Controlling Chaos Using Input–Output Linearization Approach

1997 ◽  
Vol 07 (07) ◽  
pp. 1659-1664 ◽  
Author(s):  
Xinghuo Yu
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Zero Dynamics ◽  
Input Output ◽  
Controlling Chaos ◽  
Periodic Signals ◽  
Simulation Results ◽  
The Lorenz System ◽  
Partial States ◽  
Input Output Linearization

In this article the input–output linearization approach is used for controlling chaos. It is shown that by using only partial states, the entire chaotic system is stabilizable, provided the zero dynamics is stable. Generally speaking, trajectories of chaotic systems do not grow exponentially and are usually bounded. In particular, for dissipative chaotic systems the stable zero dynamics can always be found. Hence the stabilization as well as tracking periodic signals are possible. The Lorenz system is used to inform the discussion. Simulation results are presented to show the effectiveness of the approach.

ADAPTIVE CONTROL OF UNCERTAIN LORENZ SYSTEM USING DECOUPLED BACKSTEPPING

2004 ◽  
Vol 14 (04) ◽  
pp. 1439-1445 ◽  
Author(s):  
S. S. GE
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Lorenz System ◽  
Physical Property ◽  
Asymptotic Convergence ◽  
Closed Loop System ◽  
Feedback Form ◽  
Controlling Chaos ◽  
Simulation Results ◽  
The Lorenz System

In this letter, we reconsider the problem of controlling chaos in the well-known Lorenz system. Firstly, the difficulty in controlling the Lorenz system is discussed in the general strict-feedback form. Then, singularity-free adaptive control is presented for the Lorenz system with three key parameters unknown by exploiting the physical property of the system using decoupled backstepping design. The proposed controller guarantees the asymptotic convergence of the output and the boundedness of all the signals in the closed-loop system. Simulation results are conducted to show the effectiveness of the approach.

ADAPTIVE BACKSTEPPING CONTROL OF UNCERTAIN LORENZ SYSTEM

2001 ◽  
Vol 11 (04) ◽  
pp. 1115-1119 ◽  
Author(s):  
C. WANG ◽  
S. S. GE
Keyword(s):  
Closed Loop ◽  
Lorenz System ◽  
Backstepping Design ◽  
Closed Loop System ◽  
Adaptive Backstepping ◽  
Feedback Form ◽  
Controlling Chaos ◽  
Simulation Results ◽  
The Lorenz System ◽  
Adaptive Backstepping Design

In this paper, we consider the problem of controlling chaos in the well-known Lorenz system. Firstly we show that the Lorenz system can be transformed into a kind of nonlinear system in the so-called general strict-feedback form. Then, adaptive backstepping design is used to control the Lorenz system with three key parameters unknown. By exploiting the property of the system, the resulting controller is singularity free, and the closed-loop system is stable globally. Simulation results are conducted to show the effectiveness of the approach.

Parameter estimation for chaotic systems using improved bird swarm algorithm

2017 ◽  
Vol 31 (36) ◽  
pp. 1750346 ◽  
Author(s):  
Chuangbiao Xu ◽  
Renhuan Yang
Keyword(s):  
Parameter Estimation ◽  
Optimization Problem ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Learning Strategy ◽  
Research Fields ◽  
Simulation Results ◽  
Swarm Algorithm ◽  
Bird Swarm Algorithm ◽  
The Lorenz System

Parameter estimation of chaotic systems is an important problem in nonlinear science and has aroused increasing interest of many research fields, which can be basically reduced to a multidimensional optimization problem. In this paper, an improved boundary bird swarm algorithm is used to estimate the parameters of chaotic systems. This algorithm can combine the good global convergence and robustness of the bird swarm algorithm and the exploitation capability of improved boundary learning strategy. Experiments are conducted on the Lorenz system and the coupling motor system. Numerical simulation results reveal the effectiveness and with desirable performance of IBBSA for parameter estimation of chaotic systems.

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.

scholarly journals Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

2007 ◽  
Vol 14 (5) ◽  
pp. 615-620 ◽  
Author(s):  
Y. Saiki
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Infinite Number ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Complex Phenomenon ◽  
Unstable Periodic Orbits ◽  
Newton Raphson ◽  
The Lorenz System

Abstract. An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

ACTIVE TRACKING CONTROL OF THE HYPERCHAOTIC LORENZ SYSTEM

2008 ◽  
Vol 22 (19) ◽  
pp. 1859-1865 ◽  
Author(s):  
XINGYUAN WANG ◽  
DAHAI NIU ◽  
MINGJUN WANG
Keyword(s):  
Numerical Simulation ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
The Self ◽  
Hyperchaotic System ◽  
Reference Signals ◽  
Tracking Controller ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results

A nonlinear active tracking controller for the four-dimensional hyperchaotic Lorenz system is designed in the paper. The controller enables this hyperchaotic system to track all kinds of reference signals, such as the sinusoidal signal. The self-synchronization of the hyperchaotic Lorenz system and the different-structure synchronization with other chaotic systems can also be realized. Numerical simulation results show the effectiveness of the controller.

PARTIAL STATE IMPULSIVE SYNCHRONIZATION OF A CLASS OF NONLINEAR SYSTEMS

2009 ◽  
Vol 19 (01) ◽  
pp. 387-393 ◽  
Author(s):  
YAN-WU WANG ◽  
CHANGYUN WEN ◽  
YENG CHAI SOH ◽  
ZHI-HONG GUAN
Keyword(s):  
Nonlinear System ◽  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Hyperchaotic System ◽  
Impulsive Synchronization ◽  
Partial State ◽  
Simulation Results ◽  
System States ◽  
Synchronization Scheme

Impulsive synchronization of chaotic systems is an attractive topic and a number of interesting results have been obtained in recent years. However, all of these results on impulsive synchronization need to employ full states of the system to achieve the desired objectives. In this paper, impulsive synchronization that needs only part of system states is studied for a class of nonlinear system. Typical chaotic systems, such as Lorenz system, Chen's system, and a 4D hyperchaotic system, are taken as examples. A new scheme is proposed to select the impulsive intervals. After some theoretical analysis, simulation results show the effectiveness of the proposed synchronization scheme.

CHAOS SYNCHRONIZATION VIA CONTROLLING PARTIAL STATE OF CHAOTIC SYSTEMS

2001 ◽  
Vol 11 (06) ◽  
pp. 1737-1741 ◽  
Author(s):  
XINGHUO YU ◽  
YANXING SONG
Keyword(s):  
Invariant Manifold ◽  
Fourth Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Dynamic Properties ◽  
Rossler System ◽  
Rössler System ◽  
Partial State ◽  
The Lorenz System

An invariant manifold based chaos synchronization approach is proposed in this letter. A novel idea of using only a partial state of chaotic systems to synchronize the coupled chaotic systems is presented by taking into account the inherent dynamic properties of the chaotic systems. The effectiveness of the approach and idea is tested on the Lorenz system and the fourth-order Rossler system.

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.

When Two Dual Chaotic Systems Shake Hands

2014 ◽  
Vol 24 (06) ◽  
pp. 1450086 ◽  
Author(s):  
J. C. Sprott ◽  
Xiong Wang ◽  
Guanrong Chen
Keyword(s):  
Parameter Space ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Time Variable ◽  
Chen System ◽  
Common Parameter ◽  
The Lorenz System ◽  
The Relationship

This letter reports an interesting finding that the parametric Lorenz system and the parametric Chen system "shake hands" at a particular point of their common parameter space, as the time variable t → +∞ in the Lorenz system while t → -∞ in the Chen system. This helps better clarify and understand the relationship between these two closely related but topologically nonequivalent chaotic systems.

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