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Wyszukujesz frazę "geometric approach" wg kryterium: Temat

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    Wyświetlanie 1-6 z 6
    Tytuł:
    On the geometric structure of characteristic vector fields related with nonlinear equations of the Hamilton-Jacobi type
    Autorzy:
    Prykarpatska, N. K.
    Wachnicki, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255568.pdf
    Data publikacji:
    2007
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Hamilton-Jacobi equations
    Cartan-Monge geometric approach
    Hopf-Lax type representation
    Opis:
    The Cartan-Monge geometric approach to the characteristics method for Hamilton-Jacobi type equations and nonlinear partial differential equations of higher orders is analyzed. The Hamiltonian structure of characteristic vector fields related with nonlinear partial differential equations of first order is analyzed, the tensor fields of special structure are constructed for defining characteristic vector fields naturally related with nonlinear partial differential equations of higher orders. The generalized characteristics method is developed in the framework of the symplectic theory within geometric Monge and Cartan pictures. The related characteristic vector fields are constructed making use of specially introduced tensor fields, carrying the symplectic structure. Based on their inherited geometric properties, the related functional-analytic Hopf-Lax type solutions to a wide class of boundary and Cauchy problems for nonlinear partial differential equations of Hamilton-Jacobi type are studied. For the non-canonical Hamilton-Jacobi equations there is stated a relationship between their solutions and a good specified functional-analytic fixed point problem, related with Hopf-Lax type solutions to specially constructed dual canonical Hamilton-Jacobi equations.
    Źródło:
    Opuscula Mathematica; 2007, 27, 1; 89-111
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear diagnostic filter design: Algebraic and geometric points of view
    Autorzy:
    Shumsky, A.
    Zhirabok, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/908458.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    filtr diagnostyczny
    system nieliniowy
    podejście geometryczne
    detekcja uszkodzeń
    lokalizacja uszkodzeń
    diagnostic filter
    nonlinear systems
    geometric approach
    algebraic approach
    fault detection
    fault isolation
    Opis:
    The problem of diagnostic filter design is studied. Algebraic and geometric approaches to solving this problem are investigated. Some relations between these approaches are established. New definitions of fault detectability and isolability are formulated. On the basis of these definitions, a procedure for diagnostic filter design is given in both algebraic and geometric terms.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2006, 16, 1; 115-127
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Redundancy relations for fault diagnosis in nonlinear uncertain systems
    Autorzy:
    Shumsky, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/929809.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    detekcja uszkodzeń
    lokalizacja uszkodzeń
    system nieliniowy
    podejście algebraiczne
    podejście geometryczne
    fault detection and isolation
    nonlinear systems
    redundancy relations
    full decoupling
    algebraic approach
    geometric approach
    Opis:
    The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into a strict feedback form. Algebraic and geometric tools are used for this transformation. The features of the method are made particular for uncertain systems with a linear structure.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 4; 477-489
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A geometric approach to structural model matching by output feedback in linear impulsive systems
    Autorzy:
    Zattoni, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/330301.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    linear impulsive system
    hybrid system
    model matching
    disturbance decoupling
    geometric approach
    structural properties
    układ liniowy impulsowy
    układ hybrydowy
    dopasowanie modelu
    właściwości strukturalne
    Opis:
    This paper provides a complete characterization of solvability of the problem of structural model matching by output feedback in linear impulsive systems with nonuniformly spaced state jumps. Namely, given a linear impulsive plant and a linear impulsive model, both subject to sequences of state jumps which are assumed to be simultaneous and measurable, the problem consists in finding a linear impulsive compensator that achieves exact matching between the respective forced responses of the linear impulsive plant and of the linear impulsive model, by means of a dynamic feedback of the plant output, for all the admissible input functions and for all the admissible sequences of jump times. The solution of the stated problem is achieved by reducing it to an equivalent problem of structural disturbance decoupling by dynamic feedforward. Indeed, this latter problem is formulated for the so-called extended linear impulsive system, which consists of a suitable connection between the given plant and a modified model. A necessary and sufficient condition for the solution of the structural disturbance decoupling problem is first shown. The proof of sufficiency is constructive, since it is based on the synthesis of the compensator that solves the problem. The proof of necessity is based on the definition and the geometric properties of the unobservable subspace of a linear impulsive system subject to unequally spaced state jumps. Finally, the equivalence between the two structural problems is formally established and proven.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2018, 28, 1; 25-38
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Active fault tolerant control of nonlinear systems: the cart-pole example
    Autorzy:
    Bonfe, M.
    Castaldi, P.
    Mimmo, N.
    Simani, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/907604.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    detekcja uszkodzeń
    lokalizacja uszkodzeń
    filtracja nieliniowa
    sterowanie tolerujące uszkodzenia
    fault detection
    fault isolation
    nonlinear filter
    nonlinear geometric approach
    fault tolerant control
    cart pole nonlinear model
    Opis:
    This paper describes the design of fault diagnosis and active fault tolerant control schemes that can be developed for nonlinear systems. The methodology is based on a fault detection and diagnosis procedure relying on adaptive filters designed via the nonlinear geometric approach, which allows obtaining the disturbance de-coupling property. The controller reconfiguration exploits directly the on-line estimate of the fault signal. The classical model of an inverted pendulum on a cart is considered as an application example, in order to highlight the complete design procedure, including the mathematical aspects of the nonlinear disturbance de-coupling method based on the nonlinear differential geometry, as well as the feasibility and efficiency of the proposed approach. Extensive simulations of the benchmark process and Monte Carlo analysis are practical tools for assessing experimentally the robustness and stability properties of the developed fault tolerant control scheme, in the presence of modelling and measurement errors. The fault tolerant control method is also compared with a different approach relying on sliding mode control, in order to evaluate benefits and drawbacks of both techniques. This comparison highlights that the proposed design methodology can constitute a reliable and robust approach for application to real nonlinear processes.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2011, 21, 3; 441-455
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Prospective teachers work on defining quadrilaterals through an exploratory approach
    Autorzy:
    Brunheira, Lina
    da Ponte, Joao Pedro
    Powiązania:
    https://bibliotekanauki.pl/articles/748908.pdf
    Data publikacji:
    2016
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    teacher education
    geometry
    geometric reasoning
    quadrilaterals
    definitions
    exploratory approach
    Opis:
    This research addresses elementary school prospective teachers’ education in geometry and takes place in Portugal, in the context of a geometry course taught by the first author of this paper. We aim to characterize the activity of prospective teachers in defining quadrilaterals as they work on exploratory tasks in a design-based research study for a geometry course at the 2nd year of their teacher education program. The teaching-learning conjecture is based on the relevance of exploratory work, also valuing prospective teachers’ reflection on their learning. We also assume that the activity of defining quadrilaterals plays an important role in developing reasoning, deepens the knowledge of its properties and supports a more complete view of mathematics. Data was gathered from the participants’ reports and portfolios, as well as audio and video records of classroom discussions. The results show that initially the participants had misconceptions about what a definition is, just focusing on the necessary properties of the figures. However, at the end of the sequence of tasks, they were able to take into account that the set of properties has to be sufficient to identify the defined figure, revealing the development of their knowledge. At the end of the sequence, most participants presented correct definitions, using properties that they previously ignored and showing comprehension of the underlying concepts. They produced economical definitions in few cases, and performed better in inductive than deductive reasoning. We conclude that the exploratory work allowed participants to construct their knowledge in a meaningful way and reflection played an important role in making them aware of personal preconceptions and knowledge. In the beginning, the participants analysed definitions strictly focusing on the necessary properties of the figure, which seemed to be simple when the properties related to visible elements or were well known facts. In the final stage of the sequence of tasks, the participants also took into account that the set of properties has to be sufficient to identify the defined figure and, in the construction of definitions, they presented mostly correct definitions using properties that they previously ignored, showing an understanding of the underlying concepts and properties. Doing this process after investigating and classifying quadrilaterals encouraged the prospective teachers to mobilize different kinds of properties and to reason according to the established classifications, which was a very challenging activity.
    Źródło:
    Didactica Mathematicae; 2016, 38
    2353-0960
    Pojawia się w:
    Didactica Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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