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Lyapunov matrices approach to the parametric optimization of a system with two delay sand a PD-controller

Józef Duda

Archives of Control Sciences | 2018 | vol. 28 | No 4 | 585-600 | DOI: 10.24425/acs.2018.125484

Keywords neutral system Lyapunov matrix Lyapunov functional

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Abstract

In the paper the parametric optimization problem for a linear system with two delays and a PD-controller is presented. In the parametric optimization problem the quadratic performance index is considered. The value of the quadratic index of quality is calculated due to the Lyapunov functional and is equal to the value of that functional for the initial function of the neutral system with two delays. The Lyapunov functional is determined by means of the Lyapunov matrix.

Authors and Affiliations

Józef Duda

The parametric optimization of a system with two delays and a PI controller

Jozef Duda

Archives of Control Sciences | 2019 | vol. 29 | No 4 | 667-686 | DOI: 10.24425/acs.2019.131231

Keywords time-delay system Lyapunov matrix Lyapunov functional

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Abstract

In the paper a Lyapunov matrices approach to the parametric optimization problem of a time-delay system with two commensurate delays and a PI-controller is presented. The value of integral quadratic performance index is equal to the value of the Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix. In the paper is presented the example of a scalar system with two delays and a PI controller.

Authors and Affiliations

Jozef Duda

A new chaotic system with axe-shaped equilibrium, its circuit implementation and adaptive synchronization

Sundarapandian Vaidyanathan Aceng Sambas Mustafa Mamat

Archives of Control Sciences | 2018 | vol. 28 | No 3 | 443–462 | DOI: 10.24425/acs.2018.124711

Keywords chaos chaotic systems curve equilibrium Lyapunov exponents circuit design synchronization

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Abstract

In the recent years, chaotic systems with uncountable equilibrium points such as chaotic systems with line equilibrium and curve equilibrium have been studied well in the literature. This reports a new 3-D chaotic system with an axe-shaped curve of equilibrium points. Dynamics of the chaotic system with the axe-shaped equilibrium has been studied by using phase plots, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Furthermore, an electronic circuit implementation of the new chaotic system with axe-shaped equilibrium has been designed to check its feasibility. As a control application, we report results for the synchronization of the new system possessing an axe-shaped curve of equilibrium points.

Authors and Affiliations

Sundarapandian Vaidyanathan

Aceng Sambas

Mustafa Mamat

Global rational stabilization of a class of nonlinear time-delay systems

Nadhem Echi Boulbaba Ghanmi

Archives of Control Sciences | 2019 | vol. 29 | No 2 | 259–278 | DOI: 10.24425/acs.2019.129381

Keywords rational stability delay system nonlinear observer Lyapunov functional

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Abstract

The Bulletin of the Polish Academy of Sciences: Technical Sciences (Bull.Pol. Ac.: Tech.) is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred: Artificial and Computational Intelligence, Biomedical Engineering and Biotechnology, Civil Engineering, Control, Informatics and Robotics, Electronics, Telecommunication and Optoelectronics, Mechanical and Aeronautical Engineering, Thermodynamics, Material Science and Nanotechnology, Power Systems and Power Electronics.

Journal Metrics: JCR Impact Factor 2018: 1.361, 5 Year Impact Factor: 1.323, SCImago Journal Rank (SJR) 2017: 0.319, Source Normalized Impact per Paper (SNIP) 2017: 1.005, CiteScore 2017: 1.27, The Polish Ministry of Science and Higher Education 2017: 25 points.

Abbreviations/Acronym: Journal citation: Bull. Pol. Ac.: Tech., ISO: Bull. Pol. Acad. Sci.-Tech. Sci., JCR Abbrev: B POL ACAD SCI-TECH Acronym in the Editorial System: BPASTS.

Authors and Affiliations

Nadhem Echi

Boulbaba Ghanmi

Assignability of numerical characteristics of time-varying systems

A. Babiarz A. Czornik J. Klamka

Bulletin of the Polish Academy of Sciences Technical Sciences | 2019 | 67 | No. 6 | 107-1022 | DOI: 10.24425/bpasts.2019.130890

Keywords assignability controllability Lyapunov spectrum linear time-varying systems

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Abstract

The main aim of this article is to survey and discuss the existing state of art concerning the assignability by a feedback of numerical characteristics of linear continuous and discrete time-varying systems. Most of the results present necessary or sufficient conditions for different formulation of the Lyapunov spectrum assignability problem. These conditions are expressed in terms of various controllability types and optimalizability of the controlled systems and certain properties of the free system such as: regularity, diagonalizability, boundness away, integral separation and reducibility.

Authors and Affiliations

A. Babiarz

A. Czornik

J. Klamka

Dynamics, control, stability, diffusion and synchronization of modified chaotic Colpitts oscillator

Suresh Rasappan K.A. Niranjan Kumar

Archives of Control Sciences | 2021 | vol. 31 | No 3 | 731-759 | DOI: 10.24425/acs.2021.138699

Keywords chaos Colpitts oscillator Lyapunov exponent diffusion stability synchronization

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Abstract

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.

Bibliography

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Authors and Affiliations

Suresh Rasappan

1

K.A. Niranjan Kumar

1

Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India

Different linear control laws for fractional chaotic maps using Lyapunov functional

A. Othman Almatroud Adel Ouannas Giuseppe Grassi Iqbal M. Batiha Ahlem Gasri M. Mossa Al-Sawalha

Archives of Control Sciences | 2021 | vol. 31 | No 4 | 765-780 | DOI: 10.24425/acs.2021.139729

Keywords discrete fractional calculus chaotic maps linear control Lyapunov method

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Abstract

Dynamics and control of discrete chaotic systems of fractional-order have received considerable attention over the last few years. So far, nonlinear control laws have been mainly used for stabilizing at zero the chaotic dynamics of fractional maps. This article provides a further contribution to such research field by presenting simple linear control laws for stabilizing three fractional chaotic maps in regard to their dynamics. Specifically, a one-dimensional linear control law and a scalar control law are proposed for stabilizing at the origin the chaotic dynamics of the Zeraoulia-Sprott rational map and the Ikeda map, respectively. Additionally, a two-dimensional linear control law is developed to stabilize the chaotic fractional flow map. All the results have been achieved by exploiting new theorems based on the Lyapunov method as well as on the properties of the Caputo h-difference operator. The relevant simulation findings are implemented to confirm the validity of the established linear control scheme.

Bibliography

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[3] K. Oprzedkiewicz and K. Dziedzic: Fractional discrete-continuous model of heat transfer process. Archives of Control Sciences, 31(2), (2021), 287– 306, DOI: 10.24425/acs.2021.137419.
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Authors and Affiliations

A. Othman Almatroud

1

Adel Ouannas

2

Giuseppe Grassi

3

Iqbal M. Batiha

4

Ahlem Gasri

5

M. Mossa Al-Sawalha

1

Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy
Department of Mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid, Jordan and Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
Department of Mathematics, University of Larbi Tebessi, Tebessa 12002, Algeria

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

Khaoula Aitdaraou Mohamed Essabre Abdellatif El Assoudi El Hassane El Yaagoubi

Archives of Control Sciences | 2023 | vol. 33 | No 2 | 321-328 | DOI: 10.24425/acs.2023.146278

Keywords observer design unmeasurable decision variable SVD approach Lyapunov function LMIs

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Abstract

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.

Authors and Affiliations

Khaoula Aitdaraou

1 2

Mohamed Essabre

3

Abdellatif El Assoudi

1 2

El Hassane El Yaagoubi

1 2

Laboratory of High Energy Physics and Condensed Matter, Faculty of Science, Hassan II University of Casablanca, B.P 5366, Maarif Casablanca, Morocco
ECPI, Department of Electrical Engineering, ENSEM Hassan II University of Casablanca, B.P 8118, Oasis Casablanca, Morocco
Laboratory of Materials, Energy and Control Systems, Faculty of Sciences and Technologies Mohammedia, Hassan II University of Casablanca, Morocco

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

M.A. Hammami N.H. Rettab

Archives of Control Sciences | 2020 | vol. 30 | No 3 | 389-409 | DOI: 10.24425/acs.2020.134671

Keywords nonlinear dynamical systems Lyapunov function Basin of attraction Lorenz equations

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Abstract

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 method is 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.

Authors and Affiliations

M.A. Hammami

N.H. Rettab

Mittag-Leffler stability analysis of a class of homogeneous fractional systems

Tarek Fajraoui Boulbaba Ghanmi Fehmi Mabrouk Faouzi Omri

Archives of Control Sciences | 2021 | vol. 31 | No 2 | 401-415 | DOI: 10.24425/acs.2021.137424

Keywords homogeneous fractional systems Lyapunov homogeneous function Mittag-Leffler stability

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Abstract

In this paper,we start by the research of the existence of Lyapunov homogeneous function for a class of homogeneous fractional Systems, then we shall prove that local and global behaviors are the same. The uniform Mittag-Leffler stability of homogeneous fractional time-varying systems is studied. A numerical example is given to illustrate the efficiency of the obtained results.

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[10] T. Menard, E. Moulay, and W. Perruquetti: Homogeneous approximations and local observer design. ESAIM: Control, Optimization and Calculus of Variations, 19 (2013), 906–929, DOI: 10.1051/cocv/2012038.
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Authors and Affiliations

Tarek Fajraoui

1

Boulbaba Ghanmi

1

e-mail:

ORCID:

Fehmi Mabrouk

1

Faouzi Omri

1

University of Gafsa, Tunisia, Faculty of Sciences of Gafsa, Department of Mathematics, University campus Sidi Ahmed Zarroug 2112 Gafsa, Tunisia

The Floquet-Lyapunov transformation for fractional discrete-time linear systems with periodic parameters

Tadeusz Kaczorek Andrzej Ruszewski

Archives of Control Sciences | 2024 | vol. 34 | No 1 | 83-89 | DOI: 10.24425/acs.2024.149653

Keywords Floquet-Lyapunov transformation fractional discrete-time linear periodic parameters

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Abstract

The Floquet-Lyapunov transformation is extended to fractional discrete-time linear systems with periodic parameters. A procedure for computation of the transformation is proposed and illustrated by a numerical example.

Authors and Affiliations

Tadeusz Kaczorek

1

e-mail: t.kaczorek@pb.edu.pl

ORCID:

Andrzej Ruszewski

1

e-mail: a.ruszewski@pb.edu.pl

ORCID:

Bialystok University of Technology, Faculty of Electrical Engineering,Wiejska 45D, 15-351 Białystok, Poland

Synchronization of FitzHugh-Nagumo reaction-diffusion systems via one-dimensional linear control law

Adel Ouannas Fatiha Mesdoui Shaher Momani Iqbal Batiha Giuseppe Grassi

Archives of Control Sciences | 2021 | vol. 31 | No 2 | 333-345 | DOI: 10.24425/acs.2021.137421

Keywords FitzHugh-Nagumo synchronization uni-dimensional control linear control reaction-diffusion system neuronal networks Lyapunov’s second method

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Abstract

The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one- and/or two-spatial dimensions.

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Authors and Affiliations

Adel Ouannas

1

Fatiha Mesdoui

2

Shaher Momani

2 3

Iqbal Batiha

4 3

Giuseppe Grassi

5

Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
Department of Mathematics, Faculty of Science and Technology, Irbid National University, 2600 Irbid, Jordan
Dipartimento Ingegneria Innovazione, Universitadel Salento, 73100 Lecce, Italy

Synchronization of fractional order Rabinovich-Fabrikant systems using sliding mode control techniques

Sanjay Kumar Chaman Singh Sada Nand Prasad Chandra Shekhar Rajiv Aggrawal

Archives of Control Sciences | 2019 | vol. 29 | No 2 | 307-322 | DOI: 10.24425/acs.2019.129384

Keywords fractional-order chaotic system chaos synchronization Rabinovich-Fabrikant system Lyapunov exponents

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Abstract

The Bulletin of the Polish Academy of Sciences: Technical Sciences (Bull.Pol. Ac.: Tech.) is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred: Artificial and Computational Intelligence, Biomedical Engineering and Biotechnology, Civil Engineering, Control, Informatics and Robotics, Electronics, Telecommunication and Optoelectronics, Mechanical and Aeronautical Engineering, Thermodynamics, Material Science and Nanotechnology, Power Systems and Power Electronics.

Journal Metrics: JCR Impact Factor 2018: 1.361, 5 Year Impact Factor: 1.323, SCImago Journal Rank (SJR) 2017: 0.319, Source Normalized Impact per Paper (SNIP) 2017: 1.005, CiteScore 2017: 1.27, The Polish Ministry of Science and Higher Education 2017: 25 points.

Abbreviations/Acronym: Journal citation: Bull. Pol. Ac.: Tech., ISO: Bull. Pol. Acad. Sci.-Tech. Sci., JCR Abbrev: B POL ACAD SCI-TECH Acronym in the Editorial System: BPASTS.

Authors and Affiliations

Sanjay Kumar

Chaman Singh

Sada Nand Prasad

Chandra Shekhar

Rajiv Aggrawal

Stability analysis of engineering/physical dynamic systems using residual energy function

Cim Civelek

Archives of Control Sciences | 2018 | vol. 28 | No 2 | DOI: 10.24425/123456

Keywords stability analysis residual energy function as Lyapunov function physicaldynamic systems coupled engineering systems

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Abstract

In this article, an engineering/physical dynamic system including losses is analyzed inrelation to the stability from an engineer’s/physicist’s point of view. Firstly, conditions for a Hamiltonian to be an energy function, time independent or not, is explained herein. To analyze stability of engineering system, Lyapunov-like energy function, called residual energy function is used. The residual function may contain, apart from external energies, negative losses as well. This function includes the sum of potential and kinetic energies, which are special forms and ready-made (weak) Lyapunov functions, and loss of energies (positive and/or negative) of a system described in different forms using tensorial variables. As the Lypunov function, residual energy function is defined as Hamiltonian energy function plus loss of energies and then associated weak and strong stability are proved through the first time-derivative of residual energy function. It is demonstrated how the stability analysis can be performed using the residual energy functions in different formulations and in generalized motion space when available. This novel approach is applied to RLC circuit, AC equivalent circuit of Gunn diode oscillator for autonomous, and a coupled (electromechanical) example for nonautonomous case. In the nonautonomous case, the stability criteria can not be proven for one type of formulation, however, it can be proven in the other type formulation.

Authors and Affiliations

Cim Civelek

Synchronization of neuronal bursting using backstepping control with recursive feedback

Suresh Rasappan

Archives of Control Sciences | 2019 | vol. 29 | No 4 | 617-642 | DOI: 10.24425/acs.2019.131229

Keywords Hindmarsh-Rose neuronal bursting system chaos synchronization backstepping control Lyapunov stability

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Abstract

J.L. Hindmarsh, R.M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.

Authors and Affiliations

Suresh Rasappan

Stability and positivity with respect to part of the variables for positive Markovian jump systems

L. Socha

Bulletin of the Polish Academy of Sciences Technical Sciences | 2019 | 67 | No. 4 | 769-775 | DOI: 10.24425/bpasts.2019.130186

Keywords hybrid system Lyapunov method Markov jump system stability and positivity with respect to the part of variables

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Abstract

The stability and positivity of linear positive Markovian jump systems with respect to part of the variables is considered. The methodologies of stability of positive systems with known transition probabilities based on common linear copositive Lyapunov function and stability of linear systems with respect to part of the variables are combined to find sufficient conditions of the stochastic stability and positivity of Markovian jump systems with respect to part of the variables. The results are extended for a class of nonlinear positive Markovian jump systems with respect to part of the variables. An example is given to illustrate the obtained results.

Authors and Affiliations

L. Socha

Trajectory tracking and collision avoidance for the formation of two-wheeled mobile robots

W. Kowalczyk K. Kozłowski

Bulletin of the Polish Academy of Sciences Technical Sciences | 2019 | No. 5 | 915-924 | DOI: 10.24425/bpas.2019.128652

Keywords robot formation nonholonomic robot stability analysis Lyapunov-like function path following artificial potential function

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Abstract

This paper presents control method for multiple two-wheeled mobile robots moving in formation. Trajectory tracking algorithm from [7] is extended by collision avoidance, and is applied to the different type of formation task: each robot in the formation mimics motion of the virtual leader with a certain displacement. Each robot avoids collisions with other robots and circular shaped, static obstacles existing in the environment. Artificial potential functions are used to generate repulsive component of the control. Stability analysis of the closed-loop system is based on Lyapunov-like function. Effectiveness of the proposed algorithm is illustrated by simulation results.

Authors and Affiliations

W. Kowalczyk

K. Kozłowski

Dynamical properties of a modified chaotic Colpitts oscillator with triangular wave non-linearity

Rasappan Suresh Kumaravel Sathish Kumar Murugesan Regan K.A. Niranjan Kumar R. Narmada Devi Ahmed J. Obaid

Archives of Control Sciences | 2023 | vol. 33 | No 1 | 25-53 | DOI: 10.24425/acs.2023.145112

Keywords chaos Colpitts oscillator Lyapunov exponent diffusion stability synchronization triangular wave non-linearity

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Abstract

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.

Authors and Affiliations

Rasappan Suresh

1

Kumaravel Sathish Kumar

2

Murugesan Regan

2

K.A. Niranjan Kumar

2

R. Narmada Devi

2

Ahmed J. Obaid

3

Mathematics Section, Department of Information Technology, College of Computing and Information Sciences, University of Technology and Applied Sciences, Ibri, Sultanate of Oman
Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R& D Institute of Science and Technology, Avadi, Chennai-62, India
Faculty of Computer Science and Mathematics, University of Kufa, Iraq

Exponential stability of impulsive delayed nonlinear hybrid differential systems

Qianqian Jia Chaoying Xia

Archives of Electrical Engineering | 2019 | vol. 68 | No 3 | 553-564 | DOI: 10.24425/aee.2019.129341

Keywords impulsive delayed nonlinear hybrid systems global exponential Lyapunov function Razumikhin technique

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Abstract

In recent years, with the rapid development of digital components, digital electronic computers, especially microprocessors, digital controllers have replaced analog controllers on many occasions. The application of digital controller makes the performance analysis of impulsive system more and more important. This paper considers global exponential stability (GES) of impulsive delayed nonlinear hybrid differential systems (IDNHDS).Through the application of the Lyapunov method and the Razumikhin technique, a series of uncomplicated and useful guiding principles have been obtained. The results of a numerical simulation are presented to demonstrate that the method is correct and effective.

Authors and Affiliations

Qianqian Jia

Chaoying Xia

Design of a Taguchi-GRA optimized PID and adaptive PID controllers for speed control of DC motor

Mary Ann George Dattaguru V. Kamat

Archives of Electrical Engineering | 2021 | vol. 70 | No 4 | 759-775 | DOI: 10.24425/aee.2021.138259

Keywords analysis of variance Lyapunov rule MIT rule model reference adaptive control Taguchi-grey relational analysis

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Abstract

DC motors have wide acceptance in industries due to their high efficiency, low costs, and flexibility. The paper presents the unique design concept of a multi-objective optimized proportional-integral-derivative (PID) controller and Model Reference Adaptive Control (MRAC) based controllers for effective speed control of the DC motor system. The study aims to optimize PID parameters for speed control of a DC motor, emphasizing minimizing both settling time (Ts ) and % overshoot (% OS) of the closed-loop response. The PID controller is designed using the Ziegler Nichols (ZN) method primarily subjected to Taguchi-grey relational analysis to handle multiple quality characteristics. Here, the Taguchi L9 orthogonal array is defined to find the process parameters that affect Ts and %OS. The analysis of variance shows that the most significant factor affecting Ts and %OS is the derivative gain term. The result also demonstrates that the proposed Taguchi-GRA optimized controller reduces Ts and %OS drastically compared to the ZN-tuned PID controller. This study also uses MRAC schemes using the MIT rule, Lyapunov rule, and a modified MIT rule. The DC motor speed tracking performance is analyzed by varying the adaptation gain and reference signal amplitude. The results also revealed that the proposed MRAC schemes provide desired closed-loop performance in real-time in the presence of disturbance and varying plant parameters. The study provides additional insights into using a modified MIT rule and the Lyapunov rule in protecting the response from signal amplitude dependence and the assurance of a stable adaptive controller, respectively.

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[26] George M.A., Kamath D.V., Thirunavukkarasu I., An Optimized Fractional-Order PID (FOPID) Controller for a Non-Linear Conical Tank Level Process, Proceedings of IEEE Applied Signal Processing Conference (ASPCON), Kolkata, India, pp. 134–138 (2020).

Authors and Affiliations

Mary Ann George

1

e-mail:

ORCID:

Dattaguru V. Kamat

1

e-mail:

ORCID:

Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal Academy of Higher Education (MAHE), Manipal – 576104, Udupi District, Karnataka State, India

ℎ-Stability of set differential equations

Sihem Boukthir Boulbaba Ghanmi Imed Basdouri Dalil Ichalal Jean Lerbet

Archives of Control Sciences | 2023 | vol. 33 | No 4 | 761-788 | DOI: 10.24425/acs.2023.148880

Keywords ℎ-stability Lyapunov theory set-valued differential generalized Hukuhara derivative perturbed system cascaded systems

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Abstract

In this paper, we introduce the notion of h-stability for set-valued differential equations. Necessary and sufficient conditions are established by using Lyapunov theory. Then, based on the obtained results, we study the ℎ-stability of perturbed and cascaded systems. Finally, an example illustrates the proposed theorems

Authors and Affiliations

Sihem Boukthir

1 2

e-mail:

ORCID:

Boulbaba Ghanmi

3

e-mail:

ORCID:

Imed Basdouri

3

e-mail:

ORCID:

Dalil Ichalal

4

e-mail:

ORCID:

Jean Lerbet

5

Department of Mathematics, Faculty of Sciencesof Sfax, Route Soukra Km 4, BP 802, 3018, Sfax, Tunisia
The IBISC laboratory, University ofEvry Val d’Essonne, University of Paris Saclay University, 40, rue de Pelvoux, 91020, Evry Courcouronnes,France
Department of Mathematics, Faculty of Sciences of Gafsa, Sidi AhmedZarroug, 2112, Gafsa, Tunisia
The IBISC laboratory, University of Evry Vald’Essonne, University of Paris Saclay University, 40, rue de Pelvoux, 91020, Evry Courcouronnes, France
The LaMME laboratory, UMR CNRS 8071, Universityof Evry Val d’Essonne, University of Paris Saclay, 23 Bd de France, 91037, Evry CEDEX, France

A new modified WINDMI jerk system with exponential and sinusoidal nonlinearities, its bifurcation analysis, multistability, circuit simulation and synchronization design

Mohamad Afendee Mohamed Sundarapandian Vaidyanathan Fareh Hannachi Aceng Sambas P. Darwin

Archives of Control Sciences | 2023 | vol. 33 | No 4 | 711-735 | DOI: 10.24425/acs.2023.148878

Keywords chaos jerk systems chaotic systems Lyapunov exponents bifurcation multistability circuit simulation backstepping control

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Abstract

In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.

Authors and Affiliations

Mohamad Afendee Mohamed

1

Sundarapandian Vaidyanathan

2 3

Fareh Hannachi

4

Aceng Sambas

1

P. Darwin

5

Faculty of Information and Computing,Universiti Sultan Zainal Abidin, Terengganu, Malaysia
Centre for ControlSystems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600062 Tamil Nadu, India
Faculty of Information and Computing, Universiti Sultan Zainal Abidin Terengganu, Malaysia
Larbi Tebessi University – Tebessi routede constantine, 12022, Tebessa, Algeria
Department of Computer Science and EngineeringRajalakshmi Institute of Technology, Kuthambakkam, Chennai-600 124, Tamil Nadu, India

The Stability Interval of the Set of Linear System

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

International Journal of Electronics and Telecommunications | 2021 | vol. 67 | No 2 | 155-161 | DOI: 10.24425/ijet.2021.135958

Keywords automatic control system stability matrix minor characteristic polynomial Hurwitz criterion Lienard-Shipard criterion of interval mathematics Lyapunov function

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Abstract

The article considers the problem of stability of interval-defined linear systems based on the Hurwitz and Lienard- Shipar 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.

Bibliography

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Authors and Affiliations

Talgat Mazakov

1

Waldemar Wójcik

2

Sholpan Jomartova

1

Nurgul Karymsakova

3

Gulzat Ziyatbekova

1

Aisulu Tursynbai

3

Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Lublin Technical University, Poland
Al-Farabi Kazakh National University, Almaty, Kazakhstan

Robust hybrid synchronization control of chaotic 3-cell CNN with uncertain parameters using smooth super twisting algorithm

Nazam Siddique Fazal ur Rehman Uzair Raoof Shahid Iqbal Muhammad Rashad

Bulletin of the Polish Academy of Sciences Technical Sciences | 2023 | 71 | 5 | e146474 | DOI: 10.24425/bpasts.2023.146474

Keywords hybrid synchronization cellular neural network sliding mode control smooth super twisting algorithm Lyapunov stability theory

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Abstract

This paper presents the control design framework for the hybrid synchronization (HS) and parameter identification of the 3-Cell Cellular Neural Network. The cellular neural network (CNN) of this kind has increasing practical importance but due to its strong chaotic behavior and the presence of uncertain parameters make it difficult to design a smooth control framework. Sliding mode control (SMC) is very helpful for this kind of environment where the systems are nonlinear and have uncertain parameters and bounded disturbances. However, conventional SMC offers a dangerous chattering phenomenon, which is not acceptable in this scenario. To get chattering-free control, smooth higher-order SMC formulated on the smooth super twisting algorithm (SSTA) is proposed in this article. The stability of the sliding surface is ensured by the Lyapunov stability theory. The convergence of the error system to zero yields hybrid synchronization and the unknown parameters are computed adaptively. Finally, the results of the proposed control technique are compared with the adaptive integral sliding mode control (AISMC). Numerical simulation results validate the performance of the proposed algorithm.

Authors and Affiliations

Nazam Siddique

1

e-mail:

ORCID:

Fazal ur Rehman

2

Uzair Raoof

3

Shahid Iqbal

1

Muhammad Rashad

3

University of Gujrat, Gujrat, Pakistan
Capital University of Science and Technology, Islamabad, Pakistan
University of Lahore, Lahore, Pakistan

1
2

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