Inhalt des Dokuments
Preprint 13-2011
Self-adjoint differential-algebraic equations
Author(s) :
Peter Kunkel
,
Volker Mehrmann
,
Lena Scholz
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 13-2011
MSC 2000
- 93C10 Nonlinear systems
-
93C15 Systems governed by ordinary differential equations
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.
Keywords :
Differential-algebraic equation, self-conjugate operator, self-adjoint pair, optimal control, necessary optimality condition, strangeness index, condensed form, congruence transformation, Hamiltonian system, symplectic flow