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.
We, furthermore, show that the optimality system has a self-adjoint structure that is associated with a self-conjugate operator and derive local structure preserving condensed forms that allow to study existence and uniqueness of solutions.  The relationship between DAEs with self-conjugate operator and Hamiltonian systems is analyzed and it is characterized when there is an underlying symplectic flow.
Finally, we also discuss the numerical solution of the resulting two-point boundary value problems.
It is joint work with Peter Kunkel and Lena Scholz.
