Numerical procedure for optimal control of higher index DAEs

Radoslaw Pytlak

doi:10.3934/dcds.2011.29.647

Article Contents

2011, Volume 29, Issue 2: 647-670. Doi: 10.3934/dcds.2011.29.647

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Numerical procedure for optimal control of higher index DAEs

Radoslaw Pytlak^1,

1.
Institute of Automatic Control and Robotics, Warsaw University of Technology, 02-525 Warsaw

Received: August 31, 2009

Revised: February 28, 2010

Published: May 2011

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Abstract

The paper deals with optimal control problems described by higher index DAEs. We introduce a numerical procedure for solving these problems. The procedure, based on the appropriately defined adjoint equations, refers to an implicit Runge--Kutta method for differential--algebraic equations. Assuming that higher index DAEs can be solved numerically the gradients of functionals defining the control problem are evaluated with the help of well--defined adjoint equations. The paper presents numerical examples related to index three DAEs showing the validity of the proposed approach.

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Mathematics Subject Classification: Primary: 49K99, 34A09; Secondary: 49M05.

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