SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Self-conjugate differential and difference operators arising in the optimal control of descriptor systems

L. Scholz and V. Mehrmann

Abstract
We analyze the structure of the linear differential and difference operators associated with the necessary optimality conditions of optimal control problems for descriptor systems in continuous- and discrete-time. It has been shown in [2] that in continuous-time the associated optimality system is a self-conjugate operator associated with a self-adjoint pair of coefficient matrices. We show that the necessary optimality conditions for discrete-time linear quadratic control problems with variable coefficients leads to self-conjugate difference operators associated with self-adjoint triples of coefficient functions, thus achieving a similar result as in the continuous time case. We also extend the results to higher order differential or difference equation constraints and shown how first order reductions can be carried out that lead to first order systems with the same structural properties.

Bibliography
[1] V. Mehrmann and L. Scholz, Self-conjugate differential and difference operators arising in the optimal control of descriptor systems, accepted for Publication in OaM, 2013. Preprint 26, Institut für Mathematik, TU Berlin, 2012.
[2] P. Kunkel, V. Mehrmann and L. Scholz, Self-adjoint differential-algebraic equations, appeared electronically in MCSS, 2013. DOI: 10.1007/s00498-013-0109-3.

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