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    Tytuł:
    Optimal control of constrained delay-differential inclusions with multivalued initial conditions
    Autorzy:
    Mordukhovich, B. S.
    Wang, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/970519.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    aproksymacja dyskretna
    warunek konieczny optymalności
    analiza wariacyjna
    stabilność
    optymalizacja niegładka
    różniczkowanie uogólnione
    delay-differential inclusions
    discrete approximations
    necessary optimality conditions
    variational analysis
    stability
    nonsmooth optimization
    generalized differentiation
    Opis:
    This paper studies a general optimal control problem for nonconvex delay-differential inclusions with endpoint constraints. In contrast to previous publications on this topic, we incorporate time-dependent set constraints on the initial interval, which are specific for systems with delays and provide an additional source for optimization. Our variational analysis is based on well-posed discrete approximations of constrained delay-differential inclusions by a family of time-delayed systems with discrete dynamics and perturbed constraints. Using convergence results for discrete approximations and advanced tools of nonsmooth variational analysis, we derive necessary optimality conditions for constrained delay-differential inclusions in both Euler-Lagrange and Hamiltonian forms involving nonconvex generalized differential constructions for nonsmooth functions, sets, and set-valued mappings.
    Źródło:
    Control and Cybernetics; 2003, 32, 3; 585-609
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions
    Autorzy:
    Mordukhovich, B. S.
    Wang, D.
    Wang, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/969562.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    discrete approximations
    optimal control
    variational analysis
    endpoint constraints
    delay-differential inclusions
    multivalued initial conditions
    extended Euler-Lagrange formalism
    generalized differentiation
    Banach and Asplund spaces
    necessary optimality conditions
    Opis:
    This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except for some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the three major parts: (a) constructing a well-posed sequence of discrete-time problems that approximate in an appropriate sense the original continuous-time problem of dynamic optimization; (b) deriving necessary optimality conditions for the approximating discrete-time problems by reducing them to infinite-dimensional problems of mathematical programming and employing then generalized differential calculus; (c) passing finally to the limit in the obtained results for discrete approximations to establish necessary conditions for the given optimal solutions to the original problem. This method is fully realized in the delay-differential systems under consideration.
    Źródło:
    Control and Cybernetics; 2008, 37, 2; 393-428
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results for delay second order differential inclusions
    Autorzy:
    Azzam-Laouir, Dalila
    Haddad, Tahar
    Powiązania:
    https://bibliotekanauki.pl/articles/729461.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    boundary-value problems
    delay differential inclusions
    fixed point
    retract
    Opis:
    In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 133-146
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay
    Autorzy:
    Gomaa, Adel Mahmoud
    Powiązania:
    https://bibliotekanauki.pl/articles/746625.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Differential inclusions
    mutifunctions
    measures of noncompactness
    delay
    Opis:
    We consider the problem \(\dot{x}(t) \in A(t)x(t) + F (t, θ_t x))\) a.e. on \([0, b]\), \(x = \kappa\) on \([-d, 0]\) in a Banach space \(E\), where \(\kappa\) belongs to the Banach space, \(C_E ([-d, 0])\), of all continuous functions from \([-d, 0]\) into \(E\). A multifunction \(F\) from \([0, b] \times C_E ([-d, 0])\) into the set, \(P_{f_c} (E)\), of all nonempty closed convex subsets of \(E\) is weakly sequentially hemi-continuous, \(θ_t x(s) = x(t + s)\) for all \(s \in [-d, 0]\) and \(\{A(t) : 0 \leq t \leq b\}\) is a family of densely defined closed linear operators generating a continuous evolution operator \(S(t, s)\). Under a generalization of the compactness assumptions, we prove an existence result and give some topological properties of our solution sets that generalizes earlier theorems by Papageorgiou, Rolewicz, Deimling, Frankowska and Cichoń.
    Źródło:
    Commentationes Mathematicae; 2008, 48, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces
    Autorzy:
    Hammouche, Hadda
    Guerbati, Kaddour
    Benchohra, Mouffak
    Abada, Nadjat
    Powiązania:
    https://bibliotekanauki.pl/articles/729312.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional calculus
    caputo fractional derivative
    multivalued map
    differential inclusions
    mild solution
    fixed point
    Opis:
    In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 149-170
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and solution sets of impulsive functional differential inclusions with multiple delay
    Autorzy:
    Helal, M.
    Ouahab, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/256052.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    impulsive functional differential inclusions
    decomposable set
    parameter differential inclusions
    AR-set
    control theory
    Opis:
    In this paper, we present some existence results of solutions and study the topological structure of solution sets for the following first-order impulsive neutral functional differential inclusions with initial condition: [formula] where J : = [0; b] and 0 = t0 < t1 < ... < tm < tm+1 = b (m ∈ N*), F is a set-valued map and g is single map. The functions Ik characterize the jump of the solutions at impulse points tk (k = 1, ... m). Our existence result relies on a nonlinear alternative for compact u.s.c. maps. Then, we present some existence results and investigate the compactness of solution sets, some regularity of operator solutions and absolute retract (in short AR). The continuous dependence of solutions on parameters in the convex case is also examined. Applications to a problem from control theory are provided.
    Źródło:
    Opuscula Mathematica; 2012, 32, 2; 249-283
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional integro-differential inclusions with state-dependent delay
    Autorzy:
    Aissani, Khalida
    Benchohra, Mouffak
    Ezzinbi, Khalil
    Powiązania:
    https://bibliotekanauki.pl/articles/729499.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional integro-differential inclusions
    Caputo fractional derivative
    mild solution
    multivalued map
    Bohnenblust-Karlin's fixed point
    state-dependent delay
    Opis:
    In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 2; 153-167
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Delay perturbed evolution problems involving time dependent subdifferential operators
    Autorzy:
    Saïdi, Soumia
    Yarou, Mustapha
    Powiązania:
    https://bibliotekanauki.pl/articles/729544.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Differential inclusions
    subdifferential operator
    Lipschitz functions
    set-valued map
    delay
    perturbation
    absolutely continuous map
    Opis:
    We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 1; 61-87
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces
    Autorzy:
    Abada, Nadjat
    Benchohra, Mouffak
    Hammouche, Hadda
    Ouahab, Abdelghani
    Powiązania:
    https://bibliotekanauki.pl/articles/729413.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    semilinear functional differential inclusions
    impulses
    mild solution
    fixed point
    controllability
    extrapolation space
    nondensely defined operator
    Opis:
    In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 329-347
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An abstract Cauchy problem for higher order functional differential inclusions with infinite delay
    Autorzy:
    Ke, Tran
    Obukhovskii, Valeri
    Wong, Ngai-Ching
    Yao, Jen-Chih
    Powiązania:
    https://bibliotekanauki.pl/articles/729357.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Cauchy problem
    functional differential inclusion
    infinite delay
    higher order
    existence family
    phase space
    fixed point
    multivalued map
    measure of noncompactness
    condensing map
    Opis:
    The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 2; 199-229
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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