93C15 Systems governed by ordinary differential equations [See also 34H05]
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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.