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Tytuł:
A double window state observer for detection and isolation of abrupt changes in parameters
Autorzy:
Byrski, J.
Byrski, W.
Powiązania:
https://bibliotekanauki.pl/articles/330142.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fault detection
fault isolation
exact state observer
parameter abrupt changes
derivative reconstruction
linear continuous system
detekcja uszkodzeń
lokalizacja uszkodzeń
dokładny obserwator stanu
układ ciągły liniowy
Opis:
The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of exact state observer will be used. The canonical state will be represented by the derivatives of the measured output signal. Hence the exact state observer will play the role of virtual sensors for reconstruction of the derivatives of the output signal. For designing the exact state observer, the model parameters before and after the moment of fault occurrence must be known. To this end, a special identification method with modulating functions will be used. A novel concept presented in this paper concerns the structure of the observer. It will take the form of a double moving window observer which consists of two signal processing windows, each of width T . These windows are coupled to each other with a common edge. The right-hand side edge of the left-side moving window in the interval [t − 2T, t − T ] is connected to the left-hand side edge of the right-side window which operates in the interval [t − T, t]. The double observer uses different measurements of input/output signals in both the windows, and for each current time t simultaneously reconstructs two values of the state—the final value of the state in the left-side window zT (t − T ) and the initial value of the state z0(t − T ) in the right-side window. If the process parameters are constant, the values of both the states on the common joint edge are the same. If an abrupt change (fault) in some parameter at the moment tA = t − T occurs in the system, then step changes in some variables of the canonical state vector will also occur and the difference between the states will be detected. This will enable localization of the faulty parameter in the system.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2016, 26, 3; 585-602
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generation of synchronizing state machines from a transition system: A region-based approach
Autorzy:
Teren, Viktor
Cortadella, Jordi
Villa, Tiziano
Powiązania:
https://bibliotekanauki.pl/articles/2201022.pdf
Data publikacji:
2023
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
transition system
Petri net
state machine
theory of regions
SAT
pseudo Boolean optimization
układ przejściowy
sieć Petriego
maszyna stanów
teoria regionów
Opis:
Transition systems (TSs) and Petri nets (PNs) are important models of computation ubiquitous in formal methods for modeling systems. A crucial problem is how to extract, from a given TS, a PN whose reachability graph is equivalent (with a suitable notion of equivalence) to the original TS. This paper addresses the decomposition of transition systems into synchronizing state machines (SMs), which are a class of Petri nets where each transition has one incoming and one outgoing arc. Furthermore, all reachable markings (non-negative vectors representing the number of tokens for each place) of an SM have only one marked place with only one token. This is a significant case of the general problem of extracting a PN from a TS. The decomposition is based on the theory of regions, and it is shown that a property of regions called excitation-closure is a sufficient condition to guarantee the equivalence between the original TS and a decomposition into SMs. An efficient algorithm is provided which solves the problem by reducing its critical steps to the maximal independent set problem (to compute a minimal set of irredundant SMs) or to satisfiability (to merge the SMs). We report experimental results that show a good trade-off between quality of results vs. computation time.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2023, 33, 1; 133--149
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positivity and linearization of a class of nonlinear continuous-time systems by state feedbacks
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/329778.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
positive
nonlinear
continuous-time system
linearization
state feedback
układ dodatni
układ ciągły
sprzężenie zwrotne
Opis:
The positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback it is possible to obtain an asymptotically stable and controllable linear system, and if the closed-loop system is positive then it is unstable.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2015, 25, 4; 827-831
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sensors and boundary state reconstruction of hyperbolic systems
Autorzy:
Zerrik, E. H.
Bourray, H.
Ben Hadid, S.
Powiązania:
https://bibliotekanauki.pl/articles/907762.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
system rozproszony
system hyperboliczny
czujnik strategiczny
distributed system
hyperbolic system
regional observability
boundary reconstruction
strategic sensor
Opis:
This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained results are illustrated with numerical examples and simulations.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2010, 20, 2; 227-238
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Design of the state predictive model following control system with time-delay
Autorzy:
Wang, D.
Wu, S.
Okubo, S.
Powiązania:
https://bibliotekanauki.pl/articles/907660.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
sterowanie predykcyjne
opóźnienie
kontrola przeciążeń
state predictive control
time delay
model following control system (MFCS)
TCP/AQM network
congestion control
Opis:
Time-delay systems exist in many engineering fields such as transportation systems, communication systems, process engineering and, more recently, networked control systems. It usually results in unsatisfactory performance and is frequently a source of instability, so the control of time-delay systems is practically important. In this paper, a design of the state predictive model following control system (PMFCS) with time-delay is discussed. The bounded property of the internal states for the control is given, and the utility of this control design is guaranteed. Finally, examples are given to illustrate the effectiveness of the proposed method, and state predictive control techniques are applied to congestion control synthesis problems for a TCP/AQM network.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 2; 247-254
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
State estimation for a class of nonlinear systems
Autorzy:
Schwaller, B.
Ensminger, D.
Dresp-Langley, B.
Ragot, J.
Powiązania:
https://bibliotekanauki.pl/articles/330611.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
nonlinear system
state observer
continuous time
układ nieliniowy
obserwator stanu
układ ciągły
Opis:
We propose a new type of Proportional Integral (PI) state observer for a class of nonlinear systems in continuous time which ensures an asymptotic stable convergence of the state estimates. Approximations of non-linearity are not necessary to obtain such results, but the functions must be, at least locally, of the Lipschitz type. The obtained state variables are exact and robust against noise. Naslin’s damping criterion permits synthesizing gains in an algebraically simple and efficient way. Both the speed and damping of the observer response are controlled in this way. Model simulations based on a Sprott strange attractor are discussed as an example.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2013, 23, 2; 383-394
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stochastic controllability of linear systems with state delays
Autorzy:
Klamka, J.
Powiązania:
https://bibliotekanauki.pl/articles/911240.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
sterowalność
liniowy system sterowania
sterowanie z minimalną energią
controllability
linear control systems
stochastic control systems
delayed state variables
minimum energy control
Opis:
A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2007, 17, 1; 5-13
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:
Local analysis of hybrid systems on polyhedral sets with state-dependent switching
Autorzy:
Leth, J.
Wisniewski, R.
Powiązania:
https://bibliotekanauki.pl/articles/330556.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
inkluzja różniczkowa
badanie stabilności
układ hybrydowy
stability analysis
switched system
hybrid system
differential inclusion
Opis:
This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 341-355
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An adaptive identification method based on the modulating functions technique and exact state observers for modeling and simulation of a nonlinear MISO glass melting process
Autorzy:
Byrski, Witold
Drapała, Michał
Byrski, Jędrzej
Powiązania:
https://bibliotekanauki.pl/articles/907805.pdf
Data publikacji:
2019
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
continuous system
modulating functions
system identification
exact state observer
glass forehearths
układ ciągły
identyfikacja systemu
dokładny obserwator stanu
Opis:
The paper presents new concepts of the identification method based on modulating functions and exact state observers with its application for identification of a real continuous-time industrial process. The method enables transformation of a system of differential equations into an algebraic one with the same parameters. Then, these parameters can be estimated using the least-squares approach. The main problem is the nonlinearity of the MISO process and its noticeable transport delays. It requires specific modifications to be introduced into the basic identification algorithm. The main goal of the method is to obtain on-line a temporary linear model of the process around the selected operating point, because fast methods for tuning PID controller parameters for such a model are well known. Hence, a special adaptive identification approach with a moving window is proposed, which involves using on-line registered input and output process data. An optimal identification method for a MISO model assuming decomposition to many inner SISO systems is presented. Additionally, a special version of the modulating functions method, in which both model parameters and unknown delays are identified, is tested on real data sets collected from a glass melting installation.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2019, 29, 4; 739-757
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global stability of discrete-time feedback nonlinear systems with descriptor positive linear parts and interval state matrices
Autorzy:
Kaczorek, Tadeusz
Ruszewski, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/2055149.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
global stability
positive system
nonlinear system
discrete-time system
stabilność globalna
układ dodatni
układ nieliniowy
układ czasu dyskretnego
Opis:
The global stability of discrete-time nonlinear systems with descriptor positive linear parts, positive scalar feedbacks and interval state matrices is addressed. Sufficient conditions for the global stability of this class of nonlinear systems are established. The effectiveness of these conditions is illustrated using numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2022, 32, 1; 5--10
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
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:
Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
Autorzy:
Grzymkowski, Łukasz
Trofimowicz, Damian
Stefański, Tomasz P.
Powiązania:
https://bibliotekanauki.pl/articles/1838161.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
stability analysis
discrete time system
fractional order system
analiza stabilności
układ czasu dyskretnego
układ rzędu ułamkowego
Opis:
In this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained theoretical results lead to a numerical test for stability evaluation of interconnected FO systems. It is based on modern root-finding techniques on the complex plane employing triangulation of the unit circle and Cauchy’s argument principle. The developed numerical test is simple, intuitive and can be applied to a variety of systems. Furthermore, because it evaluates the function related to the characteristic equation on the complex plane, it does not require computation of state-matrix eigenvalues. The obtained numerical results confirm the efficiency of the developed test for the stability analysis of interconnected discrete-time FO LTI state-space systems.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 4; 649-658
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A memory-efficient noninteger-order discrete–time state–space model of a heat transfer process
Autorzy:
Oprzędkiewicz, K.
Mitkowski, W.
Powiązania:
https://bibliotekanauki.pl/articles/331055.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
noninteger order system
heat transfer equation
infinite dimensional system
continuous fraction expansion
układ niecałkowitego rzędu
wymiana ciepła
układ nieskończenie wymiarowy
Opis:
A new, state space, discrete-time, and memory-efficient model of a one-dimensional heat transfer process is proposed. The model is derived directly from a time-continuous, state-space semigroup one. Its discrete version is obtained via a continuous fraction expansion method applied to the solution of the state equation. Fundamental properties of the proposed model, such as decomposition, stability, accuracy and convergence, are also discussed. Results of experiments show that the model yields good accuracy in the sense of the mean square error, and its size is significantly smaller than that of the model employing the well-known power series expansion approximation.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2018, 28, 4; 649-659
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Similarity transformation of matrices to one common canonical form and its applications to 2D linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/929586.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
postać kanoniczna
podobieństwo
stan sprzężenia zwrotnego
system 2D
common canonical form
similarity transformation
2D linear system
state feedback
Opis:
The notion of a common canonical form for a sequence of square matrices is introduced. Necessary and sufficient conditions for the existence of a similarity transformation reducing the sequence of matrices to the common canonical form are established. It is shown that (i) using a suitable state vector linear transformation it is possible to decompose a linear 2D system into two linear 2D subsystems such that the dynamics of the second subsystem are independent of those of the first one, (ii) the reduced 2D system is positive if and only if the linear transformation matrix is monomial. Necessary and sufficient conditions are established for the existence of a gain matrix such that the matrices of the closed-loop system can be reduced to the common canonical form.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2010, 20, 3; 507-512
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł

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