G T X S Z T S Z T S Q T X a T S Zunclassified

Investigation of discrete analogue of one boundary problem of optimal control

Agamaliyeva

2022

Applied Mathematics and Control Sciences

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“…Con tinuing this process yields a sequence of control func tions (4) which implement feedback in the considered control process.…”

Section: Definition 4 the Functionmentioning

confidence: 99%

“…When such feedback is implemented, the control process can terminate before the time t* because the state x*(τ) leaves the controllability domain X τ of the mathematical model. To obtain guar anteed results, we can use the methods of [3,4], where optimal feedback is constructed using nondeterminis tic models. Remark 4.…”

Section: Remarkmentioning

confidence: 99%

Optimal control of a dynamic system using perfect measurements of its states

2012

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“…Одним із важливих етапів на шляху розуміння багатьох теоретичних проблем і методів оптимізації є їх геометрична інтерпретація (див., наприклад, [1][2][3][4][5][6][7][8][9]). Тому створення програм, які б надавали можливість користувачу розв'язувати задачі оптимізації графічним методом, використовуючи лише браузер, є актуальною проблемою.…”

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Web-oriented software for solving linear programming problems by graphical method

Zaloyko

Tryus

2015

CTE Workshop Proc.

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The aim of work is to create web-oriented software for solving mathematical programming problems by graphical methods. Object of research is graphical methods for solving some mathematical programming problems. The subject of research is software for solving some mathematical programming problems by graphical methods.The results of research can be used for teaching students graphical methods for solving problems of linear, quadratic and fractional-linear programming and matrix games.

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Adaptive methods for solvings minimax problems^∗

Cited by 6 publications

References 13 publications

Investigation of discrete analogue of one boundary problem of optimal control

Investigation of discrete analogue of one boundary problem of optimal control

Optimal control of a dynamic system using perfect measurements of its states

Web-oriented software for solving linear programming problems by graphical method

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Adaptive methods for solvings minimax problems∗

Cited by 6 publications

References 13 publications

Investigation of discrete analogue of one boundary problem of optimal control

Investigation of discrete analogue of one boundary problem of optimal control

Optimal control of a dynamic system using perfect measurements of its states

Web-oriented software for solving linear programming problems by graphical method

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Product

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Adaptive methods for solvings minimax problems^∗