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Tytuł:
Further results on robust fuzzy dynamic systems with LMI D-stability constraints
Autorzy:
Assawinchaichote, W.
Powiązania:
https://bibliotekanauki.pl/articles/331041.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fuzzy controller
robust control
LMI approach
D-stability
Takagi-Sugeno fuzzy model
regulator rozmyty
sterowanie odporne
stabilność
model Takagi-Sugeno
Opis:
This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi–Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 785-794
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties
Autorzy:
Balasubramaniam, P.
Lakshmanan, S.
Rakkiyappan, R.
Powiązania:
https://bibliotekanauki.pl/articles/331417.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
opóźnienie zależne
liniowa nierówność macierzowa
system stochastyczny
stabilność odporna
delay-dependent stability
linear matrix inequality
Lyapunov-Krasovskii functional
stochastic systems
Opis:
This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2012, 22, 2; 339-351
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Robust stability of positive continuous-time linear systems with delays
Autorzy:
Busłowicz, M.
Powiązania:
https://bibliotekanauki.pl/articles/908143.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
czas ciągły
system liniowy
opóźnienie
stabilność odporna
niepewność liniowa
positive continuous-time linear system
delay
robust stability
linear uncertainty
interval system
Opis:
The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2010, 20, 4; 665-670
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global Stability of Linearizing Control With a New Robust Nonlinear Observer of The Induction Motor
Autorzy:
Chenafa, M.
Mansouri, A.
Bouhenna, A.
Etien, E.
Belaidi, A.
Denai, M. A.
Powiązania:
https://bibliotekanauki.pl/articles/911129.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
obserwatory nieliniowe
sterowanie liniowe
silnik indukcyjny
stabilność globalna
nonlinear observer
linearizing control
induction motor
global stability
Opis:
This paper mainly deals with the design of an advanced control law with an observer for a special class of nonlinear systems. We design an observer with a gain as a function of speed. We study the solution to the output feedback torque and rotor flux-tracking problem for an induction motor model given in the natural frame. We propose a new robust nonlinear observer and prove the global stability of the interlaced controller-observer system. The control algorithm is studied through simulations and applied in many configurations (various set points, flux and speed profiles and torque disturbances), and is shown to be very efficient.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2005, 15, 2; 235-243
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A robust controller design method and stability analysis of an underactuated underwater vehicle
Autorzy:
Chin, C. S.
Lau, M. W. S.
Low, E.
Seet, G. G. L.
Powiązania:
https://bibliotekanauki.pl/articles/908396.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
pojazd podwodny
stabilność
sterowanie odporne
symulacja
underwater vehicle
underactuated
stabilizable
robust controller
simulation
Opis:
The problem of designing a stabilizing feedback controller for an underactuated system is a challenging one since a nonlinear system is not stabilizable by a smooth static state feedback law. A necessary condition for the asymptotical stabilization of an underactuated vehicle to a single equilibrium is that its gravitational field has nonzero elements corresponding to unactuated dynamics. However, global asymptotical stability (GAS) cannot be guaranteed. In this paper, a robust proportional-integralderivative (PID) controller on actuated dynamics is proposed and unactuated dynamics are shown to be global exponentially bounded by the Sordalen lemma. This gives a necessary and sufficient condition to guarantee the global asymptotic stability (GAS) of the URV system. The proposed method is first adopted on a remotely-operated vehicle RRC ROV II designed by the Robotic Research Centre in the Nanyang Technological University (NTU). Through the simulation using the ROV Design and Analysis toolbox (RDA) written at the NTU in the MATLAB/SIMULINK environment, the RRC ROV II is robust against parameter perturbations.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2006, 16, 3; 345-356
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A hierarchical decomposition of decision process Petri nets for modeling complex systems
Autorzy:
Clempner, J.
Powiązania:
https://bibliotekanauki.pl/articles/907753.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
hierarchia
rozkład
składnik wielokrotnego użycia
proces decyzyjny
stabilność
optymalizacja
metoda Lyapunova
DPPN
hierarchy
decomposition
structuring mechanisms
re-usable components
decision process
stability
Lyapunov methods
optimization
Opis:
We provide a framework for hierarchical specification called Hierarchical Decision Process Petri Nets (HDPPNs). It is an extension of Decision Process Petri Nets (DPPNs) including a hierarchical decomposition process that generates less complex nets with equivalent behavior. As a result, the complexity of the analysis for a sophisticated system is drastically reduced. In the HDPPN, we represent the mark-dynamic and trajectory-dynamic properties of a DPPN. Within the framework of the mark-dynamic properties, we show that the HDPPN theoretic notions of (local and global) equilibrium and stability are those of the DPPN. As a result in the trajectory-dynamic properties framework, we obtain equivalent characterizations of that of the DPPN for final decision points and stability. We show that the HDPPN mark-dynamic and trajectory-dynamic properties of equilibrium, stability and final decision points coincide under some restrictions. We propose an algorithm for optimum hierarchical trajectory planning. The hierarchical decomposition process is presented under a formal treatment and is illustrated with application examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2010, 20, 2; 349-366
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An analytical method for well-formed workflow/Petri net verification of classical soundness
Autorzy:
Clempner, J.
Powiązania:
https://bibliotekanauki.pl/articles/331027.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Lyapunov stability
Petri net
decidability
workflow net
soundness
verification
sieć Petriego
sieć przepływu pracy
stabilność Lapunova
Opis:
In this paper we consider workflow nets as dynamical systems governed by ordinary difference equations described by a particular class of Petri nets. Workflow nets are a formal model of business processes. Well-formed business processes correspond to sound workflow nets. Even if it seems necessary to require the soundness of workflow nets, there exist business processes with conditional behavior that will not necessarily satisfy the soundness property. In this sense, we propose an analytical method for showing that a workflow net satisfies the classical soundness property using a Petri net. To present our statement, we use Lyapunov stability theory to tackle the classical soundness verification problem for a class of dynamical systems described by Petri nets. This class of Petri nets allows a dynamical model representation that can be expressed in terms of difference equations. As a result, by applying Lyapunov theory, the classical soundness property for workflow nets is solved proving that the Petri net representation is stable. We show that a finite and non-blocking workflow net satisfies the sound property if and only if its corresponding PN is stable, i.e., given the incidence matrix A of the corresponding PN, there exists a Φ strictly positive m vector such that AΦ ≤ 0. The key contribution of the paper is the analytical method itself that satisfies part of the definition of the classical soundness requirements. The method is designed for practical applications, guarantees that anomalies can be detected without domain knowledge, and can be easily implemented into existing commercial systems that do not support the verification of workflows. The validity of the proposed method is successfully demonstrated by application examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 931-939
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modeling shortest path games with Petri nets: A Lyapunov based theory
Autorzy:
Clempner, J.
Powiązania:
https://bibliotekanauki.pl/articles/908393.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Nash equilibrium point
shortest path game
game theory
Lyapunov equilibrium point
Bellman’s equation
Lyapunov-like fuction
stability
teoria gier
funkcja Lapunowa
równanie Bellmana
stabilność
Opis:
In this paper we introduce a new modeling paradigm for shortest path games representation with Petri nets. Whereas previous works have restricted attention to tracking the net using Bellman’s equation as a utility function, this work uses a Lyapunov-like function. In this sense, we change the traditional cost function by a trajectory-tracking function which is also an optimal cost-to-target function. This makes a significant difference in the conceptualization of the problem domain, allowing the replacement of the Nash equilibrium point by the Lyapunov equilibrium point in game theory. We show that the Lyapunov equilibrium point coincides with the Nash equilibrium point. As a consequence, all properties of equilibrium and stability are preserved in game theory. This is the most important contribution of this work. The potential of this approach remains in its formal proof simplicity for the existence of an equilibrium point.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2006, 16, 3; 387-397
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Neural network-based MRAC control of dynamic nonlinear systems
Autorzy:
Debbache, G.
Bennia, A.
Goléa, N.
Powiązania:
https://bibliotekanauki.pl/articles/908401.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
sieć neuronowa
model odniesienia
system nieliniowy
sterowanie adaptacyjne
obserwator
stabilność
neural networks
reference model
nonlinear systems
adaptive control
observer
stability
Opis:
This paper presents direct model reference adaptive control for a class of nonlinear systems with unknown nonlinearities. The model following conditions are assured by using adaptive neural networks as the nonlinear state feedback controller. Both full state information and observer-based schemes are investigated. All the signals in the closed loop are guaranteed to be bounded and the system state is proven to converge to a small neighborhood of the reference model state. It is also shown that stability conditions can be formulated as linear matrix inequalities (LMI) that can be solved using efficient software algorithms. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation results are presented to show the effectiveness of the approach.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2006, 16, 2; 219-232
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear stabilizing control of an uncertain bioprocess model
Autorzy:
Dimitrova, N.
Krastanov, M.
Powiązania:
https://bibliotekanauki.pl/articles/930090.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
oczyszczanie ścieków
stabilność asymptotyczna
sterowanie nieliniowe
wastewater treatment model
local bifurcations of steady states
asymptotic stabilization
extremum seeking
uncertain data
Opis:
In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a previously chosen operating point. A numerical extremum seeking algorithm is designed to stabilize the dynamics towards the maximum methane output flow rate in the presence of coefficient uncertainties. Computer simulations in Maple are reported to illustrate the theoretical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 3; 441-454
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination
Autorzy:
Ding, D.
Ma, Q.
Ding, X.
Powiązania:
https://bibliotekanauki.pl/articles/330497.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
nonstandard finite difference
unconditional positivity
stability
Lyapunov function
metoda różnic skończonych
stabilność
funkcja Lyapunova
Opis:
In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our proof of global stability utilizes the method of Lyapunov functions. Numerical simulation illustrates the effectiveness of our results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 3; 635-646
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A multi-model approach to Saint-Venant equations: A stability study by LMIs
Autorzy:
Dos Santos Martins, V.
Rodrigues, M.
Diagne, M.
Powiązania:
https://bibliotekanauki.pl/articles/330130.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
równanie Saint-Venanta
system nieskończenie wymiarowy
stabilność wykładnicza
Saint-Venant equation
multi-model
LMIs
infinite dimensional system
exponential stability
strongly continuous semigroup
internal model boundary control
Opis:
This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2012, 22, 3; 539-550
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability of Multi-Dimensional Discrete Systems With Varying Structure
Autorzy:
Dymkov, M.
Gaishun, I.
Powiązania:
https://bibliotekanauki.pl/articles/908265.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
układ wielowymiarowy
złożenie krzywoliniowe
stabilność
multi-dimensional systems
total solvability
curvilinear composition
stability
Opis:
A new class of multi-dimensional discrete systems with varying structureis introduced. The notions of total solvability, p_t-boundedness, p_t-stability and asymptotic stability are defined. For studying properties of the solutions for the considered systems a curvilinear composition of mappings along discrete curves is used. Total solvability conditions similar to the Frobenius ones are obtained. Sufficient conditions for p_t-stability and asymptotic stability based on the Lyapunov functional method are also established. A two-dimensional system of Volterra equations is presented as an example of equations with varying structure.
Źródło:
International Journal of Applied Mathematics and Computer Science; 1999, 9, 4; 789-799
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability of a class of adaptive nonlinear systems
Autorzy:
Dzieliński, A.
Powiązania:
https://bibliotekanauki.pl/articles/908445.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
system nieliniowy
stabilność Lapunova
układ adaptacyjny
nonlinear systems
Lyapunov stability
adaptive systems
Opis:
This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear systems is investigated and it is shown how the problem of model following control may be tackled using this methodology.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2005, 15, 4; 455-462
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Dynamics of a Chemostat Model With Delayed Nutrient Recycling
Autorzy:
Fergola, P.
Jiang, L.
Ma, Z.
Powiązania:
https://bibliotekanauki.pl/articles/929727.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
stabilność
sterowanie populacją
chemostat model
delayed nutrient recycling
stability
uniform persistence
population control
Opis:
This paper studies the dynamics of a chemostat model with n populations competing for one nutrient which can be recycled due to decomposition of dead biomass. Several kinds of results about local and global stability of non-negative equilibria, uniform persistence and control of populations are obtained.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2000, 10, 1; 81-96
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 44

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