Self-adjoint differential-algebraic equations

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Date
2011-05-24MFO Scientific Program
Research in Pairs 2010Series
Oberwolfach Preprints;2011,27Author
Kunkel, Peter
Mehrmann, Volker
Scholz, Lena
Metadata
Show full item recordOWP-2011-27
Abstract
Motivated from linear-quadratic optimal control problems for differential-algebraic equations (DAEs), we study the functional analytic properties of the operator associated with the necessary optimality boundary value problem and show that it is associated with a self-conjugate operator and a self-adjoint pair of matrix functions. We then study general self-adjoint pairs of matrix valued functions and derive condensed forms under orthogonal congruence transformations that preserve the self-adjointness. We analyze the relationship between self-adjoint DAEs and Hamiltonian systems with symplectic flows. We also show how to extract self-adjoint and Hamiltonian reduced systems from derivative arrays.