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Wyświetlanie 1-15 z 653
Tytuł:
Finite length triple estimation algorithm and its application to gyroscope mems noise identification
Autorzy:
Macias, Michał
Sierociuk, Dominik
Powiązania:
https://bibliotekanauki.pl/articles/2204616.pdf
Data publikacji:
2023
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
fractional calculus
fractional Kalman filter
estimation of fractional order systems
fractional order noise
Opis:
The noises associated with MEMS measurements can significantly impact their accuracy. The noises characterised by random walk and bias instability errors strictly depend on temperature effects that are difficult to specify during direct measurements. Therefore, the paper aims to estimate the fractional noise dynamics of the stationary MEMS gyroscope based on finite length triple estimation algorithm (FLTEA). The paper deals with the state, order and parameter estimation of fractional order noises originating from the MEMS gyroscope, being part of the popular Inertial Measurement Unit denoted as SparkFun MPU9250. The noise measurements from , and gyroscope axes are identified using a modified triple estimation algorithm (TEA) with finite approximation length. The TEA allows a simultaneous estimation of the state, order and parameter of fractional order systems. Moreover, as it is well-known that the number of samples in fractional difference approximations plays a key role, we try to show the influence of applying the TEA with various approximation length constraints on final estimation results. The validation of finite length TEA in the noise estimation process coming from MEMS gyroscope has been conducted for implementation length reduction achieving 50% of samples needed to estimate the noise with no implementation losses. Additionally, the capabilities of modified TEA in the analysis of fractional constant and variable order systems are confirmed in several numerical examples.
Źródło:
Acta Mechanica et Automatica; 2023, 17, 2; 219--229
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo
Autorzy:
Piotrowska, E.
Powiązania:
https://bibliotekanauki.pl/articles/141097.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
conformable fractional derivative
fractional electrical circuit
different fractional order system
Opis:
The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.
Źródło:
Archives of Electrical Engineering; 2018, 67, 3; 629--639
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence results for random fractional differential equations
Autorzy:
Lupulescu, V.
O’Regan, D.
Rahman ur, G.
Powiązania:
https://bibliotekanauki.pl/articles/255930.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
random fractional differential equations
fractional integral
Caputo fractional derivative
existence
Opis:
In this paper, an existence result for a random fractional differential equation is established under a Carathéodory condition. Existence results for extremal random solutions are also proved. Finally, an existence and uniqueness result is given.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 813-825
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On fractional random differential equations with delay
Autorzy:
Vu, H.
Phung, N. N.
Phuong, N.
Powiązania:
https://bibliotekanauki.pl/articles/254723.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
sample path fractional integral
sample path fractional derivative
fractional differential equations
sample fractional random differential equations
Caputo fractional derivative
delay
Opis:
In this paper, we consider the existence and uniqueness of solutions of the fractional random differential equations with delay. Moreover, some kind of boundedness of the solution is proven. Finally, the applicability of the theoretical results is illustrated with some real world examples.
Źródło:
Opuscula Mathematica; 2016, 36, 4; 541-556
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of a solution for the fractional forced pendulum
Autorzy:
Torres, C.
Powiązania:
https://bibliotekanauki.pl/articles/122603.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional calculus
fractional boundary value problem
mountain pass theorem
fractional space
Opis:
In this work we study the fractional forced pendulum equation with combined fractional derivatives - tDαT 0Dαt u( t ) + g ( u ( t )) = f ( t ), t ∈ ( 0, T ) ( 0. 1 ) u ( 0 ) = u ( T ) = 0 where ½ < α < 1, g ∈ C ( R, R ), bounded f ∈ C [ 0, T ]. Using minimization techniques form variational calculus we show that ( 0. 1 ) has a nontrivial solution.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 1; 125-142
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of fractional electrical circuit with rectangular input signal using Caputo and conformable derivative definitions
Autorzy:
Piotrowska, E.
Powiązania:
https://bibliotekanauki.pl/articles/140842.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order system
Caputo definition
conformable fractional definition
fractional electrical circuit
Opis:
An analysis of a given electrical circuit using a fractional derivative. The statespace equation was developed. The dynamics of tensions described by Kirchhoff’s laws equations. The paper used the definition of the integral derivative Caputo and CDF conformable fractional definition. An electrical circuit solution using Caputo and CDF definitions for rectangular with zero initial conditions was developed. The results obtained using the Caputo and CDF definitions were compared. The solutions are shown for capacitor voltages, for fractional derivative orders of 0.6, 0.8, 1. The results were compared using graphs.
Źródło:
Archives of Electrical Engineering; 2018, 67, 4; 789-802
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional Kalman Filter algorithms for correlated system and measurement noises
Autorzy:
Sierociuk, D.
Powiązania:
https://bibliotekanauki.pl/articles/206137.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
fractional order calculus
discrete fractional state-space systems
fractional Kalman filter
Opis:
The paper presents a generalization of the Fractional Kalman Filter to a case when correlated system and measurement noises appear. The algorithm proposed is derived in detail for a linear generalized discrete fractional order state-space system for both constant and variable order cases. In order to present the efficiency of the proposed algorithm, results of numerical simulations are presented. Results of numerical experiments are compared with the effect of estimation obtained when using the traditional Fractional Kalman Filter algorithm.
Źródło:
Control and Cybernetics; 2013, 42, 2; 471-490
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Formulation of the simple Markovian model using fractional calculus approach and its application to analysis of queue behavior of severe patients
Autorzy:
Dhar, Soma
Mahanta, Lipi B.
Das, Kishore Kumar
Powiązania:
https://bibliotekanauki.pl/articles/1359228.pdf
Data publikacji:
2019-04-25
Wydawca:
Główny Urząd Statystyczny
Tematy:
fractional order
arrival rate
patients
fractional calculus
Opis:
In this paper, we introduce a fractional order of a simple Markovian model where the arrival rate of the patient is Poisson, i.e. independent of the patient size. Fraction is obtained by replacing the first order time derivative in the difference differential equations which govern the probability law of the process with the Mittag-Leffler function. We derive the probability distribution of the number N(t) of patients suffering from severe disease at an arbitrary time t. We also obtain the mean size (number) of the patients suffering from severe disease waiting for service at any given time t, in the form of E ν 0.5,0.5 (t), for different fractional values of server activity status, ν = 1,0.95,0.90 and for arrival rates α = β = 0.5. A numerical example is also evaluated and analysed by using the simple Markovian model with the help of simulation techniques.
Źródło:
Statistics in Transition new series; 2019, 20, 1; 117-129
1234-7655
Pojawia się w:
Statistics in Transition new series
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional Integral Approximation and Caputo Derivatives with Modification of Trapezoidal Rule
Autorzy:
Pandiangan, Naomi
Johar, Dwindi
Purwani, Sri
Powiązania:
https://bibliotekanauki.pl/articles/1193326.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Caputo fractional derivative
Fractional integral
Modified trapezoidal rule
Rieman Liouville fractional integral
Opis:
In classical calculus, a function can be derived or integrated as many as natural numbers. Then a question arises regarding the fractional order of derivatives and integrals. There is a development of classical calculus called fractional calculus. Fractional calculus may be a department of science that amplifies the orders of derivatives and integrals into the order of rational numbers or even real numbers. The difficulty of finding solutions analytically for a complicated function of fractional integrals or fractional derivatives often occurs. In this paper, we will solve Rieman Liouville's fractional integral and Caputo's fractional derivative analytically using the trapezoidal rule modification method. Trapezoidal method is an approximation method that is resulted from the linear interpolation function. In this paper, we will find numerical simulations with modified trapezoidal method, to estimate some functions, and the results will be compared with previous research related to the Rieman Liouville fractional integral approximation and the Caputo fractional derivative. The result from simulation find that modified trapezoidal can approximate Caputo fractional derivative by replace α with -α and Quadratic schemes method is the best method to approximate Rieman Liouville fractional integral and Caputo fractional derivative.
Źródło:
World Scientific News; 2021, 153, 2; 169-180
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New perspectives of analog and digital simulations of fractional order systems
Autorzy:
Charef, A.
Charef, M.
Djouambi, A.
Voda, A.
Powiązania:
https://bibliotekanauki.pl/articles/229183.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
adjustable fractional operators
Charef approximation
fractional differential equation
ractional integrator
fractional systems
Opis:
In the recent decades, fractional order systems have been found to be useful in many areas of physics and engineering. Hence, their efficient and accurate analog and digital simulations and numerical calculations have become very important especially in the fields of fractional control, fractional signal processing and fractional system identification. In this article, new analog and digital simulations and numerical calculations perspectives of fractional systems are considered. The main feature of this work is the introduction of an adjustable fractional order structure of the fractional integrator to facilitate and improve the simulations of the fractional order systems as well as the numerical resolution of the linear fractional order differential equations. First, the basic ideas of the proposed adjustable fractional order structure of the fractional integrator are presented. Then, the analog and digital simulations techniques of the fractional order systems and the numerical resolution of the linear fractional order differential equation are exposed. Illustrative examples of each step of this work are presented to show the effectiveness and the efficiency of the proposed fractional order systems analog and digital simulations and implementations techniques
Źródło:
Archives of Control Sciences; 2017, 27, 1; 91-118
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On geometrical interpretation of the fractional strain concept
Autorzy:
Sumelka, W.
Powiązania:
https://bibliotekanauki.pl/articles/280568.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
fractional strain
fractional calculus
non-local models
Opis:
In this paper, for the first time, the geometrical interpretation of fractional strain tensor components is presented. In this sense, previous considerations by this author are shown in a new light. The fractional material and spatial line elements concept play a crucial role in the interpretation.
Źródło:
Journal of Theoretical and Applied Mechanics; 2016, 54, 2; 671-674
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cone solutions of multi-order fractional difference systems
Autorzy:
Girejko, E.
Mozyrska, D.
Powiązania:
https://bibliotekanauki.pl/articles/206510.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
fractional difference operator
fractional difference equation
cone solutions
Opis:
The fractional difference system of equations with different fractional orders is considered. We obtain the existence and uniqueness results for the initial value problem. Cone solutions are presented. An example is given to illustrate the results.
Źródło:
Control and Cybernetics; 2013, 42, 2; 419-429
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The use of simulated annealing method for optimization of fractional order PID controller
Autorzy:
Mikulski, S.
Powiązania:
https://bibliotekanauki.pl/articles/97234.pdf
Data publikacji:
2015
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
fractional order controller
optimization
fractional calculus
simulated annealing
Opis:
The paper describes method of parameters selection for control system with fractional order PIλDμ controller steering second order oscillated object. As a selection algorithm was used simulated annealing optimization method with random variant of cooling strategy. As a target function for optimization was selected Integral Squared Error (ISE).
Źródło:
Computer Applications in Electrical Engineering; 2015, 13; 178-187
1508-4248
Pojawia się w:
Computer Applications in Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional Signals and Systems
Autorzy:
Ortigueira, M. D.
Machado, J. T. M.
Ostalczyk, P.
Powiązania:
https://bibliotekanauki.pl/articles/201998.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional signals
fractional systems
model ułamkowy
system ułamkowy
Opis:
The special section in the current volume of the Bulletin of the Polish Academy of Sciences, entitled “Fractional Signals and Systems”, includes selected papers from the FSS17 International Conference, which was held in Łódź, Poland on October 9–11, 2017. The founder of the conference is Manuel Duarte Ortigueira from the New University of Lisbon, Portugal. The FSS17 is yet another in a series of conferences, which had previously taken place in: 1. Caparica, Portugal, 2009 2. Coimbra, Portugal, 2011 3. Ghent, Belgium, 2013 4. Cluj-Napoca, Romania, 2015. The FSS17 conference addressed a broad spectrum of the Fractional Calculus (FC) applications in technical sciences. Main topics included the fractional-order continuous-, and discrete-time linear or non-linear fractional-order control, dynamic system identification via fractional models, fractional order filtering, as well as image processing using fractional methods. The conference’s main organizers included the Institute of Applied Computer Science (Instytut Informatyki Stosowanej Politechniki Łódzkiej), the Lodz University of Technology (Politechnika Łódzka) and the Polish Information Processing Society – Łódź Branch (Polskie Towarzystwo Informatyczne – Oddział Łódzki).
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 385-387
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Wyświetlanie 1-15 z 653

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