IMPULSIVE CONTROL OF CHAOTIC SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1181-1190 ◽  
Author(s):  
XINZHI LIU ◽  
KOK LAY TEO
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Equilibrium Point ◽  
Chaotic System ◽  
Lyapunov Functions ◽  
Lorenz System ◽  
Impulsive Control ◽  
The Lorenz System ◽  
Impulsive Stabilization

This paper studies an impulsive control problem. By utilizing the method of Lyapunov functions, a set of impulsive stabilization criteria are established. These results are then applied to the Lorenz system. It is shown that by using impulsive feedback control, all the solutions of the Lorenz system will converge to an equilibrium point.

scholarly journals Finite-Time Lyapunov Functions and Impulsive Control Design

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Huijuan Li ◽  
Qingxia Ma
Keyword(s):  
Finite Time ◽  
Lyapunov Functions ◽  
Lorenz System ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Impulsive Systems ◽  
Lyapunov Theorem ◽  
The Lorenz System ◽  
The Stability

In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

A Memristor-Based Lorenz Circuit and Its Stabilization via Variable-Time Impulsive Control

2017 ◽  
Vol 27 (03) ◽  
pp. 1750031 ◽  
Author(s):  
Po Wu ◽  
Chuandong Li ◽  
Xing He ◽  
Tingwen Huang
Keyword(s):  
Chaotic System ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Fixed Time ◽  
Impulsive System ◽  
Variable Time ◽  
Memristive System ◽  
The Stability ◽  
Memristor Emulator ◽  
Impulsive Stabilization

In this paper, an off-the-shelf memristor emulator of the quadratic memristor is developed and applied to a Lorenz circuit. The impulsive stabilization of the chaotic system by variable moments of impulses is investigated. By B-equivalence method, the considered variable-time impulsive system can be reduced to the fixed-time impulsive one. The simulations of the chaotic behavior verify the effectiveness of the emulator-based memristive system. The stability simulations support the validity of the method.

CHAOS IN DIFFUSIONLESS LORENZ SYSTEM WITH A FRACTIONAL ORDER AND ITS CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250088 ◽  
Author(s):  
YONG XU ◽  
RENCAI GU ◽  
HUIQING ZHANG ◽  
DONGXI LI
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Fractional Order ◽  
Lorenz System ◽  
Equilibrium Points ◽  
Control Technique ◽  
Order System ◽  
System Parameters ◽  
Simulation Results ◽  
The Stability

This paper aims to investigate the phenomenon of Diffusionless Lorenz system with fractional-order. We discuss the stability of equilibrium points of the fractional-order system theoretically, and analyze the chaotic behaviors and typical bifurcations numerically. We find rich dynamics in fractional-order Diffusionless Lorenz system with appropriate fractional order and system parameters. Besides, the control problem of fractional-order Diffusionless Lorenz system is examined using feedback control technique, and simulation results show the effectiveness of the method.

Generating the New Chaotic Attractors of the Lorenz System Family via Anti-Controlling Method

2012 ◽  
Vol 542-543 ◽  
pp. 1042-1046 ◽  
Author(s):  
Xin Deng
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Attractors ◽  
Chen System ◽  
Lü System ◽  
New Chaotic System ◽  
Dynamical Properties ◽  
The Lorenz System ◽  
Lu System

In this paper, the first new chaotic system is gained by anti-controlling Chen system,which belongs to the general Lorenz system; also, the second new chaotic system is gained by anti-controlling the first new chaotic system, which belongs to the general Lü system. Moreover,some basic dynamical properties of two new chaotic systems are studied, either numerically or analytically. The obtained results show clearly that Chen chaotic system and two new chaotic systems also can form another Lorenz system family and deserve further detailed investigation.

CONSTRUCTION OF SUBOPTIMAL FEEDBACK CONTROL FOR CHAOTIC SYSTEMS USING B-SPLINES WITH OPTIMALLY CHOSEN KNOT POINTS

2001 ◽  
Vol 11 (09) ◽  
pp. 2375-2387 ◽  
Author(s):  
H. W. J. LEE ◽  
K. L. TEO ◽  
W. R. LEE ◽  
S. WANG
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Numerical Approach ◽  
Optimal Feedback Control ◽  
B Splines ◽  
Decision Variables ◽  
Spline Basis ◽  
The Lorenz System

In this paper we consider a class of optimal control problem involving a chaotic system, where all admissible controls are required to satisfy small boundedness constraints. A numerical approach is developed to seek for an optimal feedback control for the optimal control problem. In this approach, the state space is partitioned into subregions, and the controller is approximated by a linear combination of a modified third order B-spline basis functions. The partition points are also taken as decision variables in this formulation. An algorithm based on this approach is proposed. To show the effectiveness of the proposed method, a control problem involving the Lorenz system is solved by the proposed approach. The numerical results demonstrate that the method is efficient in the construction of a robust, near-optimal control.

scholarly journals Time-Delayed Impulsive Control of Chaotic System Based on T-S Fuzzy Model

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Cheng Hu ◽  
Haijun Jiang
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Impulsive Control ◽  
Fuzzy Model ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
The Stability ◽  
Control And Synchronization ◽  
Time Delayed Feedback ◽  
Delayed Impulsive Control

This paper is concerned with the time-delayed impulsive control and synchronization of general chaotic system based on T-S fuzzy model. By utilizing impulsive control theory, time-delayed feedback control technique, and T-S fuzzy model, some useful and new conditions are derived to guarantee the stability and synchronization of the addressed chaotic system. Finally, some numerical simulations are given to illustrate the effectiveness of the derived results.

The global finite-time synchronization of a class of chaotic systems via the variable-substitution and feedback control

2021 ◽  
Author(s):  
Yun Chen ◽  
Yanyi Xu ◽  
Qian Lin
Keyword(s):  
Feedback Control ◽  
Finite Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Time Synchronization ◽  
Optimization Technique ◽  
Third Order ◽  
Variable Substitution ◽  
The Lorenz System ◽  
Synchronization Scheme

Abstract This paper deals with the global finite-time synchronization of a class of third-order chaotic systems with some intersecting nonlinearities, which cover many famous chaotic systems. First, a simple, continuous and dimension-reducible control by the name of the variable-substitution and feedback control is designed to construct a master–slave finite-time synchronization scheme. Then, a global finite-time synchronization criterion for the synchronization scheme is proven and the synchronization time is analytically estimated. Subsequently, the criterion and optimization technique are applied to the well-known brushless direct current motor (BLDCM) system and the classic Lorenz system, respectively, further obtaining some new optimized synchronization criteria in the form of algebra. Two numerical examples for the BLDCM system and a numerical example for the Lorenz system are simulated and analyzed to verify the effectiveness of the theoretical results obtained in this paper.

Hidden Coexisting Attractors in a Chaotic System Without Equilibrium Point

2018 ◽  
Vol 28 (10) ◽  
pp. 1830033 ◽  
Author(s):  
Wei Zhou ◽  
Guangyi Wang ◽  
Yiran Shen ◽  
Fang Yuan ◽  
Simin Yu
Keyword(s):  
Equilibrium Point ◽  
Chaotic System ◽  
Dynamic Characteristics ◽  
Three Dimensional ◽  
Digital Signal ◽  
Chaotic Signal ◽  
Coexisting Attractors ◽  
Pseudorandom Sequences ◽  
The Lorenz System ◽  
Chaotic Signal Generator

This paper proposes a new three-dimensional chaotic system with no equilibrium point but can generate hidden chaotic attractors. Dynamic characteristics of the system are analyzed in detail by theoretical analysis and simulating experiments, including hidden attractors, transient period and coexisting attractors. Different hidden coexisting attractors exist in this system, which shows abundant and complex dynamic characteristics and can be used to generate pseudorandom sequences for encryption fields. Besides, the presented system is realized by the digital signal processing (DSP) technology to construct a chaotic signal generator, whose statistical properties are tested by National Institute of Standards and Technology (NIST) software. The obtained results are better than that of the Lorenz system and imply the presented system can be used in the encrypted fields.

Sign in / Sign up

Export Citation Format

Share Document