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    Wyświetlanie 1-14 z 14
    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:
    Shape derivatives for general objective functions and the incompressible Navier-Stokes equations
    Autorzy:
    Schmidt, S.
    Schulz, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/969869.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    shape optimization
    shape derivative
    Navier-Stokes
    adjoint calculus
    Opis:
    The aim of this paper is to present the shape derivative for a wide array of objective functions using the incompressible Navier-Stokes equations as a state constraint. Most real world applications of computational fluid dynamics are shape optimization problems in nature, yet special shape optimization techniques are seldom used outside the field of elliptic partial differential equations and linear elasticity. This article tries to be self contained, also presenting many useful results from the literature. We conclude with a comparison of different objective functions for the shape optimization of an obstacle in a channel, which can be done quite conveniently when one knows the general form of the shape gradient.
    Źródło:
    Control and Cybernetics; 2010, 39, 3; 677-713
    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:
    Pre-shape calculus and its application to mesh quality optimization
    Autorzy:
    Luft, Daniel
    Schulz, Volker
    Powiązania:
    https://bibliotekanauki.pl/articles/2183466.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    shape optimization
    mesh quality
    mesh deformation method
    shape calculus
    Opis:
    Deformations of the computational mesh, arising from optimization routines, usually lead to decrease of mesh quality or even destruction of the mesh. We propose a theoretical framework using pre-shapes to generalize the classical shape optimization and calculus. We define pre-shape derivatives and derive corresponding structure and calculus theorems. In particular, tangential directions are featured in pre-shape derivatives, in contrast to classical shape derivatives, featuring only normal directions. Techniques from classical shape optimization and calculus are shown to carry over to this framework. An optimization problem class for mesh quality is introduced, which is solvable with the use of pre-shape derivatives. This class allows for simultaneous optimization of the classical shape objectives and mesh quality without deteriorating the classical shape optimization solution. The new techniques are implemented and numerically tested for 2D and 3D.
    Źródło:
    Control and Cybernetics; 2021, 50, 3; 263--301
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Simultaneous shape and mesh quality optimization using pre-shape calculus
    Autorzy:
    Luft, Daniel
    Schulz, Volker
    Powiązania:
    https://bibliotekanauki.pl/articles/2183472.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    shape optimization
    mesh quality
    mesh deformation method
    shape calculus
    Opis:
    Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase both shape and volume mesh quality. For this, we employ pre-shape calculus as established in Luft and Schulz (2021). Existence of regularized solutions is guaranteed. Further, consistency of modified pre-shape gradient systems is established. We present pre-shape gradient system modifications, which permit simultaneous shape optimization with mesh quality improvement. Optimal shapes to the original problem are left invariant under regularization. The computational burden of our approach is limited, since additional solution of possibly larger (non-)linear systems for regularized shape gradients is not necessary. We implement and compare pre-shape gradient regularization approaches for a 2D problem, which is prone to mesh degeneration. As our approach does not depend on the choice of metrics representing shape gradients, we employ and compare several different metrics.
    Źródło:
    Control and Cybernetics; 2021, 50, 4; 473--520
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    PLC implementation of fractional PI controller in positioning of electrohydraulic servodrive
    Autorzy:
    Rybarczyk, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/206664.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    fractional order controller
    electrohydraulic drive
    electrohydraulic servovalve
    fractional order calculus
    Opis:
    The article describes the implementation of fractional order PI controller with the Programmable Logic Controller (PLC). The control system proposed is used for positioning of an electrohydraulic drive with Bosch Rexroth servo valve. The controller is based on PLC, working under real time operating system Automation Runtime. User interface is equipped with the touch panel of Power Panel 500 type. In the first part of the paper the fractional order calculus theory is introduced. In addition, some examples of fractional controller implementations in different kinds of objects are presented. The subsequent section focuses on author’s own research. The Oustaloup’s method description is recalled along with its computer implementation. Further, the impact of finite order of the approximation function is verified. The article includes the description of test stand structure, code generation and implementation of PI controller on the dedicated PLC.
    Źródło:
    Control and Cybernetics; 2016, 45, 3; 301-316
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional Kalman Filter algorithms for correlated system and measurement noises
    Autorzy:
    Sierociuk, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/206137.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    fractional order calculus
    discrete fractional state-space systems
    fractional Kalman filter
    Opis:
    The paper presents a generalization of the Fractional Kalman Filter to a case when correlated system and measurement noises appear. The algorithm proposed is derived in detail for a linear generalized discrete fractional order state-space system for both constant and variable order cases. In order to present the efficiency of the proposed algorithm, results of numerical simulations are presented. Results of numerical experiments are compared with the effect of estimation obtained when using the traditional Fractional Kalman Filter algorithm.
    Źródło:
    Control and Cybernetics; 2013, 42, 2; 471-490
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Vector space of increments
    Autorzy:
    Borawski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/206256.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    incremental arithmetic
    vector space
    vector calculus
    standard deviation increment
    variance increment
    Opis:
    The article discusses definitions of vector space for variance increment and standard deviation increment, as well as definition of scalar product for variance increment. This justifies using a vector calculus for variance increment and allows for emplyoing vector calculus methods for variance recalculated into variance increment. The paper also presents a practical example of combining images from sector-scan sonar based on comparison made between local increments of variance.
    Źródło:
    Control and Cybernetics; 2012, 41, 1; 145-170
    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:
    Yet another object-oriented data model and its application
    Jeszcze jeden obiektowo zorientowany model danych i jego zastosowanie
    Autorzy:
    Jankowska, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/206751.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    model danych
    język zapytań
    rachunek obiektowy
    data model
    calculus for objects
    query language
    Opis:
    In this paper we propose a certain object-oriented data model. It originates from the calculus for complex objects of Bancilhon and Khoshafian. These two models differ mainly in terms of the set objects' interpretation. In our model a set object stands for a set of items denoting different forms of the same object. As a consequence, a new sub object relation must be defined. Then, new functions of union, intersection and complement are defined. It is proven that the new data model is not only a lattice, but also a Boolean algebra. Finally, the model is expanded into a new calculus for objects. It is shown that the calculus provides a firm background for some interesting query language.
    W artykule zaproponowano pewien obiektowo zorientowany model danych. Wywodzi się on z rachunku dla obiektów złożonych, wprowadzonego przez Bancilhona i Koshafiana. Te dwa modele różnią się między sobą w zakresie interpretacji obiektów typu zbioru. W zaproponowanym modelu obiekt typu zbioru oznacza zbiór pewnych przedmiotów oznaczających różne formy tego samego obiektu. W konsekwencji, trzeba zdefiniować nową relację, sub object. Wówczas definiuje się nowe funkcje: union (suma), intersection (przecięcie) oraz complement (dopełnienie). Wykazuje się, że nowy model nie tylko jest kratą, ale i algebrą Boole'owską. W końcu, zaproponowany model jest rozszerzony do postaci nowego rachunku dla obiektów. Pokazano, że ten rachunek stanowi dobrą podstawę do pewnego interesującego języka zapytań.
    Źródło:
    Control and Cybernetics; 2003, 32, 1; 175-195
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some summations formulae in commutative Leibniz algebras with logarithms
    Autorzy:
    Przeworska-Rolewicz, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/970261.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    algebra with unit
    Leibniz condition
    logarithmic mapping
    antilogarithmic mapping
    true shift
    binomial formula
    harmonic logarithm
    umbral calculus
    generic function
    Opis:
    A survey of summation formulae in commutative Leibniz algebras with logarithms is given. New results concerning generic functions and related summation formulae, which generalize well-known properties of the Bessel functions, are demonstrated.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 841-857
    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:
    Towards historical roots of necessary conditions of optimality: Regula of Peano
    Autorzy:
    Dolecki, S.
    Greco, G. H.
    Powiązania:
    https://bibliotekanauki.pl/articles/970285.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    różniczkowalność
    zbiór wypukły
    differentiability
    convex set
    Kuratowski limit of sets
    tangent cones
    condition of optimality
    mean value theorem
    Peano remainder
    Peano's regula
    strict derivability
    Peano's Formulario Mathematico
    Peano's Geometric Calculus
    Grassmann's Ausdehnungslehre
    Opis:
    At the end of 19th century Peano discerned vector spaces, differentiability, convex sets, limits of families of sets, tangent cones, and many other concepts, in a modern perfect form. He applied these notions to solve numerous problems. The theorem on necessary conditions of optimality (Regula) is one of these. The formal language of logic that he developed, enabled him to perceive mathematics with great precision and depth. Actually he built mathematics axiomatically based exclusively on logical and set-theoretic primitive terms and properties, which was a revolutionary turning point in the development of mathematics.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 491-518
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-14 z 14

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