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Wyszukujesz frazę "operator measures" wg kryterium: Temat

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    Wyświetlanie 1-4 z 4
    Tytuł:
    Vector and operator valued measures as controls for infinite dimensional systems: optimal control
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729468.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    evolution equations
    Banach spaces
    operator valued measures
    strong operator topology
    existence of solutions
    optimal control
    Opis:
    In this paper we consider a general class of systems determined by operator valued measures which are assumed to be countably additive in the strong operator topology. This replaces our previous assumption of countable additivity in the uniform operator topology by the weaker assumption. Under the relaxed assumption plus an additional assumption requiring the existence of a dominating measure, we prove some results on existence of solutions and their regularity properties both for linear and semilinear systems. Also presented are results on continuous dependence of solutions on operator and vector valued measures, and other parameters determining the system which are then used to prove some results on control theory including existence and necessary conditions of optimality. Here the operator valued measures are treated as structural controls. The paper is concluded with some examples from classical and quantum mechanics and a remark on future direction.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 95-131
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of systems determined by strongly nonlinear operator valued measures
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729396.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    evolution equations
    strongly nonlinear operator valued measures
    existence of solutions
    regularity properties
    optimal control
    Opis:
    In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by
    dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T]
    where A is a strongly nonlinear operator valued measure mapping Σ × V to V* with Σ denoting the sigma algebra of subsets of the set I and f is a nonlinear operator mapping I × H to H, γ is a countably additive bounded positive measure and the control u is a suitable vector measure. We present existence, uniqueness and regularity properties of weak solutions and then prove the existence of optimal controls (vector valued measures) for a class of control problems.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 165-189
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak compactness in the space of operator valued measures $M_ba(Σ,(X,Y))$ and its applications
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729361.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    space of operator valued measures
    weak compactness
    semigroups of bounded linear operators
    optimal structural control
    Opis:
    In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures $M_{ba}(Σ,(X,Y))$. This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures $M_{ba}(Σ,₁(X,Y))$. This result has interesting applications in optimization and control theory as illustrated by several examples.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 2; 231-247
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topological dual of $B_∞(I, ₁(X,Y))$ with application to stochastic systems on Hilbert space
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729390.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    representation theory
    topological dual
    finitely additive operator-valued measures
    polish space
    Hilbert space
    stochastic systems
    structural control
    uncertainty abatement
    Opis:
    In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural control, is to be chosen so as to minimize fluctuation (volatility). Both existence of optimal policy and necessary conditions of optimality are presented including a conceptual algorithm.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 67-90
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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