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    Item type:Publication, Access status: with files ,
    Hidden regularity in singular optimal control of port-Hamiltonian systems
    (TIB Open Publishing, 2025-01-20)
    Faulwasser, Timm
    ;
    Kirchhoff, Jonas
    ;
    Mehrmann, Volker
    ;
    Philipp, Friedrich
    ;
    Schaller, Manuel
    We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy supply is intrinsic to the port-Hamiltonian structure, the necessary conditions of optimality resulting from Pontryagin's maximum principle may yield singular arcs. The underlying reason is the linear dependence on the control, which makes the problem of determining the optimal control as a function of the state and the adjoint more complicated or even impossible. To resolve this issue, we fully characterize regularity of the (differential-algebraic) optimality system by using the interplay of the cost functional and the dynamics. In case of the optimality DAE being characterized by a regular matrix pencil, we fully determine the control on the singular arc. In case of singular matrix pencils of the optimality system, we propose an approach to compute rank-minimal quadratic perturbations of the objective such that the optimal control problem becomes regular. We illustrate the applicability of our results by a general second-order mechanical system and a discretized boundary-controlled heat equation.
    Publicationtype: Journal Article
      10  14
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    Item type:Publication, Access status: with files ,
    Nonlinear Eigenvalue Problems: A Challenge for Modern Eigenvalue Methods
    (2004-01)
    Voß, Heinrich 
    ;
    Mehrmann, Volker
    We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as the Jacobi-Davidson, Arnoldi or the rational Krylov method and analyze their properties. We briefly introduce a new linearization technique and demonstrate how it can be used to improve structure preservation and with this the accuracy and efficiency of linearization based methods. We present several recent applications where structured and unstructured nonlinear eigenvalue problems arise and some numerical results.
    Publicationtype: Technical Report
      424  994