scholarly journals On Generalized Fractional Dynamical System With Order Lying in (0, 2): Stability Analysis, Chaotic Behaviour, Control and Synchronization

2021 ◽  
Author(s):  
Tarek Abed-Elhameed ◽  
Tarek Aboelenen
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Fractional Order ◽  
Stability Control ◽  
Linear Feedback ◽  
Fractional Order Systems ◽  
Chen System ◽  
Control Functions ◽  
Control And Synchronization ◽  
Fractional Dynamical System

Abstract The generalized fractional dynamical system with order lying in (0, 2) is investigated. We present the stability analysis of that system using Mittag-Leffler function, the Gronwall-Bellman Lemma and Laplace transform. The bifurcation diagram of generalized fractional-order Chen system is given. We investigate a theorem to control the chaotic generalized fractional-order systems by linear feedback control. Two examples to achieve the theorem of control are given. The synchronization between two different chaotic generalized fractional systems is presented. We give a theorem to calculate the control functions which achieve synchronization. This theorem is applied to achieve the synchronization between different generalized fractional-order systems with order lying in (0, 1]. And, also, used to achieve the synchronization between the identical generalized fractional-order L\"{u} systems with order lying in [1, 2). There exist an agreement among analytical results and numerical treatments for stability, control and synchronization theorems.

scholarly journals Chaos Control and Synchronization in Fractional-Order Lorenz-Like System

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Sachin Bhalekar
Keyword(s):  
Dynamical System ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Stable Region ◽  
Linear Feedback ◽  
Effective Dimension ◽  
Nonlinear Feedback ◽  
Linear Feedback Controller ◽  
Control And Synchronization

The present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. The chaos in the proposed system is controlled using simple linear feedback controller. We design a controller to place the eigenvalues of the system Jacobian in a stable region. The effectiveness of the controller in eliminating the chaotic behavior from the state trajectories is also demonstrated using numerical simulations. Furthermore, we synchronize the system using nonlinear feedback.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

Large-scale fractional-order systems: stability analysis and their decentralised functional observers design

2018 ◽  
Vol 12 (3) ◽  
pp. 359-367 ◽  
Author(s):  
Yassine Boukal ◽  
Mohamed Darouach ◽  
Michel Zasadzinski ◽  
Nour-Eddine Radhy
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Large Scale ◽  
Fractional Order Systems

GUI Toolbox for Approximation of Fractional Order Parameters With Application to Control of pH Neutralization Process

2019 ◽  
pp. 260-286
Author(s):  
Bingi Kishore ◽  
Rosdiazli Ibrahim ◽  
Mohd Noh Karsiti ◽  
Sabo Miya Hassan ◽  
Vivekananda Rajah Harindran
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Order Parameters ◽  
Fractional Order Systems ◽  
Approximation Techniques ◽  
Numerical Tools ◽  
Neutralization Process ◽  
Fractional Order Pid ◽  
Ph Neutralization ◽  
Ph Neutralization Process

Fractional-order systems have been applied in many engineering applications. A key issue with the application of such systems is the approximation of fractional-order parameters. The numerical tools for the approximation of fractional-order parameters gained attention recently. However, available toolboxes in the literature do not have a direct option to approximate higher order systems and need improvements with the graphical, numerical, and stability analysis. Therefore, this chapter proposes a MATLAB-based GUI for the approximation of fractional-order operators. The toolbox is made up of four widely used approximation techniques, namely, Oustaloup, refined Oustaloup, Matsuda, and curve fitting. The toolbox also allows numerical and stability analysis for evaluating the performance of approximated transfer function. To demonstrate the effectiveness of the developed GUI, a simulation study is conducted on fractional-order PID control of pH neutralization process. The results show that the toolbox can be effectively used to approximate and analyze the fractional-order systems.

Chaotic Control in a Fractional-Order Modified Van Der Pol Oscillator

2011 ◽  
Vol 474-476 ◽  
pp. 83-88
Author(s):  
Xin Gao
Keyword(s):  
Fractional Order ◽  
Feedback Controller ◽  
Van Der Pol Oscillator ◽  
Linear Feedback ◽  
Fractional Order Systems ◽  
Van Der Pol ◽  
Chaotic Control ◽  
Linear Feedback Controller

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we study the chaotic behaviors in a fractional-order modified van der Pol oscillator. We find that chaos exists in the fractional-order modified van der Pol oscillator with order less than 3. In addition, the lowest order we find for chaos to exist in such system is 2.4. Finally, a simple, but effective, linear feedback controller is also designed to stabilize the fractional order chaotic van der Pol oscillator.

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