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    Wyświetlanie 1-7 z 7
    Tytuł:
    Second-order conditions for boundary control problems of the Burgers equation
    Autorzy:
    Volkwein, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/206716.pdf
    Data publikacji:
    2001
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie Burgersa
    stan optymalności
    sterowanie optymalne
    wielościenność
    Burgers' eguation
    optimal control
    optimality conditions
    polyhedricity
    Opis:
    In this article control constrained optimal control problems for the Burgers equation are considered. First- and second-order optimality conditions are presented. Utilizing polyhedricity of the feasible set and the theory of Legendre-forms a second-order sufficient optimality condition is given that is very close to the second-order necessary optimality condition. For the numerical realization a prima-dual actrive set strategy is used.
    Źródło:
    Control and Cybernetics; 2001, 30, 3; 249-278
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The gradient projection method for solving an optimal control problem
    Autorzy:
    Farag, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/1339270.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    distributed parameter systems
    boundary value problems
    gradient methods
    optimal control
    Opis:
    A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.
    Źródło:
    Applicationes Mathematicae; 1996-1997, 24, 2; 141-147
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimality conditions for a class of optimal boundary control problems with quasilinear elliptic equations
    Autorzy:
    Casas, E.
    Dhamo, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/206408.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    Neumann boundary control
    quasi-linear elliptic equation
    Pontryagin principle
    second order optimality conditions
    Opis:
    First- and second-order optimality conditions are established for the boundary optimal control of quasilinear elliptic equations with pointwise constraints on the control. The theory is developed for Neumann controls in polygonal domains of dimension two. For the derivation of second-order sufficient optimality conditions, which is the main goal of this paper, the regularity of the solutions to the state equation and its linearization is studied in detail. Moreover, a Pontryagin principle is proved. The main difficulty in the analysis of these problems is the nonmonotone character of the state equation.
    Źródło:
    Control and Cybernetics; 2011, 40, 2; 457-490
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Neumann boundary optimal control problems governed by parabolic variational equalities
    Autorzy:
    Bollo, Carolina M.
    Gariboldi, Claudia M.
    Tarzia, Domingo A.
    Powiązania:
    https://bibliotekanauki.pl/articles/2183458.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    parabolic variational equalities
    optimal control
    mixed boundary conditions
    optimality conditions
    convergence
    Opis:
    We consider a heat conduction problem S with mixed boundary conditions in an n-dimensional domain with regular boundary and a family of problems Sα with also mixed boundary conditions in , where α > 0 is the heat transfer coefficient on the portion of the boundary Г1. In relation to these state systems, we formulate Neumann boundary optimal control problems on the heat flux q which is definite on the complementary portion Г2 of the boundary of Ω. We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system state and the adjoint state when the heat transfer coefficient α goes to infinity. Furthermore, we formulate particular boundary optimal control problems on a real parameter λ, in relation to the parabolic problems S and Sαα
    Źródło:
    Control and Cybernetics; 2021, 50, 2; 227--252
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions
    Autorzy:
    Krug, Richard
    Leugering, Günter
    Martin, Alexander
    Schmidt, Martin
    Weninger, Dieter
    Powiązania:
    https://bibliotekanauki.pl/articles/2183473.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    time-domain decomposition
    optimal control
    semilinear hyperbolic systems
    convergence
    Opis:
    In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.
    Źródło:
    Control and Cybernetics; 2021, 50, 4; 427--455
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dirichlet control problems in smooth and nonsmooth convex plain domains
    Autorzy:
    Casas, E.
    Mateos, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/206194.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    boundary control
    Dirichlet control
    Opis:
    In this paper we collect some results about boundary Dirichlet control problems governed by linear partial differential equations. Some differences are found between problems posed on polygonal domains or smooth domains. In polygonal domains some difficulties arise in the corners, where the optimal control is forced to take a value which is independent of the data of the problem. The use of some Sobolev norm of the control in the cost functional, as suggested in the specialized literature as an alternative to the L2 norm, allows to avoid this strange behavior. Here, we propose a new method to avoid this undesirable behavior of the optimal control, consisting in considering a discrete perturbation of the cost functional by using a finite number of controls concentrated around the corners. In curved domains, the numerical approximation of the problem requires the approximation of the domain Ω typically by a polygonal domain Ωh, this introduces some difficulties in comparing the continuous and the discrete controls because of their definition on different domains Γ and Γh, respectively. We complete the existing recent analysis of these problems by proving the error estimates for a full discretization of the control problem. Finally, some numerical results are provided to compare the different alternatives and to confirm the theoretical predictions.
    Źródło:
    Control and Cybernetics; 2011, 40, 4; 931-955
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the regularization error of state constrained Neumann control problems
    Autorzy:
    Krumbiegel, K.
    Rosch, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/969594.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    elliptic equation
    state constraints
    boundary control
    regularization
    virtual control
    Opis:
    A linear elliptic optimal control problem with point-wise state constraints in the interior of the domain is considered. Furthermore, the control is given on the boundary with associated constraints. An artificial distributed control is introduced in the cost functional, in the state equation and in the state constraints. Since there are no control constraints for the artificial control, efficient numerical methods can be easily established. Based on a possible violation of the pure pointwise state constraints, an error estimate for the regularization error is derived. The theoretical results are illustrated by numerical tests.
    Źródło:
    Control and Cybernetics; 2008, 37, 2; 369-392
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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