Wyniki wyszukiwania - BazTech

1

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

Aitdaraou Khaoula, Essabre Mohamed, El Assoudi Abdellatif, El Yaagoubi El Hassane

Archives of Control Sciences

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2023

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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.

2

The Stability Interval of the Set of Linear System

Mazakov Talgat, Wójcik Waldemar, Jomartova Sholpan, Karymsakova Nurgul, Ziyatbekova Gulzat, Tursynbai Aisulu

International Journal of Electronics and Telecommunications

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2021

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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.

3

Hybrid synchronization and parameter estimation of a complex chaotic network of permanent magnet synchronous motors using adaptive integral sliding mode control

Siddique Nazam, Rehman Fazal U.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 3

art. no. e137056

EN

The synchronisation of a complex chaotic network of permanent magnet synchronous motor systems has increasing practical importance in the field of electrical engineering. This article presents the control design method for the hybrid synchronization and parameter estimation of ring-connected complex chaotic network of permanent magnet synchronous motor systems. The design of the desired control law is a challenging task for control engineers due to parametric uncertainties and chaotic responses to some specific parameter values. Controllers are designed based on the adaptive integral sliding mode control to ensure hybrid synchronization and estimation of uncertain terms. To apply the adaptive ISMC, firstly the error system is converted to a unique system consisting of a nominal part along with the unknown terms which are computed adaptively. The stabilizing controller incorporating nominal control and compensator control is designed for the error system. The compensator controller, as well as the adopted laws, are designed to get the first derivative of the Lyapunov equation strictly negative. To give an illustration, the proposed technique is applied to 4-coupled motor systems yielding the convergence of error dynamics to zero, estimation of uncertain parameters, and hybrid synchronization of system states. The usefulness of the proposed method has also been tested through computer simulations and found to be valid.

4

Non-linear control of DC-DC converters for battery power management in electric vehicle application

Araria Rabah, Negadi Karim, Boudiaf Mohamed, Marignetti Fabrizio

Przegląd Elektrotechniczny

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2020

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R. 96, nr 3

82--88

EN

In this paper, we use two DC/DC boost-buck converters powered a direct current motor. The boost converter ensures an energy flux for an ideal operation of the vehicle even in case of battery voltage drop. The buck converter his role is to controls and drives the electric motor at different operating conditions. To exploit the proposed approach in the automotive field, experimental tests were carried out. The performances obtained show the usefulness of this system for a better energy management of an electric vehicle and an ideal control under different operating conditions, mostly at nominal operation, in the presence of a load torque and even in case of battery chamber failure. The whole system has been tested experimentally using two microcontroller Arduino, We use Lyapunov nonlinear advanced control strategy and its performance has been analysed.

PL

W tym artykule wykorzystujemy dwa przekształtniki DC-DC typu boost-buck do zasilania silnika prądu stałego. Przekształtnik doładowania zapewnia strumień energii dla idealnej pracy pojazdu, nawet w przypadku spadku napięcia akumulatora. Jego rola polega na sterowaniu i zasilaniu silnika elektrycznego w różnych warunkach pracy. Aby wykorzystać proponowane podejście w branży motoryzacyjnej, przeprowadzono testy eksperymentalne. Uzyskane wyniki wskazują na przydatność tego systemu do lepszego zarządzania energią pojazdu elektrycznego i idealnego sterowania w różnych warunkach pracy, głównie przy pracy nominalnej, w obecności momentu obciążenia, a nawet w przypadku awarii celki akumulatora. Cały system został przetestowany eksperymentalnie przy użyciu dwóch mikrokontrolerów Arduino. Używamy nieliniowej zaawansowanej strategii sterowania bazującej na metodzie Lyapunova, a jego działanie zostało zilustrowano i przeanalizowane.

5

On three methods for bounding the rate of convergence for some continuous-time Markov chains

Zeifman Alexander, Satin Yacov, Kryukova Anastasia, Razumchik Rostislav, Kiseleva Ksenia, Shilova Galina

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 2

251--266

EN

Consideration is given to three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly well suited to describe evolutions of the total number of customers in (in)homogeneous M/M/S queueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services. One of the methods is based on the logarithmic norm of a linear operator function; the other two rely on Lyapunov functions and differential inequalities, respectively. Less restrictive conditions (compared with those known from the literature) under which the methods are applicable are being formulated. Two numerical examples are given. It is also shown that, for homogeneous birth-death Markov processes defined on a finite state space with all transition rates being positive, all methods yield the same sharp upper bound.

6

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

Hammami M. A., Rettab N. H.

Archives of Control Sciences

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2020

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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.

7

Lyapunov function based criteria for ship rolling in random beam seas

Üçer Erdem

Polish Maritime Research

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2019

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nr 3

6--14

EN

The aim of this study is to present a Lyapunov function which can be used to derive an intact stability criterion for a ship in random beam seas. First, the mathematical model of the rolling motion of ships in random beam seas is introduced. The random wave excitation is described by a spectrum which is depended on the wave energy spectrum and the amplitude of the moment of roll. This spectrum is generated by a second order linear filter. Second, the methodology of creating a Lyapunov function is explained briefly. Then, there is outlined the way by which Lyapunov function can be used as the intact stability criterion for a ship. The proposed criterion is derived by considering the weather criteria for German naval vessels. Finally, the coherence of the boundary of safe basin obtained by Lyapunov function with the numerical results obtained by Euler-Maruyama Method is presented. From the results it can be deduced that the Lyapunov function can be used to define an intact stability criterion.

8

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

Naderolasli Amir, Chatraei Abbas

Journal of Automation Mobile Robotics and Intelligent Systems

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2019

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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.

9

Fundamental limitations of the decay of generalized energy in controlled (discrete-time) nonlinear systems subject to state and input constraints

Selek István, Ikonen Enso

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 4

629--639

EN

This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system’s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.

10

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

Witkowska A., Śmierzchalski R.

International Journal of Applied Mathematics and Computer Science

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2018

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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.

11

Lyapunov function for cosmological dynamical system

Szydłowski M., Krawiec A.

Demonstratio Mathematica

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2017

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Vol. 50, nr 1

51--55

EN

We prove the asymptotic global stability of the de Sitter solution in the Friedmann-Robertson-Walker conservative and dissipative cosmology. In the proof we construct a Lyapunov function in an exact form and establish its relationship with the first integral of dynamical system determining evolution of the flat Universe. Our result is that de-Sitter solution is asymptotically stable solution for general form of equation of state p = p(p, H), where dependence on the Hubble function H means that the effect of dissipation are included.

12

On potential kernels associated with random dynamical systems

Hmissi M., Mokchaha F., Hmissi A.

Opuscula Mathematica

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2015

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Vol. 35, no. 4

499--515

EN

Let (Θ, φ) be a continuous random dynamical system defined on a probability space (Ω, F, P) and taking values on a locally compact Hausdorff space E. The associated potential kernel V is given by [formula]. In this paper, we prove the equivalence of the following statements: 1. The potential kernel of (Θ, φ) is proper, i.e. V ƒ is x-continuous for each bounded, x-continuous function with uniformly random compact support. 2. (Θ, φ) has a global Lyapunov function, i.e. a function L : Ω x E → (0, ∞) which is x-continuous and L,(Θ tω, φ(t, ω)x) ↓0 as t ↑ ∞. In particular, we provide a constructive method for global Lyapunov functions for gradient-like random dynamical systems. This result generalizes an analogous theorem known for deterministic dynamical systems.

13

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

Ding D., Ma Q., Ding X.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 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.

14

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

Alemi-Rostami M., Abrishamifar A.

Przegląd Elektrotechniczny

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2013

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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.

15

Projective synchronization of chaotic systems via backstepping design

Tarai A., Khan M. A.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

965--973

EN

Chaos synchronization of discrete dynamical systems is investigated. An algorithm is proposed for projective synchronization of chaotic 2D Duffing map and chaotic Tinkerbell map. The control law was derived from the Lyapunov stability theory. Numerical simulation results are presented to verify the effectiveness of the proposed algorithm.

16

Stability and controllability of switched systems

Klamka J., Czornik A., Niezabitowski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2013

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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.

17

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

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

Polish Maritime Research

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2012

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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.

18

Sharply-weak regular linear extensions of dynamical systems leading up to regular systems

Tkocz-Piszczek E.

Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska

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2011

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z. 1

51--68

EN

In this paper we consider some sign–changing Lyapunov function in research on regularity and sharply-week regularity of sets of linear extensions of dynamical systems. By regularity we mean exponential dichotomy of linear differential systems.

PL

Wartykule podjęto tematykę regularności liniowych rozszerzeń układów dynamicznych, która równoważna jest z wykładniczą dychotomią liniowych układów różniczkowych. Przeprowadzono badanie regularności przy użyciu znakozmiennych funkcji Lapunowa. Ponadto, przedstawiono doprowadzenie słabo regularnych układów do regularnych.

19

Some constructions of Lyapunov function for linear extensions of dynamical systems

Kulik V., Tkocz-Piszczek E.

Opuscula Mathematica

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2011

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Vol. 31, no. 3

399-409

EN

In this note we consider some sets of linear extensions of dynamical systems and research regularity by means of the sign-changing Lyapunov function. We examine some constructions of Lyapunov functions for given systems.

20

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

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

International Journal of Applied Mathematics and Computer Science

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2011

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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.