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

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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
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


ConferenceAmerican Control Conference (ACC 2012)
LocationFairmont Queen Elizabeth
Internet address
SeriesAmerican Control Conference

Bibliographical note

Paper number WeA08.6.

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