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    Wyświetlanie 1-13 z 13
    Tytuł:
    Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case
    Autorzy:
    Dzieliński, A.
    Czyronis, P. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/201358.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order systems
    discrete-time systems
    optimal control
    linear quadratic performance index
    Opis:
    The optimization problem for fractional discrete-time systems with a quadratic performance index has been formulated and solved. The case of fixed final time and a free final state has been considered. A method for numerical computation of optimization problems has been presented. The presented method is a generalization of the well-known method for discrete-time systems of integer order. The efficiency of the method has been demonstrated on numerical examples and illustrated by graphs. Graphs also show the differences between the fractional and classical (standard) systems theory. Results for other cases of the fractional system order (coefficient ) and not illustrated with numerical examples have been obtained through a computer algorithm written for this purpose.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 3; 681-690
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of linear convex combination of linear discrete-time fractional systems
    Autorzy:
    Kaczorek, Tadeusz
    Klamka, Jerzy
    Dzieliński, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/2173704.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order systems
    controllability
    linear convex combination
    system ułamkowego rzędu
    sterowność
    kombinacja wypukła liniowa
    Opis:
    In this paper the controllability properties of the convex linear combination of fractional, linear, discrete-time systems are characterized and investigated. The notions of linear convex combination and controllability in the context of fractional-order systems are recalled. Then, the controllability property of such a linear combination of discrete-time, linear fractional systems is proven. Further, the reduction of an infinite problem of transition matrix derivation is reduced to a finite one, which greatly simplifies the numerical burden of the controllability issue. Examples of controllable and uncontrollable, single-input, linear systems are presented. The possibility of extension of the considerations to multi-input systems is shown.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2022, 70, 5; art. no. e143102
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Results on the controllability of Caputo’s fractional descriptor systems with constant delays
    Autorzy:
    Beata, Sikora
    Powiązania:
    https://bibliotekanauki.pl/articles/27311455.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    descriptor systems
    fractional-order systems
    Caputo derivative
    Drazin inverse
    controllability
    pochodna Caputo
    odwrotność Drazina
    sterowalność
    system deskryptorowy
    system ułamkowego rzędu
    Opis:
    The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e146287
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Caputo vs. Caputo-Fabrizio operators in modeling of heat transfer process
    Autorzy:
    Oprzędkiewicz, K.
    Mitkowski, W.
    Gawin, E.
    Dziedzic, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/200001.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order systems
    Caputo operator
    Caputo-Fabrizio operator
    non singular kernel operator
    heat transfer
    simplex method
    transfer ciepła
    metoda simplex
    system ułamkowy
    pochodna Caputo
    Opis:
    In the paper two non-integer order, state space models of heat transfer process are compared. The first uses a known Caputo operator and the second – a new operator proposed by Caputo and Fabrizio in 2015. Both discussed models are modifications of a known, integer order, state space, semigroup model of heat transfer process. Parameters of both models were identified by means of optimization of MSE cost function with the use of simplex method, available in MATLAB. Both proposed models have been compared in the aspect of accuracy and convergence. Analytical and numerical results show that the Caputo-Fabrizio model is faster convergent and easier to implement than the Caputo model. However, its accuracy in the sense of MSE cost function is worse.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 501-507
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator
    Autorzy:
    Oprzędkiewicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2173561.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order systems
    heat transfer equation
    fractional order state equation
    fractional order backward difference
    Grünwald-Letnikov operator
    practical stability
    systemy ułamkowego rzędu
    równanie wymiany ciepła
    równanie stanu rzędu ułamkowego
    różnica wsteczna rzędu ułamkowego
    operator Grünwalda-Letnikowa
    stabilność praktyczna
    Opis:
    In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; art. no. e135843
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator
    Autorzy:
    Oprzędkiewicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2090693.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order systems
    heat transfer equation
    fractional order state equation
    fractional order backward difference
    Grünwald-Letnikov operator
    practical stability
    systemy ułamkowego rzędu
    równanie wymiany ciepła
    równanie stanu rzędu ułamkowego
    różnica wsteczna rzędu ułamkowego
    operator Grünwalda-Letnikowa
    stabilność praktyczna
    Opis:
    In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; e135843, 1--10
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Remarks on five equivalent forms of the fractional – order backward – difference
    Autorzy:
    Ostalczyk, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/202441.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    discrete systems
    fractional order backward difference
    fractional - order backward sum
    Opis:
    In this paper a fractional-order backward-difference/sum (FOBD/S) equivalent formulae are considered. From the Gr¨unwald- Letnikov (GL - FOBD) definition formula and its Horner equivalent form one derives the Riemann-Liouville FOBD (RL - FOBD). Also the Caputo and polynomial-like forms are defined. All forms may be useful in real-time calculations (in the evaluation of digital control strategies) due to the reduction of fractional orders. The investigations are illustrated by a numerical example.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 2; 271-278
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator
    Autorzy:
    Oprzędkiewicz, K.
    Dziedzic, K.
    Więckowski, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/200257.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non integer order systems
    heat transfer
    fractional order state equation
    fractional order backward difference
    Grünwald-Letnikov operator
    convergence
    Opis:
    The paper is intented to show a new, state space, discrete, non integer order model of a one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space model and it uses the discrete Grünwald-Letnikov operator to express the fractional order difference with respect to time. Stability and spectrum decomposition for the proposed model are recalled, the accuracy and convergence are analyzed too. The convergence of the proposed model does not depend on parameters of heater and measuring sensors. The dimension of the model assuring stability and predefined rate of convergence and stability is estimated. Analytical results are confirmed by experiments.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 5; 905-914
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system
    Autorzy:
    Kaczorek, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/201870.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional descriptor linear systems
    design
    reduced order
    descriptor
    fractional
    observer
    redukcja rzędu
    projekt
    deskryptor
    obserwator
    Opis:
    Fractional descriptor reduced-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is given and is demonstrated on two numerical examples.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 4; 889-895
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stabilization of autonomous linear time invariant fractional order derivative switched systems with different derivative in subsystems
    Autorzy:
    Balochian, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/200478.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    linear time invariant fractional order derivative
    switching systems
    linear matrix inequality
    LMI
    Opis:
    In this paper, the stabilization problem of a autonomous linear time invariant fractional order (LTI-FO) switched system with different derivative order in subsystems is outlined. First, necessary and sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems based on the convex analysis and linear matrix inequality (LMI) for two subsystems is presented and proved. Also, sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems for more than two subsystems is proved. Then a sliding sector is designed for each subsystem of the LTI-FO switched system. Finally, a switching control law is designed to switch the LTI-FO switched system among subsystems to ensure the decrease of the norm of the switched system. Simulation results are given to show the effectiveness of the proposed variable structure controller.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 3; 495-503
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non integer order, state space model of heat transfer process using Atangana-Baleanu operator
    Autorzy:
    Oprzędkiewicz, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/202078.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non integer order systems
    heat transfer equation
    infinite dimensional systems
    fractional order state equation
    Riesz operator
    Caputo operator
    Atangana-Baleanu operator
    Opis:
    In the paper a new, state space, non integer order model of an one-dimensional heat transfer process is proposed. The model uses a new operator with Mittag-Leffler kernel, proposed by Atangana and Beleanu. The non integer order spatial derivative is expressed by Riesz operator. Analytical formula of the step response is given, the convergence of the model is discussed too. Theoretical results are verified by experiments.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 1; 43-50
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non integer order, state space model of heat transfer process using Caputo-Fabrizio operator
    Autorzy:
    Oprzędkiewicz, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/201464.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non-integer order systems
    heat transfer equation
    infinite dimensional systems
    fractional order state equation
    Riesz operator
    Caputo operator
    Caputo-Fabrizio operator
    systemy niecałkowitego rzędu
    układ niecałkowitego rzędu
    twierdzenie Riesza
    pochodna Caputo
    Opis:
    The paper is intended to show a new state space, non integer order model of an one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space semigroup model. The fractional order derivative with respect to time is by a new operator proposed by Caputo and Fabrizio, the non integer order spatial derivative is expressed by Riesz operator. The Caputo-Fabrizio operator can be directly implementated using MATLAB, because it does not require us to apply any approximation. Analytical formulae of step response are given, the system decomposition was discussed also. Main results from the paper show that the use of Caputo Fabrizio operator allows us to obtain the simple in implementation and analysis model of the considered heat transfer process. The accuracy of the proposed model in the sense of a MSE cost function is satisfying.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 3; 249-255
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The positivity of the fractional order model of a two-dimensional temperature field
    Autorzy:
    Oprzędkiewicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/27311454.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    heat transfer equation
    fractional order state equation
    Caputo operator
    positivity
    thermal camera
    non-integer order systems
    równanie wymiany ciepła
    równanie stanu rzędu ułamkowego
    operator Caputo
    kamera termowizyjna
    systemy niecałkowitego rzędu
    dodatniość
    Opis:
    The paper presents analysis of the positivity for a two-dimensional temperature field. The process under consideration is described by the linear, infinite-dimensional, noninteger order state equation. It is derived from a two-dimensional parabolic equation with homogenous Neumann boundary conditions along all borders and homogenous initial condition. The form of control and observation operators is determined by the construction of a real system. The internal and external positivity of the model are associated to the localization of heater and measurement. It has been proven that the internal positivity of the considered system can be achieved by the proper selection of attachment of a heater and place of a measurement as well as the dimension of the finite-dimensional approximation of the considered model. Conditions of the internal positivity associated with construction of real experimental system are proposed. The postivity is analysed separately for control and output of the system. This allows one to analyse the positivity of thermal systems without explicit control. Theoretical considerations are numerically verified with the use of experimental data. The proposed results can be applied i.e. to point suitable places for measuring of a temperature using a thermal imaging camera.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e145675
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-13 z 13

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