Abstract

The paper discusses various approaches to solving nonlinear optimal control problems. Of all such approaches, we chose the two most characteristic. The first one uses sufficient conditions of optimality in the form of Hamilton–Jacobi–Bellman equations and the corresponding numerical method. The second is based on the reduction of optimal control problem to interval linear programming problem and finding a solution using the Gabasov’s adaptive method. The main goal is to compare the capabilities of these methods within a specific problem of optimal control. As an application, we consider the problem of constructing optimal control in a nonlinear model of macroeconomic growth with nonlinear dynamical constraints. Comparative analysis of these two approaches and corresponding numerical simulation are presented.

Original languageEnglish
Title of host publicationIntelligent Distributed Computing XIII, IDC 2019
EditorsIgor Kotenko, Vasily Desnitsky, Costin Badica, Didier El Baz, Mirjana Ivanovic
PublisherSpringer
Pages183-188
Number of pages6
ISBN (Print)9783030322571
DOIs
Publication statusPublished - 2020
Event13th International Symposium on Intelligent Distributed Computing, IDC 2019 - St. Petersburg
Duration: 7 Oct 20199 Oct 2019

Publication series

NameStudies in Computational Intelligence
Volume868
ISSN (Print)1860-949X
ISSN (Electronic)1860-9503

Conference

Conference13th International Symposium on Intelligent Distributed Computing, IDC 2019
CountryRussian Federation
CitySt. Petersburg
Period7/10/199/10/19

Fingerprint

Linear programming
Numerical methods
Computer simulation

Scopus subject areas

  • Artificial Intelligence

Cite this

Boiko, A. V., & Smirnov, N. V. (2020). On Approaches for Solving Nonlinear Optimal Control Problems. In I. Kotenko, V. Desnitsky, C. Badica, D. El Baz, & M. Ivanovic (Eds.), Intelligent Distributed Computing XIII, IDC 2019 (pp. 183-188). (Studies in Computational Intelligence; Vol. 868). Springer. https://doi.org/10.1007/978-3-030-32258-8_21
Boiko, Alina V. ; Smirnov, Nikolay V. / On Approaches for Solving Nonlinear Optimal Control Problems. Intelligent Distributed Computing XIII, IDC 2019. editor / Igor Kotenko ; Vasily Desnitsky ; Costin Badica ; Didier El Baz ; Mirjana Ivanovic. Springer, 2020. pp. 183-188 (Studies in Computational Intelligence).
@inproceedings{d1c1204cb3954962ba90c19eadfcd09a,
title = "On Approaches for Solving Nonlinear Optimal Control Problems",
abstract = "The paper discusses various approaches to solving nonlinear optimal control problems. Of all such approaches, we chose the two most characteristic. The first one uses sufficient conditions of optimality in the form of Hamilton–Jacobi–Bellman equations and the corresponding numerical method. The second is based on the reduction of optimal control problem to interval linear programming problem and finding a solution using the Gabasov’s adaptive method. The main goal is to compare the capabilities of these methods within a specific problem of optimal control. As an application, we consider the problem of constructing optimal control in a nonlinear model of macroeconomic growth with nonlinear dynamical constraints. Comparative analysis of these two approaches and corresponding numerical simulation are presented.",
keywords = "Dynamic programming method, Gabasov’s adaptive method, Optimal control",
author = "Boiko, {Alina V.} and Smirnov, {Nikolay V.}",
year = "2020",
doi = "10.1007/978-3-030-32258-8_21",
language = "English",
isbn = "9783030322571",
series = "Studies in Computational Intelligence",
publisher = "Springer",
pages = "183--188",
editor = "Igor Kotenko and Vasily Desnitsky and Costin Badica and {El Baz}, Didier and Mirjana Ivanovic",
booktitle = "Intelligent Distributed Computing XIII, IDC 2019",
address = "Germany",

}

Boiko, AV & Smirnov, NV 2020, On Approaches for Solving Nonlinear Optimal Control Problems. in I Kotenko, V Desnitsky, C Badica, D El Baz & M Ivanovic (eds), Intelligent Distributed Computing XIII, IDC 2019. Studies in Computational Intelligence, vol. 868, Springer, pp. 183-188, St. Petersburg, 7/10/19. https://doi.org/10.1007/978-3-030-32258-8_21

On Approaches for Solving Nonlinear Optimal Control Problems. / Boiko, Alina V.; Smirnov, Nikolay V.

Intelligent Distributed Computing XIII, IDC 2019. ed. / Igor Kotenko; Vasily Desnitsky; Costin Badica; Didier El Baz; Mirjana Ivanovic. Springer, 2020. p. 183-188 (Studies in Computational Intelligence; Vol. 868).

Research output

TY - GEN

T1 - On Approaches for Solving Nonlinear Optimal Control Problems

AU - Boiko, Alina V.

AU - Smirnov, Nikolay V.

PY - 2020

Y1 - 2020

N2 - The paper discusses various approaches to solving nonlinear optimal control problems. Of all such approaches, we chose the two most characteristic. The first one uses sufficient conditions of optimality in the form of Hamilton–Jacobi–Bellman equations and the corresponding numerical method. The second is based on the reduction of optimal control problem to interval linear programming problem and finding a solution using the Gabasov’s adaptive method. The main goal is to compare the capabilities of these methods within a specific problem of optimal control. As an application, we consider the problem of constructing optimal control in a nonlinear model of macroeconomic growth with nonlinear dynamical constraints. Comparative analysis of these two approaches and corresponding numerical simulation are presented.

AB - The paper discusses various approaches to solving nonlinear optimal control problems. Of all such approaches, we chose the two most characteristic. The first one uses sufficient conditions of optimality in the form of Hamilton–Jacobi–Bellman equations and the corresponding numerical method. The second is based on the reduction of optimal control problem to interval linear programming problem and finding a solution using the Gabasov’s adaptive method. The main goal is to compare the capabilities of these methods within a specific problem of optimal control. As an application, we consider the problem of constructing optimal control in a nonlinear model of macroeconomic growth with nonlinear dynamical constraints. Comparative analysis of these two approaches and corresponding numerical simulation are presented.

KW - Dynamic programming method

KW - Gabasov’s adaptive method

KW - Optimal control

UR - http://www.scopus.com/inward/record.url?scp=85075548830&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/approaches-solving-nonlinear-optimal-control-problems

U2 - 10.1007/978-3-030-32258-8_21

DO - 10.1007/978-3-030-32258-8_21

M3 - Conference contribution

AN - SCOPUS:85075548830

SN - 9783030322571

T3 - Studies in Computational Intelligence

SP - 183

EP - 188

BT - Intelligent Distributed Computing XIII, IDC 2019

A2 - Kotenko, Igor

A2 - Desnitsky, Vasily

A2 - Badica, Costin

A2 - El Baz, Didier

A2 - Ivanovic, Mirjana

PB - Springer

ER -

Boiko AV, Smirnov NV. On Approaches for Solving Nonlinear Optimal Control Problems. In Kotenko I, Desnitsky V, Badica C, El Baz D, Ivanovic M, editors, Intelligent Distributed Computing XIII, IDC 2019. Springer. 2020. p. 183-188. (Studies in Computational Intelligence). https://doi.org/10.1007/978-3-030-32258-8_21