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    Wyświetlanie 1-10 z 10
    Tytuł:
    Necessary optimality conditions for quasi-singular controls for systems with Caputo fractional derivatives
    Autorzy:
    Yusubov, Shakir Sh.
    Mahmudov, Elimhan N.
    Powiązania:
    https://bibliotekanauki.pl/articles/27321480.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    fractional derivative
    fractional optimal control
    necessary optimality condition
    Opis:
    In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First we get the linearized maximum principle. Further, the concept of a quasi-singular control is introduced and, on this basis, an analogue of the Legendre-Clebsch conditions is obtained. When the analogue of Legendre-Clebsch condition degenerates, a necessary high-order optimality condition is derived. An illustrative example is considered.
    Źródło:
    Archives of Control Sciences; 2023, 33, 3; 463--496
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On controllability of fractional positive continuous-time linear systems with delay
    Autorzy:
    Sikora, Beata
    Matlok, Natalia
    Powiązania:
    https://bibliotekanauki.pl/articles/1409030.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional systems
    positive systems
    Caputo derivative
    controllability
    delay
    Metzler matrix
    Opis:
    In the paper positive fractional continuous-time linear systems are considered. Positive fractional systems without delays and positive fractional systems with a single delay in control are studied. New criteria for approximate and exact controllability of systems without delays as well as a relative controllability criterion of systems with delay are established and proved. Numerical examples are presented for different controllability criteria. A practical application is proposed.
    Źródło:
    Archives of Control Sciences; 2021, 31, 1; 29-51
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On optimal control problem subject to fractional order discrete time singular systems
    Autorzy:
    Chiranjeevi, Tirumalasetty
    Biswas, Raj Kumar
    Devarapalli, Ramesh
    Babu, Naladi Ram
    García Márquez, Fausto Pedro
    Powiązania:
    https://bibliotekanauki.pl/articles/2083465.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional optimal control problem
    discrete time singular system
    fractional derivative
    Hamiltonian technique
    Opis:
    In this work, we present optimal control formulation and numerical algorithm for fractional order discrete time singular system (DTSS) for fixed terminal state and fixed terminal time endpoint condition. The performance index (PI) is in quadratic form, and the system dynamics is in the sense of Riemann-Liouville fractional derivative (RLFD). A coordinate transformation is used to convert the fractional-order DTSS into its equivalent non-singular form, and then the optimal control problem (OCP) is formulated. The Hamiltonian technique is used to derive the necessary conditions. A solution algorithm is presented for solving the OCP. To validate the formulation and the solution algorithm, an example for fixed terminal state and fixed terminal time case is presented.
    Źródło:
    Archives of Control Sciences; 2021, 31, 4; 849-863
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On LQ optimization problem subject to fractional order irregular singular systems
    Autorzy:
    Muhafzan, -
    Nazra, Admi
    Yulianti, Lyra
    Zulakmal, -
    Revina, Refi
    Powiązania:
    https://bibliotekanauki.pl/articles/1409212.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    linear quadratic optimization
    fractional order
    irregular singular system
    Caputo fractional derivative
    Mittag-Leffler function
    Opis:
    In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.
    Źródło:
    Archives of Control Sciences; 2020, 30, 4; 745-756
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    ℎ-Stability of set differential equations
    Autorzy:
    Boukthir, Sihem
    Ghanmi, Boulbaba
    Basdouri, Imed
    Ichalal, Dalil
    Lerbet, Jean
    Powiązania:
    https://bibliotekanauki.pl/articles/27324010.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    ℎ-stability
    Lyapunov theory
    set-valued differential
    generalized Hukuhara derivative
    perturbed system
    cascaded systems
    Opis:
    In this paper, we introduce the notion of h-stability for set-valued differential equations. Necessary and sufficient conditions are established by using Lyapunov theory. Then, based on the obtained results, we study the ℎ-stability of perturbed and cascaded systems. Finally, an example illustrates the proposed theorems.
    Źródło:
    Archives of Control Sciences; 2023, 33, 4; 761--788
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fixed terminal time fractional optimal control problem for discrete time singular system
    Autorzy:
    Chiranjeevi, Tirumalasetty
    Devarapalli, Ramesh
    Babu, Naladi Ram
    Vakkapatla, Kiran Babu
    Rao, R. Gowri Sankara
    Garcìa Màrquez, Fausto Pedro
    Powiązania:
    https://bibliotekanauki.pl/articles/2175112.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order differential equation
    discrete time singular system
    fractional derivative
    linear quadratic optimal control problem
    Opis:
    This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.
    Źródło:
    Archives of Control Sciences; 2022, 32, 3; 489--506
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equivalent diagrams of fractional order elements
    Autorzy:
    Różowicz, Sebastian
    Włodarczyk, Maciej
    Zawadzki, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/27324011.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    fractional order derivative
    Laplace transform for fractional order systems
    CFE method
    circuit synthesis
    numerical experiments
    Opis:
    This paper presents equivalent impedance and operator admittance systems for fractional order elements. Presented models of fractional order elements of the type: sαL,sub>α and 1/sαCsub>α, (0 α 1) were obtained using the Laplace transform based on the expansion of the factor sign to an infinite fraction with varying degrees of accuracy – the continued fraction expansion method (CFE). Then circuit synthesis methods were applied. As a result, equivalent circuit diagrams of fractional order elements were obtained. The obtained equivalent schemes consist both of classical RLC elements, as well as active elements built based on operational amplifiers. Numerical experiments were conducted for the constructed models, presenting responses to selected input signals.
    Źródło:
    Archives of Control Sciences; 2023, 33, 4; 801--827
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the constrained and unconstrained controllability of semilinear Hilfer fractional systems
    Autorzy:
    Sikora, Beata
    Powiązania:
    https://bibliotekanauki.pl/articles/27312002.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    Hilfer fractional derivative
    fractional systems
    semilinear control systems
    nonautonomous systems
    Rothe's fixed point theorem
    generalized Darbo fixed point theorem
    Opis:
    In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function f depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe’s fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study.
    Źródło:
    Archives of Control Sciences; 2023, 33, 1; 155--178
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems
    Autorzy:
    Basdouri, Imed
    Kasmi, Souad
    Lerbet, Jean
    Powiązania:
    https://bibliotekanauki.pl/articles/27312007.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    fractional-order systems
    Caputo derivative
    quasi-one-sided Lipschitz condition
    nonlinear systems
    observer design
    output feedback stabilization
    separation principle
    Opis:
    This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.
    Źródło:
    Archives of Control Sciences; 2023, 33, 1; 55--70
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On theoretical and practical aspects of Duhamel’s integral
    Autorzy:
    Różański, Michał
    Sikora, Beata
    Smuda, Adrian
    Wituła, Roman
    Powiązania:
    https://bibliotekanauki.pl/articles/2083463.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Duhamel’s integral
    Duhamel’s principle
    Duhamel’s formula
    Laplace transformation
    semigroup of operators
    Leibniz integral rule
    Volterra integral equation
    Caputo fractional derivative
    Opis:
    The paper is a new approach to the Duhamel integral. It contains an overview of formulas and applications of Duhamel’s integral as well as a number of new results on the Duhamel integral and principle. Basic definitions are recalled and formulas for Duhamel’s integral are derived via Laplace transformation and Leibniz integral rule. Applications of Duhamel’s integral for solving certain types of differential and integral equations are presented. Moreover, an interpretation of Duhamel’s formula in the theory of operator semigroups is given. Some applications of Duhamel’s formula in control systems analysis are discussed. The work is also devoted to the usage of Duhamel’s integral for differential equations with fractional order derivative.
    Źródło:
    Archives of Control Sciences; 2021, 31, 4; 815-847
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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