Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods

Andrea Capolei, John Bagterp Jørgensen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

In this paper, we describe a novel numerical algorithm for solution of constrained optimal control problems of the Bolza type for stiff and/or unstable systems. The numerical algorithm combines explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods with a multiple shooting algorithm. As we consider stiff systems, implicit solvers with sensitivity computation capabilities for initial value problems must be used in the multiple shooting algorithm. Traditionally, multi-step methods based on the BDF algorithm have been used for such problems. The main novel contribution of this paper is the use of ESDIRK integration methods for solution of the initial value problems and the corresponding sensitivity equations arising in the multiple shooting algorithm. Compared to BDF-methods, ESDIRK-methods are advantageous in multiple shooting algorithms in which restarts and frequent discontinuities on each shooting interval are present. The ESDIRK methods are implemented using an inexact Newton method that reuses the factorization of the iteration matrix for the integration as well as the sensitivity computation. Numerical experiments are provided to demonstrate the algorithm.
Original languageEnglish
Title of host publicationProceedings of the 2012 American Control Conference
Publication date2012
Pages295-300
ISBN (Print)978-1-4577-1094-0
Publication statusPublished - 2012
EventAmerican Control Conference (ACC 2012) - Fairmont Queen Elizabeth, Montréal, Canada
Duration: 27 Jun 201229 Jun 2012
http://a2c2.org/conferences/acc2012/index.php

Conference

ConferenceAmerican Control Conference (ACC 2012)
LocationFairmont Queen Elizabeth
CountryCanada
CityMontréal
Period27/06/201229/06/2012
Internet address
SeriesAmerican Control Conference
ISSN0743-1619

Bibliographical note

Paper number WeA08.6.

Cite this

Capolei, A., & Jørgensen, J. B. (2012). Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods. In Proceedings of the 2012 American Control Conference (pp. 295-300). American Control Conference
Capolei, Andrea ; Jørgensen, John Bagterp. / Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods. Proceedings of the 2012 American Control Conference. 2012. pp. 295-300 (American Control Conference).
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Capolei, A & Jørgensen, JB 2012, Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods. in Proceedings of the 2012 American Control Conference. American Control Conference, pp. 295-300, American Control Conference (ACC 2012), Montréal, Canada, 27/06/2012.

Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods. / Capolei, Andrea; Jørgensen, John Bagterp.

Proceedings of the 2012 American Control Conference. 2012. p. 295-300 (American Control Conference).

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Capolei A, Jørgensen JB. Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods. In Proceedings of the 2012 American Control Conference. 2012. p. 295-300. (American Control Conference).