On the numerical treatment of linear-quadratic optimal control problems for general linear time-varying differential-algebraic equations

Authors:
Stephen L. Campbell;Peter Kunkel
Affiliations:
Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, USA;Mathematisches Institut, Universität Leipzig, Augustusplatz 10, 04109 Leipzig, Federal Republic of Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

The development of numerical methods for finding optimal solutions of control problems modeled by differential-algebraic equations (DAEs) is an important task. Usually restrictions are placed on the DAE such as being semi-explicit. Here the numerical solution of optimal control problems with linear time-varying DAEs as the process and quadratic cost functionals is considered. The leading coefficient is allowed to be time-varying and the DAE may be of higher index. Both a direct transcription approach and the solution of the necessary conditions are examined for two important discretizations.