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    Wyświetlanie 1-3 z 3
    Tytuł:
    Network optimality conditions
    Autorzy:
    Osmolovskii, Nikolai P.
    Qian, Meizhi
    Sokołowski, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/31343935.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    network
    optimal control problem
    weak local minimum
    Pontryagin’s maximum principle
    critical cone
    quadratic form
    second order optimality conditions
    Riccati equation
    Opis:
    Optimality conditions for optimal control problems arising in network modeling are discussed. We confine ourselves to the steady state network models. Therefore, we consider only control systems described by ordinary differential equations. First, we derive optimality conditions for the nonlinear problem for a single beam. These conditions are formulated in terms of the local Pontryagin maximum principle and the matrix Riccati equation. Then, the optimality conditions for the control problem for networks posed on an arbitrary planar graph are discussed. This problem has a set of independent variables xi varying within their intervals [0, li], associated with the corresponding beams at network edges. The lengths li of intervals are not specified and must be determined. So, the optimization problem is non-standard, it is a combination of control and design of networks. However, using a linear change of the independent variables, it can be reduced to a standard one, and we show this. Two simple numerical examples for the single-beam problem are considered.
    Źródło:
    Control and Cybernetics; 2023, 52, 2; 129-180
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Growth control of cracks under contact conditions based on the topological derivative of the Rice’s integral
    Autorzy:
    da Silva Xavier, Marcel Duarte
    Novotny, Antonio André
    Sokołowski, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/1839141.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Rice’s integral
    Griffith’s criterion
    Eshelby’s tensor
    topological derivative
    Opis:
    In the present paper we propose a simple method for dealing with growth control of cracks under contact type boundary conditions on their lips. The aim is to find a mechanism for decreasing the energy release rate of cracked components, which means increasing their fracture toughness. The method consists in minimizing a shape functional defined in terms of the Rice’s integral, with respect to the nucleation of hard and/or soft inclusions, according to the information provided by the associated topological derivative. Based on Griffith’s energy criterion, this simple strategy allows for an increase in fracture toughness of the cracked component. Since the problem is non-linear, the domain decomposition technique, combined with the Steklov-Poincaré pseudo-differential boundary operator, is used to obtain the sensitivity of the associated shape functional with respect to the nucleation of a small circular inclusion with different material property from the background. Then, the obtained topological derivatives are used to indicate the regions, where the controls should be positioned in order to solve the minimization problem we are dealing with. Finally, a numerical example is presented showing the applicability of the proposed methodology.
    Źródło:
    Control and Cybernetics; 2019, 48, 2; 307-323
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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