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    Wyświetlanie 1-17 z 17
    Tytuł:
    Boundary control of retarded parabolic systems
    Autorzy:
    Krakowiak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/205637.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    boundary control
    retarded argument
    parabolic system
    Opis:
    Optimal boundary control problems for distributed parabolic systems in which retarded arguments appear in the integral form in the state equations are presented. Necessary and sufficient conditions of optimality are derived for the non-homogeneous Dirichlet problem. A simple example of application is also provided.
    Źródło:
    Control and Cybernetics; 2011, 40, 1; 9-23
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays
    Autorzy:
    Kowalewski, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/229185.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    distributed control
    parabolic system
    time delays
    pointwise observation
    Opis:
    Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic equation with the Neumann boundary condition involving multiple time delays are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic cost function with pointwise observation of the state and constrained control are derived.
    Źródło:
    Archives of Control Sciences; 2016, 26, 2; 189-197
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pointwise observation of the state given by complex time lag parabolic system
    Autorzy:
    Kowalewski, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/229580.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    distributed control
    parabolic system
    time lags
    pointwise observation
    Opis:
    Various optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided
    Źródło:
    Archives of Control Sciences; 2017, 27, 1; 77-89
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and nonexistence of solutions for a model of gravitational interaction of particles, III
    Autorzy:
    Biler, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/967095.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    blowing up solutions
    parabolic-elliptic system
    Źródło:
    Colloquium Mathematicum; 1995, 68, 2; 229-239
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Abstract parabolic problem with non-Lipschitz nonlinearity
    Autorzy:
    Cholewa, Jan
    Dlotko, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/1207637.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    dissipative semigroup
    parabolic system
    Cauchy problem
    global attractor
    global solution
    Opis:
    An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.
    Źródło:
    Banach Center Publications; 2000, 52, 1; 73-81
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal Control of a Drying Process with Avoiding Cracks
    Autorzy:
    Galant, Alexander
    Grossman, Christian
    Scheffler, Michael
    Wensch, Jörg
    Powiązania:
    https://bibliotekanauki.pl/articles/1373542.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
    Tematy:
    optimal control
    penalty barrier methods
    control constraints
    coupled parabolic system
    descretization
    Opis:
    The paper deals with the numerical treatment of the optimal control of drying of materials which may lead to cracks. The drying process is controlled by temperature, velocity and humidity of the surrounding air. The state equations dene the humidity and temperature distribution within a simplied wood specimen for given controls. The elasticity equation describes the internal stresses under humidity and temperature changes. To avoid cracks these internal stresses have to be limited. The related constraints are treated by smoothed exact barrier-penalty techniques. The objective functional of the optimal control problem is of tracking type. Further it contains a quadratic regularization by an energy term for the control variables (surrounding air) and barrier-penalty terms. The necessary optimality conditions of the auxiliary problem form a coupled system of nonlinear equations in appropriate function spaces. This optimality system is given by the state equations and the related adjoint equations, but also by an approximate projection onto the admissible set of controls by means of barrier-penalty terms. This system is discretized by nite elements and treated iteratively for given controls. The optimal control itself is performed by quasi-Newton techniques.
    Źródło:
    Schedae Informaticae; 2012, 21; 81-105
    0860-0295
    2083-8476
    Pojawia się w:
    Schedae Informaticae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time-optimal boundary control of a parabolic system with time lags given in integral form
    Autorzy:
    Kowalewski, A.
    Krakowiak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/908398.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    sterowanie optymalne czasowo
    system paraboliczny
    opóźnienie
    time-optimal boundary control
    parabolic system
    time lags
    Opis:
    In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2006, 16, 3; 287-295
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
    Autorzy:
    Biler, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/1289308.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonlinear parabolic-elliptic system
    Cauchy problem
    self-similar solutions
    Opis:
    The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.
    Źródło:
    Studia Mathematica; 1995, 114, 2; 181-205
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time-optimal boundary control of an infinite order parabolic system with time lags
    Autorzy:
    Kowalewski, A.
    Krakowiak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/907944.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    sterowanie optymalne
    sterowanie czasooptymalne
    system paraboliczny
    opóźnienie
    rząd nieskończony
    time-optimal boundary control
    infinite order
    parabolic system
    time lags
    Opis:
    In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2008, 18, 2; 189-198
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A class of nonlocal parabolic problems occurring in statistical mechanics
    Autorzy:
    Biler, Piotr
    Nadzieja, Tadeusz
    Powiązania:
    https://bibliotekanauki.pl/articles/967215.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonlinear boundary conditions
    stationary solutions
    existence of solutions
    parabolic-elliptic system
    Opis:
    We consider parabolic equations with nonlocal coefficients obtained from the Vlasov-Fokker-Planck equations with potentials. This class of equations includes the classical Debye system from electrochemistry as well as an evolution model of self-attracting clusters under friction and fluctuations. The local in time existence of solutions to these equations (with no-flux boundary conditions) and properties of stationary solutions are studied.
    Źródło:
    Colloquium Mathematicum; 1993, 66, 1; 131-145
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Feedback stabilization of one-dimensional parabolic systems related to formations
    Autorzy:
    Sano, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/201667.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Sturm-Liouville operator
    parabolic system
    unbounded output operator
    stabilization
    residual mode filter
    operator Sturm-Liouville
    system paraboliczny
    nieograniczony operator wyjścia
    stabilizacja
    Opis:
    This paper is concerned with the problem of stabilizing one-dimensional parabolic systems related to formations by using finitedimensional controllers of a modal type. The parabolic system is described by a Sturm-Liouville operator, and the boundary condition is different from any of Dirichlet type, Neumann type, and Robin type, since it contains the time derivative of boundary values. In this paper, it is shown that the system is formulated as an evolution equation with unbounded output operator in a Hilbert space, and further that it is stabilized by using an RMF (residual mode filter)-based controller which is of finite-dimension. A numerical simulation result is also given to demonstrate the validity of the finite-dimensional controller.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2015, 63, 1; 295-303
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and nonexistence of solutions for a model of gravitational interaction of particles, I
    Autorzy:
    Biler, Piotr
    Nadzieja, Tadeusz
    Powiązania:
    https://bibliotekanauki.pl/articles/967263.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonlinear boundary conditions
    stationary solutions
    global existence of solutions
    parabolic-elliptic system
    Opis:
    We study the existence of stationary and evolution solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles.
    Źródło:
    Colloquium Mathematicum; 1993, 66, 2; 319-334
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Source localization and sensor placement in environmental monitoring
    Autorzy:
    Khapalov, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/907701.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    lokalizacja źródła
    położenie sensora
    monitoring środowiska
    sterowalność
    identyfikowalność
    równanie paraboliczne
    source localization
    sensor placement
    environmental monitoring
    controllability
    identifiability
    parabolic system
    Opis:
    In this paper we discuss two closely related problems arising in environmental monitoring. The first is the source localization problem linked to the question How can one find an unknown 'contamination source'? The second is an associated sensor placement problem: Where should we place sensors that are capable of providing the necessary 'adequate data' for that? Our approach is based on some concepts and ideas developed in mathematical control theory of partial differential equations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2010, 20, 3; 445-458
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and nonexistence of solutions for a model of gravitational interaction of particles, II
    Autorzy:
    Biler, Piotr
    Hilhorst, Danielle
    Nadzieja, Tadeusz
    Powiązania:
    https://bibliotekanauki.pl/articles/967183.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonlinear boundary conditions
    blowing-up solutions
    global existence of solutions
    parabolic-elliptic system
    Opis:
    We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.
    Źródło:
    Colloquium Mathematicum; 1994, 67, 2; 297-308
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Discrete relaxed method for semilinear parabolic optimal control problem
    Autorzy:
    Chryssoverghi, I.
    Coletsos, J.
    Kokkinis, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/205973.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne
    accumulation points
    discrete optimisation method
    discretization
    distributed control
    minimum principle
    optimal control
    parabolic equations
    partial differential equations
    penalty method
    relaxed control
    semilinear parabolic system
    Opis:
    We consider an optimal control problem for systems governed by semilinear parabolic partial differential equations with control and state constraints, without any convexity assumptions. A discrete optimization method is proposed to solve this problem in its relaxed form which combines a penalized Armijo type method with a finite element discretization and constructs sequences of discrete Gamkrelidze relaxed controls. Under appropriate assumptions, we prove that accumulation points of these sequences satisfy the relaxed Pontryagin necessary conditions for optimality. Moreover, we show that the Gamkrelidze controls thus generated can be replaced by simulating piecewise constant classical controls.
    Źródło:
    Control and Cybernetics; 1999, 28, 2; 157-176
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal regularity and optimal control of a thermoelastic structural acoustic model with point control and clamped boundary conditions
    Autorzy:
    Lebiedzik, C.
    Triggiani, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/970762.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    point control
    parabolic/hyperbolic thermoelastic system
    hyperbolic/hyperbolic chamber/wall coupling
    Opis:
    In this paper we consider point control of a structural acoustic model with thermoelastic effects. The key feature of this paper is that the two-dimensional plate modeling the active wall of the acoustic chamber has clamped boundary conditions. For this case a new optimal regularity result has recently become available (Triggiani, 2008). Using this new result for the plate alone, we derive a sharp (optimal) regularity result for the overall coupled system of wave and thermoelastic plate equations, after overcoming a series of additional technical difficulties. This allows for the study of an optimal control problem of the coupled system.
    Źródło:
    Control and Cybernetics; 2009, 38, 4B; 1461-1499
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
    Autorzy:
    Malec, M.
    Sapa, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/255499.pdf
    Data publikacji:
    2007
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    partial differential equation
    parabolic-elliptic system
    finite difference method
    finite difference scheme
    consistence
    convergence
    stability
    error estimate
    uniqueness
    Opis:
    This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in R1+n. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
    Źródło:
    Opuscula Mathematica; 2007, 27, 2; 259-289
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-17 z 17

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