NDLI: Solution of constrained optimal control problems using multiple shooting and ESDIRK methods

Content Provider	IEEE Xplore Digital Library
Author	Capolei, A. Jorgensen, J.B.
Copyright Year	2012
Description	Author affiliation: Dept. of Inf. & Math. Modeling, Tech. Univ. of Denmark, Lyngby, Denmark (Capolei, A.; Jorgensen, J.B.)
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.
Sponsorship	IEEE Control Syst. Soc.
Starting Page	295
Ending Page	300
File Size	391998
Page Count	6
File Format	PDF
ISBN	9781457710957
ISSN	07431619
e-ISBN	9781457710964
e-ISBN	9781467321020
DOI	10.1109/ACC.2012.6315474
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-27
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Sensitivity Equations Optimal control Vectors Approximation methods Jacobian matrices Mathematical model
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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