Optimal control for unstructured nonlinear differential-algebraic equations of arbitrary index

We study optimal control problems for general unstructured nonlinear differential-algebraic equations of arbitrary index. In particular, we derive necessary conditions in the case of linear-quadratic control problems and extend them to the general nonlinear case. We also present a Pontryagin maximum principle for general unstructured nonlinear DAEs in the case of restricted controls. Moreover, we discuss the numerical solution of the resulting two-point boundary value problems and present a numerical example. Keywords. nonlinear differential-algebraic equation, optimal control, maximum principle, solvability, necessary optimality condition, behavior approach, strangeness index, regularization AMS(MOS) subject classification. 93C10, 93C15, 65L80, 49K15, 34H05

• Type: Journal
• Year: 2008
• Where: MCSS
• Authors: Peter Kunkel, Volker Mehrmann
• Keywords: Control Systems, General Unstructured Nonlinear, Maximum Principle, MCSS 2008, Optimal Control