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    Wyświetlanie 1-14 z 14
    Tytuł:
    Discrete approximation of nonconvex hyperbolic optimal control problems with state constraints
    Autorzy:
    Chryssoverghi, I.
    Bacopoulos, A.
    Coletsos, J.
    Kokkinis, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/205975.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    dyskretyzacja
    nieliniowy układ hiperboliczny
    sterowanie optymalne
    zasada minimum
    discretization
    existence theory
    minimum principle
    nonlinear hyperbolic systems
    optimal control
    relaxed controls
    Opis:
    We consider an opitmal control problem for systems defined by nonlinear hyperbolic partial differential equations with state constraints. Since no convexity assumptions are made on the data, we also consider the control problem in relaxed form. We discretize both the classical and the relaxed problenms by using a finite element method in space and a finite difference scheme in time, the controls being approximated by piecevise constant ones. We develop the existence theory and the necessary conditions for optimality, for the continous and the discrete problems. Finally, we study the behaviour in the limit of discrete optimality, admissibility and extremality properties.
    Źródło:
    Control and Cybernetics; 1998, 27, 1; 29-50
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Domain decomposition in exact controllability of second order hyperbolic systems on 1-d networks
    Autorzy:
    Lagnese, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/205985.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    domain decomposition
    exact controllability
    one-dimensional networks
    second order hyperbolic systems
    Opis:
    This paper is concerned with domain decomposition in exact controllability of a class of linear second order hyperbolic systems on one-dimensional graphs in [R^3] that in particular serve as descriptive models of the dynamics of various multi-link structures consisting of one-dimensional elements, such as networks of Timoshenko beams in [R^3]. We first consider a standard unconstrained optimal control problem in which the cost functional penalizes the deviation of the final state of the global problem from a given target state. A convergent domain decomposition for the optimality system associated with this problem was recently given by G. Leugering. This decomposition depends on the penalty parameter. On each edge of the graph and at each iteration level the local problem is itself the optimality system associated with an unconstrained optimal control problem in which the cost functional penalizes the deviation of the final state of the particular edge from the target state for that edge. The main purpose of this paper is to show that at each iteration level and on each edge the local optimality system converges as the penalty parameter approaches its limit and that the limit system is a domain decomposition for the problem of norm minimum exact control to the target state.
    Źródło:
    Control and Cybernetics; 1999, 28, 3; 531-556
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non-Smoothness in the Asymptotics of Thin Shells and Propagation of Singularities. Hyperbolic Case
    Autorzy:
    Karamian, P.
    Sanchez-Hubert, J
    Sanchez Palencia, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/907888.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    matematyka
    hyperbolic systems
    propagation of singularities
    shells
    Opis:
    We consider the limit behaviour of elastic shells when the relative thickness tends to zero. We address the case when the middle surface has principal curvatures of opposite signs and the boundary conditions ensure the geometrical rigidity. The limit problem is hyperbolic, but enjoys peculiarities which imply singularities of unusual intensity. We study these singularities and their propagation for several cases of loading, giving a somewhat complete description of the solution.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2002, 12, 1; 81-90
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Stability of an Irrigation Canal System
    Autorzy:
    Bounit, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/908097.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    matematyka
    Saint-Venant equation
    dimensionless
    symmetric hyperbolic equation
    internal stability
    transfer functions
    input-output stability
    regular systems
    Opis:
    In this paper we examine the stability of an irrigation canal system. The system considered is a single reach of an irrigation canal which is derived from Saint-Venant's equations. It is modelled as a system of nonlinear partial differential equations which is then linearized. The linearized system consists of hyperbolic partial differential equations. Both the control and observation operators are unbounded but admissible. From the theory of symmetric hyperbolic systems, we derive the exponential (or internal) stability of the semigroup underlying the system. Next, we compute explicitly the transfer functions of the system and we show that the input-output (or external) stability holds. Finally, we prove that the system is regular in the sense of (Weiss, 1994) and give various properties related to its transfer functions.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 4; 453-468
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An output controllability problem for semilinear distributed hyperbolic systems
    Autorzy:
    Zerrik, E.
    Larhrissi, R.
    Bourray, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/929815.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    system o parametrach rozłożonych
    system półliniowy
    system hyperboliczny
    sterowność wymuszona
    punkt stały
    distributed-parameter systems
    semilinear hyperbolic systems
    constrained controllability
    fixed point
    Opis:
    The paper aims at extending the notion of regional controllability developed for linear systems to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder’s fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 4; 437-446
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time-optimal control of infinite order hyperbolic systems with time delays
    Autorzy:
    Kowalewski, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/929954.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    sterowanie czasooptymalne
    systemy hyperboliczne
    opóźnienie czasowe
    time-optimal control
    infinite order
    hyperbolic systems
    time delays
    Opis:
    In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 4; 597-608
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The compact decoupling for system of thermoelasticity in viscoporous media and exponential decay
    Autorzy:
    Głowiński, P.
    Łada, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/115753.pdf
    Data publikacji:
    2011
    Wydawca:
    Fundacja na Rzecz Młodych Naukowców
    Tematy:
    stabilization of solutions
    compact decoupling
    strongly coupled hyperbolic parabolic systems
    uniform decaying
    Opis:
    The problem of exponential decay for solutions of porous-thermoelasticity system, when time t ->∞ is studied. For sufficiently small values of parameter of intensity of elasticity-porosity interactions the exponential decaying is established. The idea of compact decoupling is applied for the system of equations. Exponential decay is proved first for the simpler decoupled system, then the prop erty is derived for the original system.
    Źródło:
    Challenges of Modern Technology; 2011, 2, 4; 3-6
    2082-2863
    2353-4419
    Pojawia się w:
    Challenges of Modern Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Kinetic-induced moment systems for the Saint-Venant equations
    Autorzy:
    Gil Montoya, D. C.
    Struckmeier, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/1933941.pdf
    Data publikacji:
    2013
    Wydawca:
    Politechnika Gdańska
    Tematy:
    Saint-Venant equations
    shallow water equations
    Boltzmann equation
    hyperbolic conservation laws
    kinetic models
    kinetic representations
    relaxion systems
    shock waves
    rarefaction waves
    Opis:
    Based on the relation between kinetic Boltzmann-like transport equations and nonlinear hyperbolic conservation laws, we derive kinetic-induced moment systems for the spatially one-dimensional shallow water equations (the Saint-Venant equations). Using Chapman-Enskog-like asymptotic expansion techniques in terms of the relaxation parameter of the kinetic equation, the resulting moment systems are asymptotically closed without the need for an additional closure relation. Moreover, the new second order moment equation for the (asymptotically) third order system may act as a monitoring function to detect shock and rarefaction waves, which we confirm by a number of numerical experiments.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2013, 17, 1-2; 63-90
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Impact oscillators : fundamentals and applications
    Autorzy:
    Trzaska, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/242533.pdf
    Data publikacji:
    2015
    Wydawca:
    Instytut Techniczny Wojsk Lotniczych
    Tematy:
    nonlinear systems
    impact oscillators
    nonsmooth excitations
    nonsmooth time transformation
    hyperbolic numbers
    Opis:
    The paper presents results of the analysis of nonlinear oscillators with nonsmooth elements and nonlinear systems with nonsmooth forcing components. Main attention has been focused on highlighting specific properties of nonsmooth systems compared to their smooth counterparts. Nonsmooth transformation of the time variable and the replacement of initial issues by boundary problems have been taken as the base for the analytical method. Results of numerical simulations and computing in the form of graphs of displacements and velocity waveforms and attractors are presented. To fully identify the system's behaviour and meet high performance specifications recourse to model all dynamics together with their interactions has been taken into account. Strong interactions among the parts of the system are considered and the phenomenon of the impact is exhibited. It has been found that non-smooth dynamical systems reveal significant wealth of nonlinear phenomena, including a chaotic, that are unique to this potentially important class of nonlinear systems. In non-smooth systems at small change of parameters, a sudden transition from a stable periodic oscillation to the full range of chaotic oscillations may often occur. The dynamics of nonsmooth oscillations with shock external forcing is analysed by using a relatively new mathematical tool, which appears to be hyperbolic algebra. The key idea of this tool is steeped in of non-smooth time transformations (NSTT) for strongly nonlinear, but still smooth models.
    Źródło:
    Journal of KONES; 2015, 22, 1; 307-314
    1231-4005
    2354-0133
    Pojawia się w:
    Journal of KONES
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient
    Autorzy:
    Farahani, H. S.
    Telabi, H. A.
    Baghermenhaj, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/229317.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    drilling systems
    adaptive control
    hyperbolic partial differential equations
    wave equation
    boundary control
    Opis:
    The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.
    Źródło:
    Archives of Control Sciences; 2017, 27, 1; 63-76
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Speeds of convergence of orbits of non-elliptic semigroups of holomorphic self-maps of the unit disk
    Autorzy:
    Bracci, Filippo
    Powiązania:
    https://bibliotekanauki.pl/articles/1395934.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Semigroups of holomorphic functions
    hyperbolic geometry
    dynamical systems
    Opis:
    We introduce three quantities related to orbits of non-elliptic continuous semigroups of holomorphic self-maps of the unit disk, the total speed, the orthogonal speed, and the tangential speed and show how they are related and what can be inferred from those.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2019, 73, 2
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions
    Autorzy:
    Krug, Richard
    Leugering, Günter
    Martin, Alexander
    Schmidt, Martin
    Weninger, Dieter
    Powiązania:
    https://bibliotekanauki.pl/articles/2183473.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    time-domain decomposition
    optimal control
    semilinear hyperbolic systems
    convergence
    Opis:
    In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.
    Źródło:
    Control and Cybernetics; 2021, 50, 4; 427--455
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Extremal problems for second order hyperbolic systems involving multiple time delays
    Autorzy:
    Kowalewski, Adam
    Powiązania:
    https://bibliotekanauki.pl/articles/27312006.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    optimal control theory
    boundary control
    second order hyperbolic systems
    multiple time delays
    electric long lines
    Opis:
    Extremal problems for multiple time delay hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which multiple time delays appear both in the state equations and in the Neumann boundary conditions are solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.
    Źródło:
    Archives of Control Sciences; 2023, 33, 1; 101--126
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Extremal Problems for Second Order Hyperbolic Systems with Boundary Conditions Involving Multiple Time-Varying Delays
    Problemy ekstremalne dla systemów hiperbolicznych drugiego rzędu z warunkami brzegowymi, w których występują wielokrotne zmienne opóźnienia czasowe
    Autorzy:
    Kowalewski, Adam
    Powiązania:
    https://bibliotekanauki.pl/articles/27312434.pdf
    Data publikacji:
    2023
    Wydawca:
    Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
    Tematy:
    boundary control
    second order hyperbolic systems
    multiple time-varying delays
    sterowanie brzegowe
    systemy hiperboliczne drugiego rzędu
    wielokrotne zmienne opóźnienia czasowe
    Opis:
    Extremal problems for second order hyperbolic systems with multiple time-varying lags are presented. An optimal boundary control problem for distributed hyperbolic systems with boundary conditions involving multiple time-varying lags is solved. The time horizon is fixed. Making use of Dubovitski-Milyutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.
    Zaprezentowano ekstremalne problemy dla systemów hiperbolicznych z wielokrotnymi zmiennymi opóźnieniami czasowymi. Rozwiązano problem optymalnego sterowania brzegowego dla systemów hiperbolicznych drugiego rzędu, w których wielokrotne zmienne opóźnienia czasowe występują w warunkach brzegowych typu Neumanna. Tego rodzaju równania stanowią w liniowym przybliżeniu uniwersalny model matematyczny procesów fizycznych, w których ma miejsce przesyłanie sygnałów na odległość w liniach długich typu elektrycznego, hydraulicznego i innych. Korzystając z metody Dubowickiego-Milutina wyprowadzono warunki konieczne i wystarczające optymalności dla problemu liniowo-kwadratowego.
    Źródło:
    Pomiary Automatyka Robotyka; 2023, 27, 2; 69--76
    1427-9126
    Pojawia się w:
    Pomiary Automatyka Robotyka
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-14 z 14

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