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Tytuł:
Constrained Controllability of Dynamic Systems
Autorzy:
Klamka, J.
Powiązania:
https://bibliotekanauki.pl/articles/908304.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
sterowność wymuszona
system nieskończenie wymiarowy
system z rozproszonymi parametrami
system dynamiczny dodatni
constrained controllability
infinite-dimensional systems
distributed-parameter systems
positive dynamic systems
Opis:
The present paper is devoted to a study of constrained controllability and controllability for linear dynamic systems if the controls are taken to be non-negative. By analogy to the usual definition of controllability it is possible to introduce the concept of positive controllability. Weshall concentrate on approximate positive controllability for linear infinite-dimensional dynamic systems when the values of controls are taken from a positive closed convex cone and the operator of the system is normal and has pure discrete point spectrum. Special attention is paid to positive infinite-dimensional linear dynamic systems. General approximate constrained controllability results are then applied to distributed-parameter dynamic systems described by linear partial-differential equations of parabolic type with various kinds of boundary conditions. Several remarks and comments on the relationships between different concepts of controllability are given. Finally, a simple illustrative example is also presented.
Źródło:
International Journal of Applied Mathematics and Computer Science; 1999, 9, 2; 231-244
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Qualitative analysis of controlled drug resistance model - inverse Laplace and and semigroup approach
Autorzy:
Świerniak, A.
Polański, A.
Kimmel, M.
Bobrowski, A.
Śmieja, J.
Powiązania:
https://bibliotekanauki.pl/articles/205965.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
modele biomedyczne
proces gałązkowy
stabilność
układy nieskończenie wymiarowe
biomedical models
branching processes
infinite dimensional systems
stability
Opis:
In this paper we study some properties of infinite models of the controlled evolution of drug resistance. We combine asymptotic techniques used in previous studies of similar models with methods of control theory and of semigroup theory. It enables us to find conditions for stability of the model both when the sensitive population is annihilated and when there exists a permanent influx from the sensivite compartment into drug resistant one. The conditions are expressed in terms of relationships between amplification and deamplification ratios as well as average life times of cells and intensity of anticancer drug action.
Źródło:
Control and Cybernetics; 1999, 28, 1; 61-73
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Circle criterion and boundary control systems in factor form: input-output approach
Autorzy:
Grabowski, P.
Callier, F. M.
Powiązania:
https://bibliotekanauki.pl/articles/908133.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
układ sterowania
przepływy międzygałęziowe
infinite dimensional control systems
semigroups
input-output relations
Opis:
A circle criterion is obtained for a SISO Lur'e feedback control system consisting of a nonlinear static sector-type controller and a linear boundary control system in factor form on an infinite-dimensional Hilbert state space H previously introduced by the authors (Grabowski and Callier, 1999). It is assumed for the latter that (a) the observation functional is infinite-time admissible, (b) the factor control vector satisfies a compatibility condition, and (c) the transfer function belongs to Hinfty(Pi+) and satisfies a frequency-domain inequality of the circle criterion type. We also require that the closed-loop system be well-posed, i.e. for any initial state x0in H the truncated input and output signals uT, yT belong to L2(0,T) for any T>0. The technique of the proof adapts Desoer-Vidyasagar's circle criterion method (Desoer and Vidyasagar, 1975, Ch.3, Secs.1 and 2, pp.37-43, Ch.5, Sec.2, pp.139-142 and Ch.6, Secs.3 and 4, pp.172-174]), and uses the input-output map developed by the authors (Grabowski and Callier, 2001). The results are illustrated by two transmission line examples: (a) that of the loaded distortionless RLCG type, and (b) that of the unloaded RC type. The conclusion contains a discussion on improving the results by the loop-transformation technique.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1387-1403
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact Observability of Diagonal Systems With a One-Dimensional Output Operator
Autorzy:
Jacob, B.
Zwart, H.
Powiązania:
https://bibliotekanauki.pl/articles/908120.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
obserwator
równanie Lyapunova
infinite-dimensional systems
unbounded observation operator
exact observability
Hautus test
Lyapunov equations
Opis:
In this paper equivalent conditions for exact observability of diagonal systems with a one-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (1994). The other conditions are given in terms of the eigenvalues and the Fourier coefficients of the system data.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1277-1283
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Motion Planning, Equivalence, Infinite Dimensional Systems
Autorzy:
Rouchon, P.
Powiązania:
https://bibliotekanauki.pl/articles/908322.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
metoda elementów skończonych
układ sterowania
system opóźniania
infinite dimensional control systems
motion planning
flatness
absolute equivalence
Pfaffian systems
delay systems
Gevrey functions
Opis:
Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems (Fliess et al., 1995; 1999a), motion planning admits simple and explicit solutions. This stems from an explicit description of the trajectories by an arbitrary time function y, the flat output, and a finite number of its time derivatives. Such explicit descriptions are related to old problems on Monge equations and equivalence investigated by Hilbert and Cartan. The study of several examples (the car with n-trailers and the non-holonomic snake, pendulums in series and the heavy chain, the heat equation and the Euler-Bernoulli flexible beam) indicates that the notion of flatness and its underlying explicit description can be extended to infinite-dimensional systems. As in the finite-dimensional case, this property yields simple motion planning algorithms via operators of compact support. For the non-holonomic snake, such operators involve non-linear delays. For the heavy chain, they are defined via distributed delays. For heat and Euler-Bernoulli systems, their supports are reduced to a point and their definition domain coincides with the set of Gevrey functions of order 2.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2001, 11, 1; 165-188
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal multidrug treatment in the presence of drug resistance stemming from gene amplification
Autorzy:
Śmieja, J.
Świerniak, A.
Powiązania:
https://bibliotekanauki.pl/articles/332869.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Śląski. Wydział Informatyki i Nauki o Materiałach. Instytut Informatyki. Zakład Systemów Komputerowych
Tematy:
nieskończenie wymiarowy system
optymalna kontrola
modelowanie biomedyczne
infinite dimensional systems
optimal control
biomedical modeling
Opis:
The paper is concerned with development of optimal treatment protocols that take into account both action of several drugs and the evolution of drug resistance. It is a result of analysis of evolution of drug resistance in cancer population but presented methodology can be applied in any case involving drug resistance stemming from gene amplification. First, a biological background is given. In subsequent sections of the paper, the developed technique is presented and some early analytical results, which form a basis for more precise modeling, are shown. Afterwards, the model description is transformed into a vector integro-differential equation, which makes it possible to define necessary conditions of optimal solution to the minimization problem arising from the search for the optimal treatment. Finally, some remarks on the model applicability are presented.
Źródło:
Journal of Medical Informatics & Technologies; 2002, 3; MI13-19
1642-6037
Pojawia się w:
Journal of Medical Informatics & Technologies
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptive compensators for pertrubed positive real infinite-dimensional systems
Autorzy:
Curtain, R. F.
Demetriou, M. A.
Ito, K.
Powiązania:
https://bibliotekanauki.pl/articles/908105.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
automatyka
robotyka
infinite dimensional systems
positive real systems
adaptive controllers
Opis:
The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinite-dimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law based on the Lyapunov redesign method. We obtain conditions on the system to ensure uniform boundedness of the estimator dynamics and the parameter estimates, and the convergence of the estimator error. For the case of a known periodic exogenous input we design an adaptive compensator which forces the system to converge to a unique periodic solution. We illustrate our approach with a delay example and a diffusion example for which we obtain convincing numerical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 4; 441-452
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic analysis of three random branching walk models arising in molecular biology
Analiza asymptotyczna trzech modeli błądzenia z rozgałęzieniami z dziedziny biologii molekularnej
Autorzy:
Świerniak, A.
Polański, A.
Śmieja, J.
Kimmel, M.
Rzeszowska-Wolny, J.
Powiązania:
https://bibliotekanauki.pl/articles/206737.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
analiza asymptotyczna
modelowanie biomatematyczne
procesy rozgałęzień
systemy nieskończenie wymiarowe
asymptotic analysis
biomathematical modelling
branching processes
infinite dimensional systems
Opis:
Using asymptotic techniques based on Laplace transforms, spectral analysis and theory of feedback systems, we characterise the asymptotic behaviour of the repeat loci in microsatellite DNA and cancer cells with increasing number of copies of genes responsible for coding proteins causing drug removal or metabolisation as well as telomeres shortening, which is supposed to be the mechanism of ageing and death. These three problems are described by models in the form of infinitely many differential linear or bilinear first order equations, resulting from branching random walk processes used to represent the evolution of particles in these problems.
Wykorzystując techniki asymptotyczne oparte na transformatach Laplace'a, analizę spektralną oraz teorię układów ze sprzężeniem zwrotnym w artykule scharakteryzowano zachowanie asymptotyczne powtórek w DNA mikrosatelitarnym oraz w komórkach rakowych z rosnącą liczbą kopii genów odpowiedzialnych za kodowanie białek powodujących usuwanie lub przemianę metaboliczną leków, a także skracanie telomerów, o którym się sądzi, że jest mechanizmem starzenia się i śmierci. Te trzy zagadnienia są opisywane przy pomocy modeli w postaci nieskończonej liczby liniowych lub biliniowych równań pierwszego rzędu, wynikających z procesów błądzenia, stosowanych do opisu ewolucji cząstek w tych zagadnieniach.
Źródło:
Control and Cybernetics; 2003, 32, 1; 147-162
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Different Models of Chemotherapy Taking Into Account Drug Resistance Stemming from Gene Amplification
Autorzy:
Śmieja, J.
Świerniak, A.
Powiązania:
https://bibliotekanauki.pl/articles/908161.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
medycyna
automatyka
biomedical modelling
infinite dimensional systems
multivariable control
Opis:
This paper presents an analysis of some class of bilinear systems that can be applied to biomedical modelling. It combines models that have been studied separately so far, taking into account both the phenomenon of gene amplification and multidrug chemotherapy in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix whose form allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the other is infinite dimensional and tridiagonal. A methodology of the analysis of such models, based on system decomposition, is presented. An optimal control problem is defined in the l1 space. In order to derive necessary conditions for optimal control, the model description is transformed into an integro-differential form. Finally, biomedical implications of the obtained results are discussed.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 297-305
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Are infinite dimensional models applicable in modelling and analysis of cancer chemotherapy?
Autorzy:
Świerniak, A.
Kimmel, M.
Śmieja, J.
Rzeszowska-Wolny, J.
Powiązania:
https://bibliotekanauki.pl/articles/333061.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Śląski. Wydział Informatyki i Nauki o Materiałach. Instytut Informatyki. Zakład Systemów Komputerowych
Tematy:
odporność na leki
nieskończenie wymiarowy system
przekształcenia Laplace'a
drug resistance
branching random walk
infinite-dimensional systems
Laplace transforms
Opis:
Drug resistance and phase dependence have been regarded by many authors as the main obstacles against successful cancer chemotherapy. We propose a model which takes into account both these phenomena and give a tool to use phase specificity as an advantage rather than a fault and make it resistant of drug resistance. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy, in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which enables decomposition of the model into two interacting subsystems. While the first one, of finite dimension, can have any form, the second one is infinite dimensional and tridiagonal.
Źródło:
Journal of Medical Informatics & Technologies; 2004, 8; MM3-10
1642-6037
Pojawia się w:
Journal of Medical Informatics & Technologies
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
High-gain feedback and sliding modes in infinite dimensional systems
Autorzy:
Levaggi, L.
Powiązania:
https://bibliotekanauki.pl/articles/970418.pdf
Data publikacji:
2004
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
system nieskończenie wymiarowy
zaburzenia osobliwe
infinite dimensional systems
high-gain feedback
singular perturbations
sliding modes
Opis:
This paper focuses on the connection between sliding motions and low frequency modes of high-gain feedback systems in an infinite dimensional framework. We study a particular class of abstract control systems in a Hilbert space setting and analyse their high-gain behaviour through singular perturbations. We show that the "slow" motion derived from the reduced model approximates the evolution of the closed loop after a fast transient. Moreover we prove a relation between this slow component of the high-gain feedback system and sliding motions, in the spirit, of the analogous result in the finite dimensional setting by Young, Kokotovic and Utkin (Young et al., 1977).
Źródło:
Control and Cybernetics; 2004, 33, 1; 33-50
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximate constrained controllability of mechanical system
Sterowanie minimalno-czasowe manipulatorów hydraulicznych po zadanej ścieżce
Autorzy:
Klamka, J.
Powiązania:
https://bibliotekanauki.pl/articles/279817.pdf
Data publikacji:
2005
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
linear infinite-dimensional control systems
mechanical flexible structure vibratory systems
controllability of abstract dynamical systems
Opis:
In the present paper approximate constrained controllability of linear abstract second-order infinite-dimensional dynamical control systems is considered. First, fundamental definitions and notions are recalled. Next it is proved, using the so-called frequency-domain method, that approximate constrained controllability of second-order dynamical control system can be verified by the approximate constrained controllability conditions for the simplified, suitably defined first-order linear dynamical control system. General results are then applied for approximate constrained controllability investigation of mechanical flexible structure vibratory dynamical system. Some special cases are also considered. Moreover, many remarks, comments and corollaries on the relationships between different concepts of approximate controllability are given. Finally, the obtained results are applied for investigation of approximate constrained controllability for flexible mechanical structure. In this case linear second-order partial differential state equation describes the transverse motion of an elastic beam which occupies the given finite interval.
Praca przedstawia metodę optymalizacji minimalno-czasowej ruchów manipulatorów hydraulicznych, po zadanej ścieżce członu roboczego. Zakładane jest, że ścieżka członu roboczego jednoznacznie określa odpowiadającą jej ścieżkę manipulatora w zmiennych uogólnionych. Optymalizacja sprowadza się wówczas do znalezienia optymalnego rozkładu parametru ścieżki w czasie. Proponowana metoda optymalizacji polega na przybliżeniu ciągłego rozkładu parametru zbiorem punktów, a następnie znalezieniu ich optymalnych położeń metodami programowania nieliniowego z ograniczeniami. Zakładana jest przy tym nieściśliwość cieczy hydraulicznej, w celu przyspieszenia obliczeń. Załączone są wyniki przykładowych optymalizacji, wykonanych na modelu trójczłonowej koparki hydraulicznej.
Źródło:
Journal of Theoretical and Applied Mechanics; 2005, 43, 3; 539-554
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Well-posedness and stability analysis of hybrid feedback systems using Shkalikovs theory
Autorzy:
Grabowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/254925.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite-dimensional control systems
semigroups
spectral methods
Riesz bases
Opis:
The modern method of analysis of the distributed parameter systems relies on the transformation of the dynamical model to an abstract differential equation on an appropriately chosen Banach or, if possible, Hilbert space. A linear dynamical model in the form of a first order abstract differential equation is considered to be well-posed if its right-hand side generates a strongly continuous semigroup. Similarly, a dynamical model in the form of a second order abstract differential equation is well-posed if its right-hand side generates a strongly continuous cosine family of operators. Unfortunately, the presence of a feedback leads to serious complications or even excludes a direct verification of assumptions of the Hille-Phillips-Yosida and/or the Sova-Fattorini Theorems. The class of operators which are similar to a normal discrete operator on a Hilbert space describes a wide variety of linear operators. In the papers [12, 13] two groups of similarity criteria for a given hybrid closed-loop system operator are given. The criteria of the first group are based on some perturbation results, and of the second, on the application of Shkalikov's theory of the Sturm-Liouville eigenproblems with a spectral parameter in the boundary conditions. In the present paper we continue those investigations showing certain advanced applications of the Shkalikov's theory. The results are illustrated by feedback control systems examples governed by wave and beam equations with increasing degree of complexity of the boundary conditions.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 45-97
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The motion planning problem and exponential stabilization of a heavy chain. Part II
Autorzy:
Grabowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/255394.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite-dimensional control systems
semigroups
motion planning problem
exponential stabilization
spectral methods
Riesz bases
exact observability
Opis:
This is the second part of paper [8], where a model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [8] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was also shown that the exponential stability can be achieved by applying a stabilizer of the colocated-type. The proof used the method of Lyapunov functionals. In the present paper, we give other two proofs of the exponential stability, which provides an additional intrinsic insight into the exponential stabilizability mechanism. The first proof makes use of some spectral properties of the system. In the second proof, we employ some relationships between exponential stability and exact observability.
Źródło:
Opuscula Mathematica; 2008, 28, 4; 481-505
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Comparison between two approaches to modeling microsatellite DNA repeats: infinite dimensional model and its n-dimensional
Autorzy:
Białka, M.
Powiązania:
https://bibliotekanauki.pl/articles/229939.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
infinite-dimensional systems
asymptotic stability
chain systems
microsatellites DNA repeats
polymerase slippage
Opis:
Two approaches to modeling microsatellite DNA repeats are considered. The former is an infinite dimensional system based on the theory of branching random walks which dynamic properties are characterized using Laplace transforms and Laplace asymptotic techniques. The latter is an n-dimensional approximation where microsatellite DNA repeats model is the example of a chain system. Both models were the subject of many numerical calculations using the MATLAB software. The results allow us to evaluate the asymptotic behavior and determine the effect of the system parameters on the run of the solution and the state variables.
Źródło:
Archives of Control Sciences; 2011, 21, 4; 419-441
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
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