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    Wyświetlanie 1-13 z 13
    Tytuł:
    The lq-controller synthesis problem for infinite-dimensional systems in factor form
    Autorzy:
    Grabowski, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/254801.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    control of infinite-dimensional systems
    semigroups
    infinite-time lq-control problem
    Opis:
    The general lq-problem with infinite time horizon for well-posed infinite-dimensional systems has been investigated by George Weiss and Martin Weiss and by Olof Staffans with a complement by Kalle Mikkola and Olof Staffans. Our aim in this paper is to present a solution of a general lq-optimal controller synthesis problem for infinite-dimensional systems in factor form. The systems in factor form are an alternative to additive models, used in the theory of well-posed systems, which rely on leading the analysis exclusively within the basic state space. As a result of applying the simplified analysis in terms of the factor systems and an another derivation technique, we obtain an equivalent, however, astonishingly not the same formulae expressing the optimal controller in the time-domain and the method of spectral factorization. The results are illustrated by two examples of the construction of both the optimal control and optimal controller for some standard lq-problems met in literature: a control problem for a class of boundary controlled hyperbolic equations initiated by Chapelon and Xu, to which we give full solution and an example of the synthesis of the optimal control/controller for the standard lq-problem with infinite-time horizon met in the problem of improving a river water quality by artificial aeration, proposed by Zołopa and the author.
    Źródło:
    Opuscula Mathematica; 2013, 33, 1; 29-79
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The LQ/KYP problem for infinite-dimensional systems
    Autorzy:
    Grabowski, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255449.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    control of infinite-dimensional systems
    semigroups
    infinite-time LQ-control problem
    Lur’e feedback systems
    Opis:
    Our aim is to present a solution to a general linear-quadratic (LQ) problem as well as to a Kalman-Yacubovich-Popov (KYP) problem for infinite-dimensional systems with bounded operators. The results are then applied, via the reciprocal system approach, to the question of solvability of some Lur'e resolving equations arising in the stability theory of infinite-dimensional systems in factor form with unbounded control and observation operators. To be more precise the Lur’e resolving equations determine a Lyapunov functional candidate for some closed-loop feedback systems on the base of some properties of an uncontrolled (open-loop) system. Our results are illustrated in details by an example of a temperature of a rod stabilization automatic control system.
    Źródło:
    Opuscula Mathematica; 2017, 37, 1; 21-64
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Small-gain theorem for a class of abstract parabolic systems
    Autorzy:
    Grabowski, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255288.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    control of infinite-dimensional systems semigroups
    infinite-time LQ-control problem
    Lur'e feedback systems
    Opis:
    We consider a class of abstract control system of parabolic type with observation which the state, input and output spaces are Hilbert spaces. The state space operator is assumed to generate a linear exponentially stable analytic semigroup. An observation and control action are allowed to be described by unbounded operators. It is assumed that the observation operator is admissible but the control operator may be not. Such a system is controlled in a feedback loop by a controller with static characteristic being a globally Lipschitz map from the space of outputs into the space of controls. Our main interest is to obtain a perturbation theorem of the small-gain-type which guarantees that null equilibrium of the closed-loop system will be globally asymptotically stable in Lyapunov's sense.
    Źródło:
    Opuscula Mathematica; 2018, 38, 5; 651-680
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729348.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    optimal control
    stochastic systems
    infinite dimension
    HJB equation
    stationary feedback control
    Opis:
    In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 1; 97-126
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of a class of infinite dimensional systems with age structure
    Autorzy:
    Maity, Debayan
    Tucsnak, Marius
    Zuazua, Enrique
    Powiązania:
    https://bibliotekanauki.pl/articles/1839149.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    infinite dimensional linear system
    age structure
    admissible control operator
    null controllability
    population dynamics
    Opis:
    Given a linear dynamical system, we investigate the linear infinite dimensional system obtained by grafting an age structure. Such systems appear essentially in population dynamics with age structure when phenomena like spatial diffusion or transport are also taken into consideration. We first show that the new system preserves some of the wellposedness properties of the initial one. Our main result asserts that if the initial system is null controllable in a time small enough then the structured system is also null controllable in a time depending on the various involved parameters.
    Źródło:
    Control and Cybernetics; 2019, 48, 2; 231-260
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Comparison of direct and perturbation approaches to analysis of infinite-dimensional feedback control systems
    Autorzy:
    Grabowski, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/1838216.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    perturbation
    semigroups
    systems in factor form
    spectral operators
    Opis:
    For general boundary control systems in factor form some necessary and sufficient conditions for generation of an analytic exponentially stable semigroup are proposed in both direct and perturbation forms for comparison. The direct approach is applicable to operators with the numerical range satisfying certain additional conditions. In particular, it applies to operators similar to convexoids and therefore it generalizes previous results known for hyponormal operators. The perturbation result (indirect approach) is derived and formulated as an exponential stability robustness result using the frequence-domain considerations. It is expressed in terms of some estimates of the resolvent growth over the open right complex half-plane and compared with some recent results. The analysis is illustrated in detail with examples of an unloaded and loaded electric RC-transmission line with proportional negative feedback.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 195-218
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Well-posedness and stability analysis of hybrid feedback systems using Shkalikovs theory
    Autorzy:
    Grabowski, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/254925.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    infinite-dimensional control systems
    semigroups
    spectral methods
    Riesz bases
    Opis:
    The modern method of analysis of the distributed parameter systems relies on the transformation of the dynamical model to an abstract differential equation on an appropriately chosen Banach or, if possible, Hilbert space. A linear dynamical model in the form of a first order abstract differential equation is considered to be well-posed if its right-hand side generates a strongly continuous semigroup. Similarly, a dynamical model in the form of a second order abstract differential equation is well-posed if its right-hand side generates a strongly continuous cosine family of operators. Unfortunately, the presence of a feedback leads to serious complications or even excludes a direct verification of assumptions of the Hille-Phillips-Yosida and/or the Sova-Fattorini Theorems. The class of operators which are similar to a normal discrete operator on a Hilbert space describes a wide variety of linear operators. In the papers [12, 13] two groups of similarity criteria for a given hybrid closed-loop system operator are given. The criteria of the first group are based on some perturbation results, and of the second, on the application of Shkalikov's theory of the Sturm-Liouville eigenproblems with a spectral parameter in the boundary conditions. In the present paper we continue those investigations showing certain advanced applications of the Shkalikov's theory. The results are illustrated by feedback control systems examples governed by wave and beam equations with increasing degree of complexity of the boundary conditions.
    Źródło:
    Opuscula Mathematica; 2006, 26, 1; 45-97
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximate constrained controllability of mechanical system
    Sterowanie minimalno-czasowe manipulatorów hydraulicznych po zadanej ścieżce
    Autorzy:
    Klamka, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/279817.pdf
    Data publikacji:
    2005
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    linear infinite-dimensional control systems
    mechanical flexible structure vibratory systems
    controllability of abstract dynamical systems
    Opis:
    In the present paper approximate constrained controllability of linear abstract second-order infinite-dimensional dynamical control systems is considered. First, fundamental definitions and notions are recalled. Next it is proved, using the so-called frequency-domain method, that approximate constrained controllability of second-order dynamical control system can be verified by the approximate constrained controllability conditions for the simplified, suitably defined first-order linear dynamical control system. General results are then applied for approximate constrained controllability investigation of mechanical flexible structure vibratory dynamical system. Some special cases are also considered. Moreover, many remarks, comments and corollaries on the relationships between different concepts of approximate controllability are given. Finally, the obtained results are applied for investigation of approximate constrained controllability for flexible mechanical structure. In this case linear second-order partial differential state equation describes the transverse motion of an elastic beam which occupies the given finite interval.
    Praca przedstawia metodę optymalizacji minimalno-czasowej ruchów manipulatorów hydraulicznych, po zadanej ścieżce członu roboczego. Zakładane jest, że ścieżka członu roboczego jednoznacznie określa odpowiadającą jej ścieżkę manipulatora w zmiennych uogólnionych. Optymalizacja sprowadza się wówczas do znalezienia optymalnego rozkładu parametru ścieżki w czasie. Proponowana metoda optymalizacji polega na przybliżeniu ciągłego rozkładu parametru zbiorem punktów, a następnie znalezieniu ich optymalnych położeń metodami programowania nieliniowego z ograniczeniami. Zakładana jest przy tym nieściśliwość cieczy hydraulicznej, w celu przyspieszenia obliczeń. Załączone są wyniki przykładowych optymalizacji, wykonanych na modelu trójczłonowej koparki hydraulicznej.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2005, 43, 3; 539-554
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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:
    Different Models of Chemotherapy Taking Into Account Drug Resistance Stemming from Gene Amplification
    Autorzy:
    Śmieja, J.
    Świerniak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/908161.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    medycyna
    automatyka
    biomedical modelling
    infinite dimensional systems
    multivariable control
    Opis:
    This paper presents an analysis of some class of bilinear systems that can be applied to biomedical modelling. It combines models that have been studied separately so far, taking into account both the phenomenon of gene amplification and multidrug chemotherapy in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix whose form allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the other is infinite dimensional and tridiagonal. A methodology of the analysis of such models, based on system decomposition, is presented. An optimal control problem is defined in the l1 space. In order to derive necessary conditions for optimal control, the model description is transformed into an integro-differential form. Finally, biomedical implications of the obtained results are discussed.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 297-305
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Infinite dimensional uncertain dynamic systems on Banach spaces and their optimal output feedback control
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729515.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    partially observed
    uncertain systems
    stochastic systems
    operator valued functions
    feedback operators
    existence of optimal operators in the presence of uncertainty
    Opis:
    In this paper we consider a class of partially observed semilinear dynamic systems on infinite dimensional Banach spaces subject to dynamic and measurement uncertainty. The problem is to find an output feedback control law, an operator valued function, that minimizes the maximum risk. We present a result on the existence of an optimal (output feedback) operator valued function in the presence of uncertainty in the system as well as measurement. We also consider uncertain stochastic systems and present similar results on the question of existence of optimal feedback laws.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 1; 65-87
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal multidrug treatment in the presence of drug resistance stemming from gene amplification
    Autorzy:
    Śmieja, J.
    Świerniak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/332869.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Śląski. Wydział Informatyki i Nauki o Materiałach. Instytut Informatyki. Zakład Systemów Komputerowych
    Tematy:
    nieskończenie wymiarowy system
    optymalna kontrola
    modelowanie biomedyczne
    infinite dimensional systems
    optimal control
    biomedical modeling
    Opis:
    The paper is concerned with development of optimal treatment protocols that take into account both action of several drugs and the evolution of drug resistance. It is a result of analysis of evolution of drug resistance in cancer population but presented methodology can be applied in any case involving drug resistance stemming from gene amplification. First, a biological background is given. In subsequent sections of the paper, the developed technique is presented and some early analytical results, which form a basis for more precise modeling, are shown. Afterwards, the model description is transformed into a vector integro-differential equation, which makes it possible to define necessary conditions of optimal solution to the minimization problem arising from the search for the optimal treatment. Finally, some remarks on the model applicability are presented.
    Źródło:
    Journal of Medical Informatics & Technologies; 2002, 3; MI13-19
    1642-6037
    Pojawia się w:
    Journal of Medical Informatics & Technologies
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The motion planning problem and exponential stabilization of a heavy chain. Part II
    Autorzy:
    Grabowski, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255394.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    infinite-dimensional control systems
    semigroups
    motion planning problem
    exponential stabilization
    spectral methods
    Riesz bases
    exact observability
    Opis:
    This is the second part of paper [8], where a model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [8] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was also shown that the exponential stability can be achieved by applying a stabilizer of the colocated-type. The proof used the method of Lyapunov functionals. In the present paper, we give other two proofs of the exponential stability, which provides an additional intrinsic insight into the exponential stabilizability mechanism. The first proof makes use of some spectral properties of the system. In the second proof, we employ some relationships between exponential stability and exact observability.
    Źródło:
    Opuscula Mathematica; 2008, 28, 4; 481-505
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-13 z 13

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