Mathematics Research Institute

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“Optimal control of DAE constrained systems”

Volker Mehrmann (Technische Universität Berlin)

Fecha: 15/04/2013 17:00
Lugar: Sala de Grados I de la Facultad de Ciencias
Grupo: GIR Análisis Numérico y Estocástico, Optimización Dinámica y Aplicaciones (ANEODA)

Abstract:
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.

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