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    Wyświetlanie 1-7 z 7
    Tytuł:
    Two-dimensional stable Lavrentiev phenomenon with and without boundary conditions
    Autorzy:
    Caetano, A.
    Sarychev, A.
    Seabra, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/970549.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    multidimensional calculus of variations
    Lavrentiev phenomenon
    Opis:
    This work contains examples of regular 2D problems of the Calculus of Variations which exhibit stable Lavrentiev phenomenon, under different types of boundary conditions.
    Źródło:
    Control and Cybernetics; 2005, 34, 3; 689-707
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Extensions of the control variational method
    Autorzy:
    Sprekels, J.
    Tiba, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/206097.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    calculus of variations
    contact problems
    evolution problems
    Opis:
    The control variational method is a development of the variational approach, based on optimal control theory. In this work, we give an application to a variational inequality arising in mechanics and involving unilateral conditions both in the domain and on the boundary, and we explore the extension of the method to time-dependent problems.
    Źródło:
    Control and Cybernetics; 2011, 40, 4; 1099-1108
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    High-order variations and small-time local attainability
    Autorzy:
    Krastanov, M. I.
    Powiązania:
    https://bibliotekanauki.pl/articles/970758.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    small-time local attainability of a set
    high-order control variations
    Opis:
    We study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set, well adapted to a given closed set and prove a new attainability result.
    Źródło:
    Control and Cybernetics; 2009, 38, 4B; 1411-1427
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lagrange principle and necessary conditions
    Autorzy:
    Tikhomirov, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/970737.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    mathematical programming
    convex analysis
    calculus of variations
    optimal control
    Lagrange multiplier rule
    Opis:
    Necessary conditions of extremum (from the times of Fermat and Lagrange till our times) for extremal problems where smoothness is interlaced with convexity, and some type of regularity takes place, correspond to a unique general principle, which is due to Lagrange. This report is devoted to the Lagrange principle in the theory of optimization.
    Źródło:
    Control and Cybernetics; 2009, 38, 4B; 1589-1605
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two-dimensional Newtons problem of minimal resistance
    Autorzy:
    Silva, C. J.
    Torres, D. F.
    Powiązania:
    https://bibliotekanauki.pl/articles/969988.pdf
    Data publikacji:
    2006
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Newton's problem of minimal resistance
    dimension two
    calculus of variations
    optimal control
    Opis:
    Newton's problem of minimal resistance is one of the first problems of optimal control: it was proposed, and its solution given, by Isaac Newton in his masterful Principia Mathematica, in 1686. The problem consists of determining, in dimension three, the shape of an axis-symmetric body, with assigned radius and height, which offers minimum resistance when it is moving in a resistant medium. The problem has a very rich history and is well documented in the literature. Of course, at a first glance, one suspects that the two dimensional case should be well known. Nevertheless, we have looked into numerous references and asked at least as many experts on the problem, and we have not been able to identify a single source. Solution was always plausible to everyone who thought about the problem, and writing it down was always thought not to be worthwhile. Here we show that this is not the case: the two-dimensional problem is richer than the classical one, being, in some sense, more interesting. Novelties include: (i) while in the classical three-dimensional problem only the restricted case makes sense (without restriction on the monotonicity of admissible functions the problem does not admit a local minimum), we prove that in dimension two the unrestricted problem is also well-posed when the ratio of height versus radius of base is greater than a given quantity; (ii) while in three dimensions the (restricted) problem has a unique solution, we show that in the restricted two-dimensional problem the minimizer is not always unique - when the height of the body is less or equal than its base radius, there exists infinitely many minimizing functions.
    Źródło:
    Control and Cybernetics; 2006, 35, 4; 965-975
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Inverse shape optimization problems and application to airfoils
    Autorzy:
    Desideri, J.-A.
    Zolesio, J.-P.
    Powiązania:
    https://bibliotekanauki.pl/articles/970144.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie różniczkowe cząstkowe
    metody obliczeniowe
    optymalizacja kształtu
    rachunek wariacyjny
    Partial-Differential Equations (PDEs)
    computational methods
    shape optimization
    calculus of variations
    Opis:
    We consider a set of parameterized planar arcs (x(t), y(t)) (0 1. We first prove the strict convexity of the functional for alpha > 2. Under the less stringent condition alpha > 1, we derive the stationarity condition and the formal expression for the Hessian, and prove that if a point exists at which the functional is stationary w.r.t. variations in y = y(t), for fixed x = x(t), then it is unique and realizes a global minimum; the functional is then unimodal. We also observe that the stationarity condition (Euler-Lagrange quation) is an integral-differential equation depending only on the arc shape and not on the parameterization per se, which gives the variational problem a certain intrinsic character. Then, we solve the inverse problem: given an admissible parameterized arc, we construct a smooth weighting function omega(t) for which the stationarity condition is satisfied, thus making the functional unimodal, and derive certain asymptotics. A numerical example pertaining to optimum-shape design in aerodynamics is computed for illustration.
    Źródło:
    Control and Cybernetics; 2005, 34, 1; 165-202
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the development of Pontryagins Maximum Principle in the works of A.Ya. Dubovitskii and A.A. Milyutin
    Autorzy:
    Dmitruk, A. V.
    Powiązania:
    https://bibliotekanauki.pl/articles/970915.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Euler-Lagrange equation
    maximum principle
    classes of variations
    Pontryagin minimum
    state constraints
    measure in adjoint equation
    regular and nonregular mixed constraints
    phase points
    closure with respect to measure
    three-storey theorem
    Opis:
    We give a short review of the development and generalizations of the Pontryagin Maximum Principle, provided in the studies of Dubovitskii and Milyutin in the 1960s and later years.
    Źródło:
    Control and Cybernetics; 2009, 38, 4A; 923-957
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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