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Tytuł:
Fuzzy Predictive Control of Fractional-Order Nonlinear Discrete-Time Systems
Autorzy:
Domek, S.
Powiązania:
https://bibliotekanauki.pl/articles/387296.pdf
Data publikacji:
2011
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
model
sterowanie
system dyskretno-czasowy
discrete-time systems
control
Opis:
At the end of the 19th century Liouville and Riemann introduced the notion of a fractional-order derivative, and in the latter half of the 20th century the concept of the so-called Grünewald-Letnikov fractional-order discrete difference has been put forward. In the paper a predictive controller for MIMO fractional-order discrete-time systems is proposed, and then the concept is extended to nonlinear processes that can be modelled by Takagi-Sugeno fuzzy models. At first nonlinear and linear fractional-order discrete-time dynamical models are described. Then a generalized nonlinear fractional-order TS fuzzy model is defined, for which equations of a predictive controller are derived.
Źródło:
Acta Mechanica et Automatica; 2011, 5, 2; 23-26
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positive Realization of SISO 2D Different Orders Fractional Discrete-Time Linear Systems
Autorzy:
Sajewski, Ł.
Powiązania:
https://bibliotekanauki.pl/articles/386582.pdf
Data publikacji:
2011
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
system dyskretno-czasowy
realizacja dodatnia
discrete-time system
positive realisation
Opis:
The realization problem for single-input single-output 2D positive fractional systems with different orders is formulated and a method based on the state variable diagram for finding a positive realization of a given proper transfer function is proposed. Sufficient conditions for the existence of a positive realization of this class of 2D linear systems are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.
Źródło:
Acta Mechanica et Automatica; 2011, 5, 2; 122-127
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Reduction and Decomposition of Singular Fractional Discrete-Time Linear Systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/386227.pdf
Data publikacji:
2011
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
redukcja
system dyskretno-czasowy
system liniowy
reduction
discrete-time systems
linear systems
Opis:
Reduction of singular fractional systems to standard fractional systems and decomposition of singular fractional discrete-time linear systems into dynamic and static parts are addressed. It is shown that if the pencil of singular fractional linear discrete-time system is regular then the singular system can be reduced to standard one and it can be decomposed into dynamic and static parts The proposed procedures are based on modified version of the shuffle algorithm and illustrated by numerical examples.
Źródło:
Acta Mechanica et Automatica; 2011, 5, 4; 62-66
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains
Autorzy:
Ostalczyk, P.
Powiązania:
https://bibliotekanauki.pl/articles/330106.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
rachunek ułamkowy
system dyskretno-czasowy
system liniowy
fractional calculus
linear-discrete time system
stability domain
Opis:
Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2012, 22, 3; 533-538
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form
Autorzy:
Orłowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/929824.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
system niepewny
system dyskretno-czasowy
system nieliniowy
uncertain systems
uncertain estimates
discrete-time systems
nonlinear systems
Opis:
Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems given in the state space dependent form. The method for numerical estimation of the maximal norm of the output trajectory deviation with applications to robust control synthesis is proposed based on the introduced three-term additive uncertainty model. Theoretical deliberations are complemented with a numerical, water-tank system example.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2007, 17, 4; 505-513
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/330552.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Drazin inverse
descriptor
fractional system
discrete-time system
linear system
system ułamkowy
system dyskretno-czasowy
system liniowy
Opis:
The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2013, 23, 1; 29-33
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Simple conditions for practical stability of positive fractional discrete-time linear systems
Autorzy:
Busłowicz, M.
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/907662.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
system liniowy
system dyskretno-czasowy
system ułamkowy
stateczność
stateczność praktyczna
linear system
positive
discrete-time
fractional
stability
practical stability
Opis:
In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 2; 263-269
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An SQP trust region method for solving the discrete-time linear quadratic control problem
Autorzy:
Mostafa, E. M. E.
Powiązania:
https://bibliotekanauki.pl/articles/331409.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
programowanie sekwencyjne
programowanie kwadratowe
system dyskretno-czasowy
output feedback control design
sequential quadratic programming
trust region method
Opis:
In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution to initiate the proposed SQP trust region method. To demonstrate the effectiveness of the method, some numerical results are presented in detail.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2012, 22, 2; 353-363
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Simple stable discrete-time generalised predictive control with anticipated filtration of control error
Autorzy:
Kowalczuk, Z.
Suchomski, P.
Powiązania:
https://bibliotekanauki.pl/articles/206013.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie predykcyjne
synteza systemu sterowania
system dyskretno-czasowy
discrete-time systems
non-minimal systems
predictive control
system design
Opis:
It is shown that under some specific conditions, the solution of the generalised predictive control (GPC) design using the concept of anticipated filtering (AF) of the control error always exists, and that such a design leads to stable control systems with definite closed-loop characteristics. The plant cancellation issue is taken into account, and it is demonstrated that certain bounds on GPC design parameters have to be considered. An iterative procedure for simultaneous determination of the three basic design-tuning parameters: the control horizon, the controller gain, and the order of plant cancellation, is also supplied. An important feature of this approach is that the anticipated filtering makes it possible to reduce a disagreeable control effort associated with GPC and to make the [lambda]-tuning mechanism practicable. The bounds on the GPC design parameters are discussed, and certain optimal tuning rules are proposed and validated via simulated experiments.
Źródło:
Control and Cybernetics; 2002, 31, 1; 17-41
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Trackability and bounded output bounded input trackability of linear discrete-time systems
Autorzy:
Kurek, J.
Powiązania:
https://bibliotekanauki.pl/articles/206760.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowalność
system liniowy dyskretno-czasowy
controllability
linear discrete time systems
trackability
Opis:
The notions of systems trackability and bounded output bounded input (B0BI) trackability are given. Then, necessary and suffcient conditions are formulated for trackability of linear discrete-time systems.
Źródło:
Control and Cybernetics; 2002, 31, 1; 43-55
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positive partial realization problem for linear discrete-time systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/929624.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
system dodatni
istnienie
obliczanie
system liniowy
system dyskretno-czasowy
positive systems
partial realization
existence
computation
linear system
discrete-time systems
Opis:
A partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2007, 17, 2; 165-171
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerically robust synthesis of discrete-time H[infinity] estimators based on dual J-lossless factorisations
Autorzy:
Suchomski, P.
Powiązania:
https://bibliotekanauki.pl/articles/970576.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
system dyskretno-czasowy
estymacja
filtr liniowy
równanie Riccatiego
metody numeryczne
discrete-time systems
state estimation
linear filters
Riccati equation
numerical methods
Opis:
An approach to the numerically reliable synthesis of the H[infinity] suboptimal state estimators for discretised continuous-time processes is presented. The approach is based on suitable dual J-lossless factorisations of chain-scattering representations of estimated processes. It is demonstrated that for a sufficiently small sampling period the standard forward shift operator techniques may become ill-conditioned and numerical robustness of the design procedures can be significantly improved by employing the so-called delta operator models of the process. State-space models of all H[infinity] sub-optimal estimators are obtained by considering the suitable delta-domain algebraic Riccati equation and the corresponding generalised eigenproblem formulation. A relative condition number of this equation is used as a measure of its numerical conditioning. Both regular problems concerning models having no zeros on the boundary of the delta-domain stability region and irregular (non-standard) problems of models with such zeros are examined. For the first case, an approach based on a dual J-lossless factorisation is proposed while in the second case an extended dual J-lossless factorisation based on a zero compensator technique s required. Two numerical examples are given to illustrate some properties of the considered delta-domain approach.
Źródło:
Control and Cybernetics; 2003, 32, 4; 761-802
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances
Autorzy:
Khémiri, K.
Ben Hmida, F.
Ragot, J.
Gossa, M.
Powiązania:
https://bibliotekanauki.pl/articles/930170.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
filtracja Kalmana
estymacja stanu
zakłócenie nieznane
system liniowy
system dyskretno-czasowy
Kalman filtering
minimum variance estimation
state estimation
fault estimation
unknown disturbances
linear discrete time systems
Opis:
This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria. Two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2011, 21, 4; 629-637
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positivity of fractional descriptor linear discrete-time systems
Autorzy:
Kaczorek, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/329958.pdf
Data publikacji:
2019
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional descriptor
discrete time system
stability
solution
positivity
deskryptor ułamkowy
układ dyskretno czasowy
stabilność
Opis:
The positivity of fractional descriptor linear discrete-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear discrete-time systems are established. The discussion is illustrated with numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2019, 29, 2; 305-310
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positivity and stability of fractional descriptor time-varying discrete-time linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/331399.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional system
descriptor system
time varying system
positive system
discrete-time system
układ ułamkowy
układ deskrypcyjny
układ dodatni
układ dyskretno-czasowy
Opis:
The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor time-varying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2016, 26, 1; 5-13
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł

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