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1
Content available Almost periodic synchronization of fuzzy cellular neural networks with time-varying delays via state-feedback and impulsive control
Li Yongkun, Wang Huimei, Meng Xiaofang
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 2
337--349
EN
In this paper, we are concerned with drive-response synchronization for a class of fuzzy cellular neural networks with time varying delays. Based on the exponential dichotomy of linear differential equations, the Banach fixed point theorem and the differential inequality technique, we obtain the existence of almost periodic solutions of this class of networks. Then, we design a state feedback and an impulsive controller, and construct a suitable Lyapunov function to study the problem of global exponential almost periodic synchronization for the drive-response systems considered. At the end of the paper, we provide an example to verify the effectiveness of the theoretical results.
2
Content available Stability analysis of nonlinear time-delayed systems with application to biological models
Kruthika H. A., Mahindrakar A. D., Pasumarthy R.
International Journal of Applied Mathematics and Computer Science
|
2017
|
Vol. 27, no. 1
91--103
EN
In this paper, we analyse the local stability of a gene-regulatory network and immunotherapy for cancer modelled as nonlinear time-delay systems. A numerically generated kernel, using the sum-of-squares decomposition of multivariate polynomials, is used in the construction of an appropriate Lyapunov–Krasovskii functional for stability analysis of the networks around an equilibrium point. This analysis translates to verifying equivalent LMI conditions. A delay-independent asymptotic stability of a second-order model of a gene regulatory network, taking into consideration multiple commensurate delays, is established. In the case of cancer immunotherapy, a predator–prey type model is adopted to describe the dynamics with cancer cells and immune cells contributing to the predator–prey population, respectively. A delay-dependent asymptotic stability of the cancer-free equilibrium point is proved. Apart from the system and control point of view, in the case of gene-regulatory networks such stability analysis of dynamics aids mimicking gene networks synthetically using integrated circuits like neurochips learnt from biological neural networks, and in the case of cancer immunotherapy it helps determine the long-term outcome of therapy and thus aids oncologists in deciding upon the right approach.
3
Content available Development and sensitivity analysis of a technical object inspection model based on the delay-time concept use
Jodejko-Pietruczuk A., Werbińska-Wojciechowska S.
Eksploatacja i Niezawodność
|
2017
|
Vol. 19, no. 3
403--412
PL
W artykule autorzy skupili się na opracowaniu matematycznego modelu utrzymania obiektów technicznych podlegających kosztownym uszkodzeniom z uwzględnieniem koncepcji opóźnień czasowych. Uszkodzenie w danym przypadku oznacza awarię lub zdarzenie katastrofalne, po którym obiekt jest niezdatny do użytku do momentu wymiany. Wykorzystano politykę blokowej kontroli stanu obiektu, która zakłada, że operacje diagnozy jego stanu są przeprowadzane w regularnych odstępach co T jednostek czasu. Rozpatrzono model kosztowy oraz model gotowości dla przypadku perfekcyjnej diagnozy stanu obiektu. Pozwoliło to na przeprowadzenie analitycznej optymalizacji okresu T między kolejnymi diagnozami stanu obiektu dla nieskończonego horyzontu czasowego. Następnie, zbadano zgodność opracowanego modelu analitycznego z wynikami uzyskanymi w drodze symulacji. Głównym celem było zbadanie wpływu podstawowych parametrów czasowych opracowanego modelu na poziom współczynnika gotowości oraz oczekiwanych kosztów utrzymania badanego obiektu. Analiza została przeprowadzona w dwóch etapach. Pierwszy obejmuje analizę oczekiwanej liczby zdarzeń (uszkodzeń, wymian profilaktycznych oraz operacji kontroli stanu obiektu) dla wybranych zakresów parametrów czasowych: T i opóźnienia czasowego h. W kolejnym kroku zbadano zależność wskaźnika gotowości i oczekiwanych kosztów utrzymania obiektu od wybranych parametrów czasowych modelu. Pracę kończy wskazanie kierunków dalszych prac badawczych.
EN
n the presented paper, authors focus on the development of mathematical delay-time model for single-unit technical systems (technical objects) liable to costly failure. Failure is taken here to mean a breakdown or catastrophic event, after which the system is unusable until replacement. Implemented maintenance policy is the Block-Inspection Policy that assumes performing inspection actions at regular time intervals of T. In the perfect inspection case the availability and cost models are developed. This gives the possibility for analytical optimization of time between maintenance actions performance T for the infinite operational time of the system. Later, there is examined the compatibility of the developed analytical model with simulation results. The main target is to investigate what is the influence of the given model basic time components on the system availability ratio level and the system long-run expected maintenance costs. The analysis is conducted in the two main steps. The first one regards to analysis of expected number of events (failures, preventive replacements and inspection actions) in a single renewal cycle for the chosen range of time parameters: T and delay time h. In the next step, the availability ratio and long-run maintenance costs dependency on the chosen model’s time parameters is under consideration. At the end, the directions for further research work are defined.
4
Content available Stability conditions for linear continuous-time fractional-order state-delayed systems
Busłowicz M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2016
|
Vol. 64, nr 1
3--7
EN
The stability problem of continuous-time linear fractional order systems with state delay is considered. New simple necessary and sufficient conditions for the asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix and time delay. It is shown that in the complex plane there exists such a region that location in this region of all eigenvalues of the state matrix multiplied by delay in power equal to the fractional order is necessary and sufficient for the asymptotic stability. Parametric description of boundary of this region is derived and simple new analytic necessary and sufficient conditions for the stability are given. Moreover, it is shown that the stability of the fractional order system without delay is necessary for the stability of this system with delay. The considerations are illustrated by a numerical example.
5
Content available Analysis of maintenance models’ parameters estimation for technical systems with delay time
Jodejko-Pietruczuk A., Werbińska-Wojciechowska S.
Eksploatacja i Niezawodność
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2014
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Vol. 16, no. 2
288--294
PL
W pracy analizie poddano system trzyelementowy (struktura niezawodnościowa progowa), którego procesy obsługiwania realizowane są zgodnie z założeniami Polityki Przeglądów Blokowych (BIP). Strategia ta może być zastosowana w procesie utrzymania systemów technicznych, gdy znane są pewne jego charakterystyki niezawodnościowe, bazujące m.in. na informacjach o czasach pomiędzy uszkodzeniami elementów systemu. W badaniach skupiono się na trzech rozkładach prawdopodobieństwa tej zmiennej losowej (normalny, Weibull, prostokątny). Model symulacyjny opracowano przy wykorzystaniu oprogramowania GNU Octave. Analiza okresu opóźnienia czasowego, przy założeniu różnych postaci rozkładów prawdopodobieństwa tej zmiennej losowej, pozwoliła na ocenę: czy znajomość typu rozkładu prawdopodobieństwa zmiennej losowej h ma istotne znaczenie dla wyników ekonomicznych funkcjonowania systemu, oraz jakie konsekwencje mogą wystąpić w wyniku niewłaściwej estymacji wartości średniej E(h).
EN
In the article authors are interested in BIP performance for three-element system (“k-out-of-n” reliability structure), the maintenance policy which is one of most commonly used in practice. The BIP may be implemented in technical systems when some information about reliability characteristics is known. The basic reliability parameters that have to be specified in such systems are: an estimation of system components’ time to failure and some delay time characteristics. In order to determine the effects of possible errors and to specify sufficient accuracy of the estimation, the analysis of system costs was done for various values of the expected delay time, assuming three different probability distributions of the delay time (Weibull, Uniform, and Normal). The modelling process was based on the use of GNU Octave software. Test analysis of delay time parameter, assuming different types of probability distributions is the base to conclude: if the form of the distribution has any meaning for economic results of the system, and what kind of consequences may result from improper mean delay time estimation E(h).
6
Content available remote Impact of infrastructure type on reliability of railway transportation system
Restel F. J.
Journal of KONBiN
|
2013
|
No. 1 (25)
21--36
EN
In this paper, the author’s research work is focused on infrastructure impact on railway transportation system reliability. The aim of research described in the paper is to determine correlation between type (and age) of used infrastructure elements, and number of occurring failures. For this purpose, subsystem of infrastructure and associated with it events, were divided into main groups. Examples of groups are: track, train operation devices (related to operating control points or railway line), level crossings, etc. The second aspect is correlation between type of infrastructure and failure consequences. It is required from transportation that it is possible to achieve the right place at the right time in a safety way. Therefore, from the point of view of transportation process, which is the main goal of transportation system, the most significant failure consequences are delays. Moreover, speaking about reliability and safety of railway transportation system, the question arises what is the relation between number of trains and number of unwanted events?
PL
Celem badań opisanych w artykule jest określenie korelacji pomiędzy typem (także wiekiem) użytkowanych elementów infrastruktury, a liczbą występujących zdarzeń. W tym celu podzielono infrastrukturę oraz zdarzenia z nią związane na główne grupy. Przykładowymi grupami są: nawierzchnia, urządzenia sterowania ruchem na posterunku ruchu, urządzenia sterowania ruchem na linii, przejazdy kolejowe itp. Drugim aspektem jest korelacja pomiędzy typem infrastruktury a skutkami. Z punktu widzenia realizacji procesów transportowych, najważniejszym parametrem definiującym skutki są opóźnienia. Ponadto istotne jest pytanie, jaka jest zależność pomiędzy liczbą pociągów a liczbą zdarzeń.
7
Content available The dynamics of the cutting process with Duffing nonlinearity
Weremczuk A., Kęcik K., Rusinek R., Warmiński J.
Eksploatacja i Niezawodność
|
2013
|
Vol. 15, no. 3
209-213
EN
The paper presents the nonlinear one degree of freedom model of cutting process. To describe the dynamics the Duffing model with time delay part is used. The model is solved analytically by using the multiple time scale method. The stability lobe diagrams are determined numerically and analytically. The obtained results show that stability region depends on initial conditions of the system.
PL
W artykule przedstawiono jednowymiarowy nieliniowy model skrawania. Do opisu procesu przyjęto model Duffinga z opóźnieniem czasowym. Model rozwiązano analitycznie za pomocą metody wielu skal czasowych. Wykres stabilności otrzymano numerycznie i analitycznie. Wykazano, że obszary stabilności zależą od warunków początkowych układu.
8
Content available Rekonstrukcja atraktora Monarchy Safye na podstawie szeregów czasowych
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2012
|
R. 53 nr 1 (188)
149-172
PL
W artykule opisano zagadnienie rekonstrukcji atraktora na podstawie szeregu czasowego oraz przedstawiono oprogramowanie pozwalające wyznaczać jej parametry. Zagadnienie to zastosowano do rekonstrukcji atraktora Monarchy Safye na podstawie szeregów czasowych otrzymanych z numerycznego rozwiązania układu dynamicznego opisującego ten atraktor. Wskazano również na związek rekonstrukcji atraktora z analizą rekurencyjną szeregu czasowego.
EN
The paper describes the problem of attractor reconstruction on the basis of a time series and presents software allowing to specify the reconstruction parameters. The above problem has been applied to reconstruct the Monarch Safye attractor on the basis of time series obtained from a numerical solution of a dynamic system describing that attractor. It has also been indicated that there exists a relation between the attractor reconstruction and the recurrence analysis of a time series.
9
Content available remote Uncertainty problem in decision support system for means of transport maintenance processes performance development
Nowakowski T., Werbińska-Wojciechowska S.
Journal of KONBiN
|
2012
|
No. 3 (23)
173--192
EN
In this paper, the authors’ research work is focused on uncertainty analysis implementation in the developed DSS for transportation means’ maintenance processes performance. Thus, in the Introduction section, the transportation means’ maintenance processes issues and the uncertainty problem are described. Later, there is briefly literature overview in the research area discussed. In the next Section, the expert system for means of transport maintenance processes performance is also investigated. Following this, the uncertainty analysis is developed and the examples of expert system implementation are given. The work ends up with summary and directions for further research.
PL
W artykule autorzy skupili się na analizie niepewności danych w opracowanym systemie wsparcia decyzyjnego procesów utrzymania w stanie zdatności środków transportu. We wprowadzeniu problem niepewności oraz zagadnienia utrzymania w stanie zdatności środków transportu zostały omówione. Następnie, przedstawiono krótki przegląd literatury z badanego obszaru. W kolejnym kroku, przedstawiono system ekspertowy wspierający proces decyzyjny w badanym obszarze. Pozwoliło to na opracowanie analizy niepewności oraz jej implementację w systemie ekspertowym. Pracę kończy podsumowanie i wskazanie kierunków dalszych prac badawczych.
10
Content available remote Fault tolerant control of switched nonlinear systems with time delay under asynchronous switching
Xiang Z., Wang R., Chen Q.
International Journal of Applied Mathematics and Computer Science
|
2010
|
Vol. 20, no 3
497-506
EN
This paper investigates the problem of fault tolerant control of a class of uncertain switched nonlinear systems with time delay under asynchronous switching. The systems under consideration suffer from delayed switchings of the controller. First, a fault tolerant controller is proposed to guarantee exponentially stability of the switched systems with time delay. The dwell time approach is utilized for stability analysis and controller design. Then the proposed approach is extended to take into account switched time delay systems with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
11
Content available remote Zeros in linear systems with time delay in state
Tokarzewski J.
International Journal of Applied Mathematics and Computer Science
|
2009
|
Vol. 19, no 4
609-617
EN
The concept of invariant zeros in a linear time-invariant system with state delay is considered. In the state-space framework, invariant zeros are treated as triples: complex number, nonzero state-zero direction, input-zero direction. Such a treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is discussed. For systems of uniform rank, the first nonzero Markov parameter comprises a certain amount of information concerning invariant zeros, output-zeroing inputs and zero dynamics. General formulas for output-zeroing inputs and zero dynamics are provided.
12
Content available remote Time-optimal control of infinite order hyperbolic systems with time delays
Kowalewski A.
International Journal of Applied Mathematics and Computer Science
|
2009
|
Vol. 19, no 4
597-608
EN
In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.
13
Analiza opóźnienia czasowego w ocenie zapotrzebowania na moc cieplną miejskiej sieci ciepłowniczej
Pytel K., Hopkowicz M.
Ciepłownictwo, Ogrzewnictwo, Wentylacja
|
2009
|
R. 40, nr 5
8-12
PL
W artykule zawarto próbę oceny tego, w jakim stopniu akumulacja ciepła w przegrodach obiektów ogrzewanych w procesie nieustalonego przenikania ciepła modyfikuje wpływ aktualnych czynników meteorologicznych na zapotrzebowanie na moc cieplną do ogrzewania. Poruszono też problem estymacji zależności między zapotrzebowaniem na moc pobieraną z miejskiej sieci ciepłowniczej a podstawowymi parametrami meteorologicznymi w ujęciu dynamicznym.
EN
The paper contains an attempt to assess the extent of modification resulting from heat accumulation in building barriers of heating objects during the process of transient heat penetration. The accumulation modifies the influence of existing meteorological factors on the requirements of thermal power supply. The estimation problem of the dependence between the power required from the municipal district heating network and basic meteorological parameters has also been discussed in terms of the dynamic relationship. The paper contains an attempt to assess the extent of modification resulting from heat accumulation in building barriers of heating objects during the process of transient heat penetration. The accumulation modifies the influence of existing meteorological factors on the requirements of thermal power supply. The estimation problem of the dependence between the power required from the municipal district heating network and basic meteorological parameters has also been discussed in terms of the dynamic relationship.
14
Content available remote Immunotherapy with interleukin-2: a study based on mathematical modeling
Banerjee S.
International Journal of Applied Mathematics and Computer Science
|
2008
|
Vol. 18, no 3
389-398
EN
The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.
15
Content available remote Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2006
|
Vol. 16, no 2
169-174
EN
The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.
16
Content available remote Stability and stabilizability of a class of uncertain dynamical systems with delays
Saadni M. S., Chaabane M., Mehdi D.
International Journal of Applied Mathematics and Computer Science
|
2005
|
Vol. 15, no 3
321-329
EN
This paper deals with a class of uncertain systems with time-varying delays and norm-bounded uncertainty. The stability and stabilizability of this class of systems are considered. LinearMatrix Inequalities (LMI) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established.
17
Content available remote On The Stability of Neutral-type Uncertain Systems With Multiple Time Delays
Liu P. L.
International Journal of Applied Mathematics and Computer Science
|
2005
|
Vol. 15, no 2
221-229
EN
The problems of both single and multiple delays for neutral-type uncertain systems are considered. First, for single neutral time delay systems, based on a Razumikhin-type theorem, some delay-dependent stability criteria are derived in terms of the Lyapunov equation for various classes of model transformation and decomposition techniques. Second, robust control for neutral systems with multiple time delays is considered. Finally, we demonstrate numerical examples to illustrate the effectiveness of the proposed approaches. Compared with results existing in the literature, our methods are shown to be superior to them.
18
Content available remote Time-varying time-delay estimation for nonlinear systems using neural networks
Tan Y.
International Journal of Applied Mathematics and Computer Science
|
2004
|
Vol. 14, no 1
63-68
EN
Nonlinear dynamic processes with time-varying time delays can often be encountered in industry. Time-delay estimation for nonlinear dynamic systems with time-varying time delays is an important issue for system identification. In order to estimate the dynamics of a process, a dynamic neural network with an external recurrent structure is applied in the modeling procedure. In the case where a delay is time varying, a useful way is to develop on-line time-delay estimation mechanisms to track the time-delay variation. In this paper, two schemes called direct and indirect time-delay estimators are proposed. The indirect time-delay estimator considers the procedure of time-delay estimation as a nonlinear programming problem. On the other hand, the direct time-delay estimation scheme applies a neural network to construct a time-delay estimator to track the time-varying time-delay. Finally, a numerical example is considered for testing the proposed methods.
19
Content available remote Dynamics of the Tumor-Immune System Competition-the Effect of Time Delay
Gałach M.
International Journal of Applied Mathematics and Computer Science
|
2003
|
Vol. 13, no 3
395-406
EN
The model analyzed in this paper is based on the model set forth by V.A. Kuznetsov and M.A. Taylor, which describes a competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order to achieve a better compatibility with reality.
20
Content available remote On Delay-Dependent Stability for Neutral Delay-Differential Systems
Han Q. L.
International Journal of Applied Mathematics and Computer Science
|
2001
|
Vol. 11, no 4
965-976
EN
This paper deals with the stability problem for a class of linear neutral delay-differential systems. The time delay is assumed constant and known. Delay-dependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing results.
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