TY - JOUR

T1 - The quasidifferential descent method in a control problem with nonsmooth objective functional

AU - Fominyh, A. V.

N1 - Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.

PY - 2021/11

Y1 - 2021/11

N2 - The paper is devoted to the problem of optimal control of an object described by a system with a continuously differentiable right-hand side and a nondifferentiable (but only quasidifferentiable) quality functional. We consider a problem in the form of Mayer with both a free and a fixed right end. Admissible controls are piecewise continuous (with a finite number of discontinuity points) and bounded vector-functions, which belong to certain polyhedron at each moment of time. Standard discretization of the initial system and control parameterization are performed, and theorems on the convergence of the discrete system solution obtained to the desired solution of the continuous problem are presented. Further, for the discrete system obtained, the necessary and, in some cases, sufficient minimum conditions are written in terms of quasidifferential. The quasidifferential descent method is applied to this problem. The algorithm developed is demonstrated by examples.

AB - The paper is devoted to the problem of optimal control of an object described by a system with a continuously differentiable right-hand side and a nondifferentiable (but only quasidifferentiable) quality functional. We consider a problem in the form of Mayer with both a free and a fixed right end. Admissible controls are piecewise continuous (with a finite number of discontinuity points) and bounded vector-functions, which belong to certain polyhedron at each moment of time. Standard discretization of the initial system and control parameterization are performed, and theorems on the convergence of the discrete system solution obtained to the desired solution of the continuous problem are presented. Further, for the discrete system obtained, the necessary and, in some cases, sufficient minimum conditions are written in terms of quasidifferential. The quasidifferential descent method is applied to this problem. The algorithm developed is demonstrated by examples.

KW - Method of quasidifferential descent

KW - Nonsmooth optimal control problem

KW - Parameterization of control

KW - Quasidifferential

UR - http://www.scopus.com/inward/record.url?scp=85100570191&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0061cee1-e94d-32c6-b254-a2364103639a/

U2 - 10.1007/s11590-021-01710-7

DO - 10.1007/s11590-021-01710-7

M3 - Article

AN - SCOPUS:85100570191

VL - 15

SP - 2773

EP - 2792

JO - Optimization Letters

JF - Optimization Letters

SN - 1862-4472

IS - 8

M1 - 8

ER -