Wyniki wyszukiwania - Biblioteka Nauki

1

On the region of attraction of dynamical systems: Application to Lorenz equations

100%

Hammami M. A. , Rettab N. H.

|

tom Vol. 30, No. 3

389--409

EN

Many nonlinear dynamical systems can present a challenge for the stability analysis in particular the estimation of the region of attraction of an equilibrium point. The usual methodis based on Lyapunov techniques. For the validity of the analysis it should be supposed that the initial conditions lie in the domain of attraction. In this paper, we investigate such problem for a class of dynamical systems where the origin is not necessarily an equilibrium point. In this case, a small compact neighborhood of the origin can be estimated as an attractor for the system. We give a method to estimate the basin of attraction based on the construction of a suitable Lyapunov function. Furthermore, an application to Lorenz system is given to verify the effectiveness of the proposed method.

2

Complex lag synchronization of two identical chaotic complex nonlinear systems

100%

Mahmoud E. , Abualnaja K.

|

nr 1

63-69

EN

Much progress has been made in the research of synchronization for chaotic real or complex nonlinear systems. In this paper we introduce a new type of synchronization which can be studied only for chaotic complex nonlinear systems. This type of synchronization may be called complex lag synchronization (CLS). A definition of CLS is introduced and investigated for two identical chaotic complex nonlinear systems. Based on Lyapunov function a scheme is designed to achieve CLS of chaotic attractors of these systems. The effectiveness of the obtained results is illustrated by a simulation example. Numerical results are plotted to show state variables, modulus errors and phase errors of these chaotic attractors after synchronization to prove that CLS is achieved.

3

An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination

100%

Ding D. , Ma Q. , Ding X.

|

nr 3

635-646

EN

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.

4

Feedback Stabilization of Continuous Systems by Adding an Integrator

100%

Outbib R. , Aggoune W.

|

tom Vol. 9, no 4

871-881

EN

This note is devoted to the problem of global stabilization of continuous systems by adding an integrator. The goal is to prove that if a continuous non-linear system dot x =f(x,u) is globally asymptotically stable at the origin for u equiv 0, then the augmented system obtained by adding an integrator is stabilizable by means of a continuous feedback.

5

Control design of fin roll stabilization in beam seas based on Lyapunov’s direct method

100%

Safak C. Karakas S. C. , Erdem Ucer E. , Emre Pesman E.

Polish Maritime Research

|

2012

|

tom nr 2

25-30

EN

The aim of this study is to design a controller based on Lyapunov’s direct method for fin roll stabilization systems for ships in beam seas. A third order mathematical model consisting of uncoupled roll motion of a ship and fin hydraulic system dynamics is considered. In the model, random wind force is defined by Gaussian white noise. Both controlled and uncontrolled roll motions are presented considering stall effect by roll-time history and safe basin graphics. It is observed from the results that fin control system is successful to reduce erosion percentages of safe basins and roll amplitudes.

6

Pullback incremental attraction

88%

Kloeden P. E. , Lorenz T.

|

tom 1

EN

A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions. Its characterisation by a Lyapunov function is indicated.

7

On the region of attraction of dynamical systems: Application to Lorenz equations

88%

Hammami M. A. , Rettab N. H. , Hammami M. A. , Rettab N. H.

|

8

Discrete-time Takagi-Sugeno singular systems with unmeasurable decision variables: state and fault fuzzy observer design

88%

Aitdaraou K. , Essabre M. , El Assoudi A. , El Yaagoubi E. H.

|

tom Vol. 33, No. 2

321--338

EN

The studied problem in this paper, treat the issue of state and fault estimation using a fuzzy observer in the case of unmeasurable decision variable for Discrete-Time Takagi-Sugeno Singular Sytems (DTSSS). First, an augmented system is introduced to gather state and fault into a single vector, then on the basis of Singular Value Decomposition (SVD) approach, this observer is designed in explicit form to estimate both of state and fault of a nonlinear singular system. The exponential stability of this observer is studied using Lyapunov theory and the convergence conditions are solved with Linear Matrix Inequalities (LMIs). Finally a numerical example is simulated, and results are given to validate the offered approach.

9

Decentralized direct adaptive fuzzy control of non-linear interconnected MIMO system class

88%

Tlemcani A. , Chekireb H. , Boucherit M. S. , Labiod S.

Archives of Control Sciences

|

2007

|

tom Vol. 17, no. 4

409-425

EN

In this paper, we propose a decentralized direct adaptive fuzzy control method for a class interconnected MIMO non linear plant encountered mainly in robotics. The establishment of the control law introduces very simplest assumptions. Indeed, the functions incorporating the plant dynamic must be continuous and the interconnection terms are bounded by unknown bounds. The fuzzy direct adaptive law is designed to compensate for the interconnections effect and to ensure the closed-loop stability, convergence of the controlled outputs and `boundedness' of adaptation parameters. The proposed method is tested by simulation on the robot Puma 560. In this test the robot is controlled in the operational space as that the robot tip follows a prescribed curve on the sphere where the orientation of the last link (sixth) is maintained radial related to the center of this sphere.

10

Stability and controllability of switched systems

88%

Klamka J. , Czornik A. , Niezabitowski M.

|

tom Vol. 61, nr 3

547--555

EN

The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results.

11

Robust output predictive sequential controller design

75%

Vesely V. , Rosinova D.

Archives of Control Sciences

|

2010

|

tom Vol. 20, no. 1

31-46

EN

The paper addresses design problem of a robust parameter dependent quadratically stabilizing output/state feedback model predictive control for linear polytopic systems without constraints using original equential approach. The design procedure ensures stability, robustness properties and guaranteed cost for the closed-loop uncertain system

12

Existence results and stabilization of homogeneous conformable fractional order systems

75%

Nasra N. , Ganmi B. , Mabrouki F.

Archives of Control Sciences

|

2024

|

tom Vol. 34, No. 3

641--661

EN

In this paper, we give results on the stability of homogeneous conformable fractional order systems using assumptions on a family of compact sets and provide the stabilization of an affine control system and given an explicit homogeneous feedback control with the requirement that a control Lyapunov function exists and satisfying a homogeneous condition and we present existence and uniqueness theorems for sequential linear conformable fractional differential equations.

13

Speed Sensorless Control of Induction Motor Based on a Non-Linear Flux and Speed Observer with Parameters Estimation and Considering Iron Loss

63%

Alemi-Rostami M. , Abrishamifar A.

|

tom R. 89, nr 3a

89--97

EN

In this paper, a control method is presented for induction motor which offers high efficiency and high dynamics even considering the influences of iron loss. Recently, research to consider the influences of iron loss has been made in the vector control of an induction motor. Vector control method is a quite complex task which demands precise information about the rotor speed and the position of the magnetic flux. The vector control method presented in this paper, estimates both rotor speed and amplitude magnetic flux rotor. However, there are also applications in which even speed sensors should be omitted. In this method, three-phase motor currents and DC link voltage are measured by means of a nonlinear observer and considering the Lyapunov function for current error, motor parameters, rotor shaft and position of flux are estimated. To stabilize the control system, the Lyapunov function for error, is used. Then, using the genetic algorithm, the value of controlling coefficients their and general effects on system's behavior are obtained. The simulation and experimental results confirm the resistant performance and the proper dynamic efficiency of this method.

PL

W artykule przedstawiono algorytm sterowania maszyną indukcyjną, uwzględniający straty w żelazie. Sterowanie opiera się na bezczujnikowym pomiarze prędkości obrotowej, przy pomocy obserwatora. Korzystając z pomiarów prądów fazowych i napięcia DC-link, z funkcji Lyapunov’a wyznaczana jest prędkość i strumień wirnika. Implementacja algorytmu genetycznego pozwoliła na ocenę wpływu współczynników regulacji na odpowiedź układu. Przedstawiono wyniki symulacyjne i eksperymentalne.

14

One DOF robot manipulator control through type-2 fuzzy robust adaptive controller

63%

Naderolasli A. , Chatraei A.

|

2019

|

tom Vol. 13, No. 1

65--70

EN

In this article, the one DOF robot manipulator control is assessed through second type robust fuzzy-adaptive controller. The objective is to obtain a tracking path with appropriate accuracy. The stability of the closed loop system is verified through Lyapunov stability theory and the efficiency of tracking is analyzed subject to the constraints and uncertainty. In order to design the fuzzy controller a set of if-then fuzzy rules are considered which describe the system input-output behavior. Simulation and the results of the experiments on the one DOF robots indicate the effectiveness of the proposed methods.

15

Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

63%

Raja R. , Sakthivel R. , Anthoni S. M. , Kim H.

|

tom Vol. 21, no 1

127-135

EN

The paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as theMatlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

16

The Stability Interval of the Set of Linear System

63%

Mazakov T. , Wójcik W. , Jomartova S. , Karymsakova N. , Ziyatbekova G. , Tursynbai A. , Mazakov T. , Wójcik W. , Jomartova S. , Karymsakova N. , Ziyatbekova G. , Tursynbai A.

|

nr 2

17

Adaptive backstepping tracking control for an over-actuated DP marine vessel with inertia uncertainties

63%

Witkowska A. , Śmierzchalski R.

|

tom Vol. 28, no. 4

679--693

EN

Designing a tracking control system for an over-actuated dynamic positioning marine vessel in the case of insufficient information on environmental disturbances, hydrodynamic damping, Coriolis forces and vessel inertia characteristics is considered. The designed adaptive MIMO backstepping control law with control allocation is based on Lyapunov control theory for cascaded systems to guarantee stabilization of the marine vessel position and heading. Forces and torque computed from the adaptive control law are allocated to individual thrusters by employing the quadratic programming method in combination with the cascaded generalized inverse algorithm, the weighted least squares algorithm and the minimal least squares algorithm. The effectiveness of the proposed control scheme is demonstrated by simulations involving a redundant set of actuators. The evaluation criteria include energy consumption, robustness, as well accuracy of tracking during typical vessel operation.

18

The Stability Interval of the Set of Linear System

63%

Mazakov T. , Wójcik W. , Jomartova S. , Karymsakova N. , Ziyatbekova G. , Tursynbai A.

International Journal of Electronics and Telecommunications

|

2021

|

tom Vol. 67, No. 2

155--161

EN

The article considers the problem of stability of interval-defined linear systems based on the Hurwitz and LienardShipar interval criteria. Krylov, Leverier, and Leverier-Danilevsky algorithms are implemented for automated construction and analysis of the interval characteristic polynomial. The interval mathematics library was used while developing the software. The stability of the dynamic system described by linear ordinary differential equations is determined and based on the properties of the eigenvalues of the interval characteristic polynomial. On the basis of numerical calculations, the authors compare several methods of constructing the characteristic polynomial. The developed software that implements the introduced interval arithmetic operations can be used in the study of dynamic properties of automatic control systems, energy, economic and other non-linear systems.

19

Stability for certain fourth order nonlinear differential equations

63%

Lin S. , Liu Z. , Yu Y.

|

tom Vol. 31, nr 1

87-96

20

Dynamic feedback stabilization of nonlinear RC ladder network

63%

Skruch P. , Baranowski J. , Mitkowski W.

|

tom z. 1

119-133

EN

The goal of this paper is to study stabilization techniques for a class of RC ladder networks. The system is an electrical circuit that consists of nonlinear resistors and capacitors. The circuit's dynamic behavior can be modeled by nonlinear differential equations. The problem is to determine the dynamic feedback control law that asymptotically stabilizes the system. It is shown that with a linear and nonlinear dynamic feedback control, the energy of the closed-loop system asymptotically decays to zero. The asymptotic stability of the closed-loop system is proved by LaSalle's invariance principle using appropriate Lyapunov function. The results of numerical computations are included to verify theoretical analysis and mathematical formulation.

PL

W pracy rozważono zagadnienie stabilizacji dla wybranej klasy układów drabinkowych typu RC. Wybrana klasa układów obejmuje obwody elektryczne, składające się z rezystorów i kondensatorów o nieliniowych charakterystykach. Dynamika układu jest opisywana za pomocą nieliniowych równań różniczkowych. W pracy pokazano, że zastosowanie dynamicznego sprzężenia zwrotnego asymptotycznie stabilizuje system do zera. Rozważono zarówno liniowe, jak i nieliniowe sprzężenie zwrotne. Własność asymptotycznej stabilności układu zamkniętego została pokazana z wykorzystaniem odpowiednich funkcjonałów Lapunowa oraz twierdzenia LaSalle'a. Wyniki teoretyczne zostały zweryfikowane przez obliczenia numeryczne i symulacje komputerowe