TY - JOUR

T1 - Метод кодифференциального спуска в задаче нахождения глобального минимума кусочно-аффинного целевого функционала в линейных системах управлени

AU - Fominyh, Alexander V.

AU - Karelin, Vladimir V.

AU - Polyakova, Lyudmila N.

AU - Myshkov, Stanislav K.

AU - Tregubov, Vladimir P.

N1 - Funding Information: ∗ This work was supported by the Russian Science Foundation (project N 20-71-10032). Publisher Copyright: © 2021 Saint Petersburg State University. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - The article considers the problem of optimal control of an object described by a linear nonstationary system and with a piecewise affine quality functional. The problem is examined in Mayer's form with both free and partially fixed right endpoints. Piecewise continuous and bounded controls that lie in some parallelepiped at each moment of time are admissible. The standard discretization of the original system and the control parametrization are used, some convergence theorems of the discrete problem solution to the continuous problem solution are presented. Further, for the obtained discrete system, the necessary and sufficient minimum conditions are written out in terms of the codifferential, the method of the modified codifferential descent is applied to it, which guarantees to find the global minimum of this problem in a finite number of steps. The proposed algorithm is illustrated with examples.

AB - The article considers the problem of optimal control of an object described by a linear nonstationary system and with a piecewise affine quality functional. The problem is examined in Mayer's form with both free and partially fixed right endpoints. Piecewise continuous and bounded controls that lie in some parallelepiped at each moment of time are admissible. The standard discretization of the original system and the control parametrization are used, some convergence theorems of the discrete problem solution to the continuous problem solution are presented. Further, for the obtained discrete system, the necessary and sufficient minimum conditions are written out in terms of the codifferential, the method of the modified codifferential descent is applied to it, which guarantees to find the global minimum of this problem in a finite number of steps. The proposed algorithm is illustrated with examples.

KW - Codifferential

KW - Method of codifferential descent method

KW - Nonsmooth optimal control problem

KW - Parametrization of control

KW - Piecewise affine function

KW - HYPODIFFERENTIAL DESCENT

KW - MAXIMUM PRINCIPLE

KW - NONSMOOTH

KW - PENALTY METHOD

KW - STATE

KW - codifferential

KW - method of codifferential descent method

KW - nonsmooth optimal control problem

KW - parametrization of control

KW - piecewise affine function

KW - Method of codifferential descent method

KW - Codifferential

KW - Nonsmooth optimal control problem

KW - Piecewise affine function

KW - Parametrization of control

UR - http://www.scopus.com/inward/record.url?scp=85106904416&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/498b01ae-2176-35ed-a37b-8b57f1886cf2/

U2 - 10.21638/11701/SPBU10.2021.105

DO - 10.21638/11701/SPBU10.2021.105

M3 - статья

AN - SCOPUS:85106904416

VL - 17

SP - 47

EP - 58

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 1

ER -