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Wyświetlanie 1-15 z 17
Tytuł:
On a degenerate Riccati equation
Autorzy:
Kesavan, S.
Raymond, J. P.
Powiązania:
https://bibliotekanauki.pl/articles/970756.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
algebraic Riccati equation
optimal control
parabolic systems
Opis:
In this paper, we study the existence of solutions to a degenerate algebraic Riccati equation associated to an optimal control problem with infinite time horizon. Under some assumptions on the control system, we can select a solution to this Riccati equation providing a feedback control law able to stabilize the system.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1393-1410
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Uniqueness of the Riccati operator of the non-standard ARE of a third order dynamics with boundary control
Autorzy:
Lasiecka, Irena
Triggiani, Roberto
Powiązania:
https://bibliotekanauki.pl/articles/2183492.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
uniqueness
non-standard algebraic Riccati equation
Moore-Gibson-Thompson equation
Opis:
TheMoore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with applications in high frequency ultrasound technology. The optimal boundary feedback control is constructed in order to have on-line regulation. The above requires wellposedness of the associated Algebraic Riccati Equation. The paper by Lasiecka and Triggiani (2022) recently contributed a comprehensive study of the Optimal Control Problem for the MGT-third order dynamics with boundary control, over an infinite time-horizon. A critical missing point in such a study is the issue of uniqueness (within a specific class) of the corresponding highly non-standard Algebraic Riccati Equation. The present note resolves this problem in the positive, thus completing the study of Lasiecka and Triggiani (2022) with the final goal of having on line feedback control, which is also optimal.
Źródło:
Control and Cybernetics; 2022, 51, 2; 171--189
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Robustness of solutions of an infinite-dimensional algebraic Sylvester equation under bounded perturbations
Autorzy:
Emirsajłow, Z.
Powiązania:
https://bibliotekanauki.pl/articles/205989.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
distributed parameter systems
algebraic Sylvester equation
bounded perturbations
implemented semigroup
Opis:
The output regulation problem for distributed parameter systems, see e.g. Byrnes, Lauko, Gillian and Shubov (2000) and Paunonen (2011), and the observer design problem for such systems, see e.g. Emirsajłow (2012), are examples of import ant control problems, where analysis of infinite-dimensional algebraic Sylvester equations plays a crucial role. This paper studies bounded perturbations of the unbounded operators of the algebraic infinitedimensional Sylvester equation. We derive some estimate on the perturbation operator under which the algebraic Sylvester equation preserves a unique solution or, in the control systems terminology, a solution is robust under small bounded perturbations. In our approach we employ the concept of an implemented semigroup, see e.g. Alber (2001) and Emirsajłow (2012), which is a special case of the so-called bi-continuous semigroup, e.g. Farkas (2004).
Źródło:
Control and Cybernetics; 2013, 42, 1; 27-45
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A dominant height growth model for eucalyptus plantations in Portugal
Autorzy:
Mateus, Ayana
Tomé, Margarida
Powiązania:
https://bibliotekanauki.pl/articles/729682.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
algebraic difference equation
dynamic model
dominant height
forest planning
non linear model
Opis:
Eucalyptus globulus Labill is one of the most important economic forest species in Portugal, occupying an area of 875.10³ ha in a total forest area of 3346.10³ ha (Tomé et al., 2007). The main goal of this study is to develop a dominant height growth model for Eucalyptus, applicable throughout the country, representing an improve of the curves that are part of the whole stand model existing in Portugal, the GLOBULUS model (Tomé et al., 2001). The dominant height growth model will be built on a biological function formulated as a difference equation (Algebraic Difference Approach) to an all possible growth intervals data structure. The dynamic model proposed, obtains non biased and efficient estimates for the parameters. Comparing to the already available model, the last has the advantage of expressing the asymptote in weather variables functions, meaning that it is possible to reproduce the eucalyptus growth according to weather changes.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2009, 29, 2; 155-168
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Construction of algebraic and difference equations with a prescribed solution space
Autorzy:
Moysis, L.
Karampetakis, N. P.
Powiązania:
https://bibliotekanauki.pl/articles/330046.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
algebraic equation
difference equation
behavior
exact modeling
autoregressive representation
discrete time system
higher order system
równanie algebraiczne
równanie różnicowe
system czasu dyskretnego
system wyższego rzędu
Opis:
This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ) β (k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ) . This work deals with the inverse problem of constructing a family of polynomial matrices A(σ) such that the system A(σ) β (k) = 0 satisfies some given forward and backward behavior. Initially, the connection between the backward behavior of an AR representation and the forward behavior of its dual system is showcased. This result is used to construct a system satisfying a certain backward behavior. By combining this result with the method provided by Gohberg et al. (2009) for constructing a system with a forward behavior, an algorithm is proposed for computing a system satisfying the prescribed forward and backward behavior.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 1; 19-32
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system
Autorzy:
Kumar E, V.
Jerome, J.
Powiązania:
https://bibliotekanauki.pl/articles/140600.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
algebraic Riccatti equation
linear quadratic regulator
magnetic levitation
system
weighting matrices
command following
cost function
Opis:
This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR) for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE) and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system.
Źródło:
Archives of Electrical Engineering; 2016, 65, 1; 151-168
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical error bound of optimal control for homogeneous linear systems
Autorzy:
Daraghmeh, Adnan
Qatanani, Naji
Powiązania:
https://bibliotekanauki.pl/articles/229410.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
time-invariant systems
quadratic cost function
linear quadratic regulator
algebraic Riccati equation
Hamiltonian function
L2 norm
Opis:
In this article we focus on the balanced truncation linear quadratic regulator (LQR) with constrained states and inputs. For closed-loop, we want to use the LQR to find an optimal control that minimizes the objective function which called "the quadratic cost function” with respect to the constraints on the states and the control input. In order to do that we have used formal asymptotes for the Pontryagin maximum principle (PMP) and we introduce an approach using the so called The Hamiltonian Function and the underlying algebraic Riccati equation. The theoretical results are validated numerically to show that the model order reduction based on open-loop balancing can also give good closed-loop performance.
Źródło:
Archives of Control Sciences; 2019, 29, 2; 323-337
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Matrix Quadratic Equations, Column/row Reduced Factorizations and an Inertia Theorem for Matrix Polynomials
Autorzy:
Karelin, I.
Lerer, L.
Powiązania:
https://bibliotekanauki.pl/articles/908122.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
macierz
równanie różniczkowe Riccatiego
matrix quadratic equations
Bezoutians
inertia
column (row) reduced polynomials
factorization
algebraic Riccati equation
extremal solutions
Opis:
It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial G(lambda) (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of G(lambda). The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1285-1310
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Algebraic forms of solutions of linear state equations for determined control vectors
Autorzy:
Porada, Ryszard
Mielczarek, Norbert
Powiązania:
https://bibliotekanauki.pl/articles/376440.pdf
Data publikacji:
2020
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
state equation
solutions of state equations
algebraic forms
Opis:
Despite intensive development of numerical methods of resolution of ordinary differential equations, we still seek analytical solutions of these equations in the algebraic form. The analytical solution in an algebraic form, is very convenient in case of investigation of the course of solution in a large interval of changes of parameters, it also gives more qualitative informations. This concerns first of all linear equations which are the most often met models of physical objects. Important advantage of these solutions is also their open form regarding established state of the system. The paper proves existence of algebraic forms of solutions of control vectors with components: exponential, sinusoidal with different circular frequencies and sinusoidal multiple. Also solutions for other kind of control vectors which are mentioned in the literature are presented.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2020, 104; 75-86
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New optical solitary waves for unstable Schrödinger equation in nonlinear medium
Autorzy:
Zhou, Qin
Rezazadeh, Hadi
Korkmaz, Alper
Eslami, Mostafa
Mirzazadeh, Mohammad
Rezazadeh, Mohammadreza
Powiązania:
https://bibliotekanauki.pl/articles/173644.pdf
Data publikacji:
2019
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
solitons
new extended direct algebraic method
unstable Schrödinger equation
Opis:
In this paper and for the first time, we describe and introduce a new extended direct algebraic method which is a new method for solving nonlinear partial differential equations arising in nonlinear optics and nonlinear science. By applying this method, we have constructed new solitary wave solutions for the unstable Schrödinger equation. A large family of traveling wave type exact solutions covering exponential, generalized trigonometric, rational and generalized hyperbolic functions to this equation is determined. The solutions are expressed in explicit forms.
Źródło:
Optica Applicata; 2019, 49, 1; 135-150
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Flat structure and potential vector fields related with algebraic solutions to Painleve VI equation
Autorzy:
Kato, M.
Mano, T.
Sekiguchi, J.
Powiązania:
https://bibliotekanauki.pl/articles/254743.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
flat structure
Painleve VI equation
algebraic solution
potential vector field
Opis:
A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painleve VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.
Źródło:
Opuscula Mathematica; 2018, 38, 2; 201-252
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Transmission problems for the Helmholtz equation for a rectilinear-circular lune
Autorzy:
Denysenko, V.
Powiązania:
https://bibliotekanauki.pl/articles/255476.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Helmholtz equation
transmission problem
infinite system of linear algebraic equations
Opis:
The question related to the construction of the solution of plane transmission problem for the Helmholtz equation in a rectilinear-circular lune is considered. An approach is proposed based on the method of partial domains and the principle of reflection for the solutions of the Helmholtz equation through the segment.
Źródło:
Opuscula Mathematica; 2007, 27, 2; 197-203
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lyapunov, Sylvester and Riccati equations with some applications
Równania Lapunowa, Sylvestera i Riccatiego oraz ich niektóre zastosowania
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/157005.pdf
Data publikacji:
2007
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
algebraiczne
różniczkowe
równanie ,Lapunowa, Sylvestera, Riccatiego
algebraic
differential
equation, Lyapunov, Sylvester, Riccati
solution
application
Opis:
An overview of the differential and algebraic Lyapunov, Sylvester and Riccati equations is presented. A special attentions is focused on relationship between the equations and their applications in control systems theory. The well-known classical Cayley-Hammilton theorem is extended for the Lyapunov time-varying systems.
W pracy podano przegląd różniczkowych i algebraicznych równań Lapunowa, Sylvestera i Riccatiego. Szczególną uwagę zwrócono na związki występujące miedzy tymi równaniami oraz ich zastosowaniami w teorii sterowania i systemów. Uogólniono klasyczne twierdzenie Cayleya - Hamiltona na układy Lapunowa o zmiennych w czasie parametrach.
Źródło:
Pomiary Automatyka Kontrola; 2007, R. 53, nr 6, 6; 63-67
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Note on some infinite products for π
Autorzy:
Kahlig, P.
Matkowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/122690.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
infinite product
Wallis-type product
Dido functional equation
Dido sequence
algebraic number
transcendental number
constructible number
produkt nieskończony
liczba algebraiczna
liczba przestępna
Opis:
After a brief review of (slowly converging) Wallis-type infinite products for π , (faster converging), Dido-type infinite products for π are treated. The notion of “alternating products” facilitates error checking.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 2; 43-50
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized method of Lie-algebraic discrete approximations for solving Cauchy problems with evolution equation
Autorzy:
Kindybaliuk, A.
Powiązania:
https://bibliotekanauki.pl/articles/122439.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
generalized method of Lie-algebraic discrete approximations
dynamical systems
evolution equation
finite dimensional quasi representation
approximations
Lagrange’s polynomial
factorial convergence
układy dynamiczne
aproksymacje
wielomian Lagrange'a
Opis:
We consider solving the Cauchy problem with an abstract linear evolution equation by means of the Generalized Method of Lie-algebraic discrete approximations. Discretization of the equation is performed by all variables in equation and leads to a factorial rate of convergence if Lagrange interpolation is used for building quasi representation of differential operator. The rank of a finite dimensional operator and approximation properties have been determined. Error estimations and the factorial rate of convergence have been proved.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 2; 51-62
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 17

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