JPEG-like method of control parametrization for numerical solution of the distributed optimization problems

JPEG-like method of control parametrization for numerical solution of the distributed... The present author continued his work on the study of the control parametrization technique for solution of the distributed optimization problems. Proposed was a new method of control parametrization resembling that for information compression used in the JPEG format to reduce by the factor of several times the count of parameters describing the control without an appreciable deterioration in closeness to the optimum. Withdrawn were formulas required for application of the proposed approach to control parametrization in combination with the numerical methods of finite-dimensional optimization for solution of the mathematical programming problem approximating the original optimal control problem. The results of numerical experiments were described and analyzed in detail. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automation and Remote Control Springer Journals

JPEG-like method of control parametrization for numerical solution of the distributed optimization problems

JPEG-like method of control parametrization for numerical solution of the distributed optimization problems

ISSN 0005-1179, Automation and Remote Control, 2017, Vol. 78, No. 8, pp. 1474–1488.  c Pleiades Publishing, Ltd., 2017. Original Russian Text  c A.V. Chernov, 2017, published in Avtomatika i Telemekhanika, 2017, No. 8, pp. 145–163. OPTIMIZATION, SYSTEM ANALYSIS, AND OPERATIONS RESEARCH JPEG-Like Method of Control Parametrization for Numerical Solution of the Distributed Optimization Problems A. V. Chernov Lobachevsky Nizhny Novgorod State University, Nizhny Novgorod, Russia Alekseev Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia e-mail: chavnn@mail.ru Received May 22, 2016 Abstract—The present author continued his work on the study of the control parametrization technique for solution of the distributed optimization problems. Proposed was a new method of control parametrization resembling that for information compression used in the JPEG for- mat to reduce by the factor of several times the count of parameters describing the control without an appreciable deterioration in closeness to the optimum. Withdrawn were formulas required for application of the proposed approach to control parametrization in combination with the numerical methods of finite-dimensional optimization for solution of the mathemati- cal programming problem approximating the original optimal control problem. The results of numerical experiments were described and analyzed in detail. Keywords: optimization of the distributed-parameter systems, functional differentiation, piece- wise constant approximation of control, JPEG-like method of control parametrization. DOI: 10.1134/S0005117917080082 1. INTRODUCTION For one nonlinear controlled system of first-order partial differential equations, a procedure to reduce the problem of optimization to a finite-dimensional problem of mathematical programming by means of the finite-dimensional approximation only of control was proposed in [1] (see also [2, Ch. IV, § 8]). This technique enables one to...
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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Control, Robotics, Mechatronics; Mechanical Engineering; Computer-Aided Engineering (CAD, CAE) and Design
ISSN
0005-1179
eISSN
1608-3032
D.O.I.
10.1134/S0005117917080082
Publisher site
See Article on Publisher Site

Abstract

The present author continued his work on the study of the control parametrization technique for solution of the distributed optimization problems. Proposed was a new method of control parametrization resembling that for information compression used in the JPEG format to reduce by the factor of several times the count of parameters describing the control without an appreciable deterioration in closeness to the optimum. Withdrawn were formulas required for application of the proposed approach to control parametrization in combination with the numerical methods of finite-dimensional optimization for solution of the mathematical programming problem approximating the original optimal control problem. The results of numerical experiments were described and analyzed in detail.

Journal

Automation and Remote ControlSpringer Journals

Published: Aug 19, 2017

References

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