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Wyszukujesz frazę "fractional optimal control" wg kryterium: Temat


Wyświetlanie 1-13 z 13
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 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 the existence of optimal consensus control for the fractional Cucker-Smale model
Autorzy:
Almeida, R.
Kamocki, R.
Malinowska, A. B.
Odzijewicz, T.
Powiązania:
https://bibliotekanauki.pl/articles/1409211.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional calculus
fractional differential systems
flocking model
consensus
optimal control
Opis:
This paper addresses the nonlinear Cucker-Smale optimal control problem under the interplay of memory effect. The aforementioned effect is included by employing the Caputo fractional derivative in the equation representing the velocity of agents. Sufficient conditions for the existence of solutions to the considered problem are proved and the analysis of some particular problems is illustrated by two numerical examples.
Źródło:
Archives of Control Sciences; 2020, 30, 4; 625-651
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control problems with a fixed terminal time in linear fractional-order systems
Autorzy:
Gomoyunov, M. I.
Powiązania:
https://bibliotekanauki.pl/articles/1403685.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
optimal control
fractional derivatives
linear systems
open-loop control
feedback control
reduction
Opis:
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two terms: the first one evaluates the state of the system at a fixed terminal time, and the second one is an integral evaluation of the control on the whole time interval. In order to solve this problem, we propose to reduce it to some auxiliary optimal control problem in a dynamical system described by a first-order ordinary differential equation. The reduction is based on the representation formula for solutions to linear fractional differential equations and is performed by some linear transformation, which is called the informational image of a position of the original system and can be treated as a special prediction of a motion of this system at the terminal time. A connection between the original and auxiliary problems is established for both open-loop and feedback (closed-loop) controls. The results obtained in the paper are illustrated by examples.
Źródło:
Archives of Control Sciences; 2020, 30, 4; 721-744
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of optimal control for multi-order fractional optimal control problems
Autorzy:
Kamocki, Rafał
Powiązania:
https://bibliotekanauki.pl/articles/2134888.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
existence of optimal control
multi-order fractional control system
lower closure theorem
Opis:
In this article we focus on optimal control problems involving a nonlinear fractional control system of different orders with Caputo derivatives, associated to a Lagrange cost functional. Based on a lower closure theorem for orientor fields combined with Filippov’s approach, we derive an existence result for at least one optimal solution for such a problem.
Źródło:
Archives of Control Sciences; 2022, 32, 2; 279--303
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Recent results on well-posedness and optimal control for a class of generalized fractional Cahn–Hilliard systems
Autorzy:
Colli, Pierluigi
Gilardi, Gianni
Sprekels, Jurgen
Powiązania:
https://bibliotekanauki.pl/articles/970119.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
fractional operators
Cahn-Hilliard system
optimal control
necessary optimality conditions
Opis:
In this paper, we give an overview of results for Cahn–Hilliard systems involving fractional operators that have recently been established by the authors of this note. We address problems concerning existence, uniqueness, and regularity of the solutions to the system equations, and we study optimal control problems for the systems. The well-posedness results are valid for a wide class of fractional operators of spectral type and for the typical double-well nonlinearities appearing in the Cahn–Hilliard system equations, namely the classical differentiable, the logarithmic, and the nondifferentiable double obstacle potentials. While this also applies to the existence of optimal controls in the related optimal control problems, the establishment of first-order necessary optimality conditions requires imposing much stronger assumptions on the admissible class of fractional operators. One main reason for this is the necessity of deriving suitable differentiability properties for the associated control-to-state mapping. Nevertheless, it turns out that also in the singular case of logarithmic potentials, the first-order necessary optimality conditions can be established under suitable assumptions, and a “deep quench” approximation, based on the results derived for logarithmic nonlinearities makes even the case of double obstacle potentials accessible.
Źródło:
Control and Cybernetics; 2019, 48, 1; 153-197
0324-8569
Pojawia się w:
Control and Cybernetics
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:
Optimal control of a fractional-order enzyme kinetic model
Autorzy:
Al-Basir, F.
Elaiw, A. M.
Kesh, D.
Roy, P. K.
Powiązania:
https://bibliotekanauki.pl/articles/206336.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
enzyme kinetics
cooperative phenomenon
fractional derivative
mathematical modeling
Hamiltonian
optimal control problem
Opis:
Enzymes play a significant role in controlling the characteristics of various chemical and biochemical reactions. They act as catalysts that increase the rate of reaction without undergoing any change in quantity. Enzymatic reactions occur through the active sites, which combine with the substrates to form intermediate complexes, subsequently leading to products. An enzyme having two active sites can show cooperative phenomena. Against this background, an enzyme-kinetic mathematical model is formulated using fractional order derivatives. Optimal control mechanism has been incorporated into the fractional-order model system to maximize the product output. Euler-Lagrange optimality conditions are derived for the FOCP (fractional order control problem) using maximum principle. Numerical iterative schemes have been developed to solve the fractional order optimal control problem through Matlab.
Źródło:
Control and Cybernetics; 2015, 44, 4; 443-461
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
The optimal design of fractional sliding mode control based on multi-objective genetic algorithms for a two-link flexible manipulator
Autorzy:
Pouya, M.
Pashaki, P. V.
Powiązania:
https://bibliotekanauki.pl/articles/102531.pdf
Data publikacji:
2017
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
fractional calculations
sliding mode control
two-link flexible manipulator
Pareto optimal
genetic algorithm
Opis:
In this paper a novel optimal approach of control strategy is introduced by applying fractional calculus in the structure of sliding mode control for a range of dynamics system liable to ambiguity. So, a fractional sliding mode control was designed for dynamics of the two-link rigid-flexible manipulator. Furthermore, a multi-objective genetic algorithm was proposed in order to find the ideal variable structure of the sliding mode control. Optimal variables were achieved by the optimization of the conventional sliding mode control. Then the performance of both the conventional and the fractional sliding mode control were compared with respect to optimal variables. Results indicated that by applying the optimized fractional sliding mode control, the system’s error was significantly reduced consequently tracking the desired value was done with a higher degree of accuracy and a smoother control action was achieved.
Źródło:
Advances in Science and Technology. Research Journal; 2017, 11, 3; 56-65
2299-8624
Pojawia się w:
Advances in Science and Technology. Research Journal
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional nonlocal integrodifferential equations of mixed type with time-varying generating operators and optimal control
Autorzy:
Wang, J.
Wei, W.
Yang, Y.
Powiązania:
https://bibliotekanauki.pl/articles/254750.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional integrodifferential equations of mixed type
time-varying generating operators
nonlocal conditions
fixed point theorem
existence
optimal control
Opis:
In this paper, a class of fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is considered. Using a contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequailty, the existence and uniqueness of mild solution are given. The existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is also presented.
Źródło:
Opuscula Mathematica; 2010, 30, 2; 217-234
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Time-optimal control of linear fractional systems with variable coefficients
Autorzy:
Matychyn, Ivan
Onyshchenko, Viktoriia
Powiązania:
https://bibliotekanauki.pl/articles/2055161.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional calculus
Riemann-Liouville derivative
variable coefficients
optimal control
rachunek ułamkowy
pochodna ułamkowa Riemanna-Liouville'a
współczynnik zmienny
sterowanie optymalne
Opis:
Linear systems described by fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives are examined in the paper. For these systems, a solution of the initial-value problem is derived in terms of the generalized Peano–Baker series and a time-optimal control problem is formulated. The optimal control problem is treated from the convex-analytical viewpoint. Necessary and sufficient conditions for time-optimal control similar to that of Pontryagin’s maximum principle are obtained. Theoretical results are supported by examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2021, 31, 3; 375--386
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Boundary optimal control problem for the phase-field transition system using fractional steps method
Zadanie sterowania optymalnego brzegiem dla układu pola ze zmianą fazy z wykorzystaniem metody kroków ułamkowych
Autorzy:
Moroşanu, C.
Powiązania:
https://bibliotekanauki.pl/articles/206721.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
zagadnienie ze swobodnym brzegiem
sterowanie optymalne
metoda kroków ułamkowych
warunki optymalności
metoda elementu skończonego
metoda gradientowa
układ ze zmianą fazy
phase-field transition system
free boundary problem
optimal control
fractional steps method
optimality conditions
finite element method
gradient method
Opis:
In this paper we prove the convergence of an iterative scheme of fractional steps type for boundary optimal control problem which is governed by the phase-field transition system. The existence of an optimal control and necessary optimality conditions are given for approximating problem. A gradient type algorithm and numerical implementation of this algorithm are discussed.
W artykule dowodzi się zbieżności procedury iteracyjnej typu kroków ułamkowych dla zagadnienia sterowania optymalnego brzegiem w układzie pola ze zmianą fazy. Wykazano istnienie sterowania optymalnego i podano warunki konieczne optymalności dla zagadnienia aproksymującego. Rozpatrzono odpowiedni algorytm gradientowy oraz realizację numeryczną tego algorytmu.
Źródło:
Control and Cybernetics; 2003, 32, 1; 5-32
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-13 z 13

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