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    Wyświetlanie 1-3 z 3
    Tytuł:
    Trust region methods with hierarchical finite element models for PDE-constrained optimization
    Autorzy:
    Kirchner, A.
    Meidner, D.
    Vexler, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/206108.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    trust region
    model hierarchy
    finite elements
    PDE-constrained optimization
    Opis:
    In this paper, a Hierarchical Trust Region Algorithm for solving PDE-constrained optimization problems is developed. A hierarchy of finite element meshes is used to define a hierarchy of quadratic models for the approximation of the discrete reduced cost functional on the finest mesh. The proposed algorithm simultaneously controls the choice of the model and the size of the trust region radius. Application of the trust region convergence theory allows for proving that every accumulation point of the sequence produced by the algorithm is a stationary point of the discretized problem. Numerical examples illustrate the behavior of the method and show a considerable reduction of computation time compared to the standard Newton trust region scheme.
    Źródło:
    Control and Cybernetics; 2011, 40, 4; 1019-1042
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Exact controllability of a string to rest with a moving boundary
    Autorzy:
    Gugat, Martin
    Powiązania:
    https://bibliotekanauki.pl/articles/970107.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    pde constrained optimization
    optimal control of pdes
    optimal boundary control
    wave equation
    analytic solution
    exact controllability
    moving boundaries
    mining elevator
    Opis:
    We consider the problem of steering a finite string to the zero state in finite time from a given initial state by controlling the state at one boundary point while the other boundary point moves. As a possible application we have in mind the optimal control of a mining elevator, where the length of the string changes during the transportation process. During the transportation process, oscillations of the elevator-cable can occur that can be damped in this way. We present an exact controllability result for Dirichlet boundary control at the fixed end of the string that states that there exist exact controls for which the oscillations vanish after finite time. For the result we assume that the movements are Lipschitz continuous with a Lipschitz constant, whose absolute value is smaller than the wave speed. In the result, we present the minimal time, for which exact controllability holds, this time depending on the movement of the boundary point. Our results are based upon travelling wave solutions. We present a representation of the set of successful controls that steer the system to rest after finite time as the solution set of two point-wise equalities. This allows for a transformation of the optimal control problem to a form where no partial differential equation appears. This representation enables interesting insights into the structure of the successful controls. For example, exact bang-bang controls can only exist if the initial state is a simple function and the initial velocity is zero.
    Źródło:
    Control and Cybernetics; 2019, 48, 1; 69-87
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some new phenomena in state-constrained optimal control if ODEs as well as PDEs are involved
    Autorzy:
    Pesch, H. J.
    Rund, A.
    Wahl, V.
    Wendl, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/969885.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control of partial differential equations
    ODE-PDE-constrained optimization
    state constraints
    non-local state-constraints
    integro-state constraints
    optimal control problems for integro-differential equations
    jump conditions
    Opis:
    In this paper we investigate a new class of optimal control problems with ODE as well as PDE constraints. We would like to call them "hypersonic rocket car problems", since they were inspired, on the one hand, by the well known rocket car problem from the early days of ODE optimal control, on the other hand by a recently investigated flight path trajectory optimization problem for a hypersonic aircraft. The hypersonic rocket car problems mimic the latter's coupling structure, yet in a strongly simplified form. They can therefore be seen as prototypes of ODE-PDE control problems. Due to their relative simplicity they allow to a certain degree to obtain analytical solutions and insights into the structure of the adjoints, which would currently be unthinkable with complex real life problems. Our main aim is to derive and verify the necessary optimality conditions. Most of the obtained results bear a lot of similarities with state constrained ODE optimal control problems, yet we also observed some new phenomena.
    Źródło:
    Control and Cybernetics; 2010, 39, 3; 647-660
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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