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- ItemSelf-adjoint differential-algebraic equations(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kunkel, Peter; Mehrmann, Volker; Scholz, LenaMotivated 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.
- ItemFormal adjoints of linear DAE operators and their role in optimal control(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kunkel, Peter; Mehrmann, VolkerFor regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze the properties of the formal adjoints and their implications in solving linear-quadratic optimal control problems with DAE constraints.