scholarly journals Tracking Control of a Class of Chaotic Systems

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 568 ◽  
Author(s):  
Anqing Yang ◽  
Linshan Li ◽  
Zuoxun Wang ◽  
Rongwei Guo
Keyword(s):  
Control Problem ◽  
Periodic Orbits ◽  
Chaotic System ◽  
Tracking Control ◽  
Reference System ◽  
Chaotic Systems ◽  
Asymptotic Tracking ◽  
The Given

This paper investigates the asymptotic tracking control problem of the chaotic system. Firstly, a reference system is presented, the output of which can asymptotically track a given command. Then, a both physically implementable and simple controller is designed, by which the given chaotic system synchronizes the reference system, and thus the output of such chaotic systems can asymptotically track the given command. It should be pointed out that the output of the given chaotic system can asymptotically track arbitrary desired periodic orbits. Finally, several illustrative examples are taken as example to show the validity and effectiveness of the obtained results.

scholarly journals New Results on Fuzzy Synchronization for a Kind of Disturbed Memristive Chaotic System

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Wang ◽  
L. L. Chen
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Control Method ◽  
Fuzzy Controller ◽  
Fuzzy Theory ◽  
Fuzzy Model ◽  
H Infinity ◽  
The Given

This paper concerns the problem on the fuzzy synchronization for a kind of disturbed memristive chaotic system. First, based on fuzzy theory, the fuzzy model for a memristive chaotic system is presented; next, based on H-infinity technique, a multidimensional fuzzy controller and a single-dimensional fuzzy controller are designed to realize the synchronization of master-slave chaotic systems with disturbances. Finally, some typical examples are included to illuminate the correctness of the given control method.

scholarly journals An Adaptive Tracking Control of Fractional-Order Chaotic Systems with Uncertain System Parameter

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Tracking Control ◽  
System Parameter ◽  
Chaotic Systems ◽  
Reference Signal ◽  
Uncertain System ◽  
Uncertain Parameter ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking

An adaptive tracking control scheme is presented for fractional-order chaotic systems with uncertain parameter. It is theoretically proved that this approach can make the uncertain parameter fractional-order chaotic system track any given reference signal and the uncertain system parameter is estimated through the adaptive tracking control process. Furthermore, the reference signal may belong to other integer-orders chaotic system or belong to different fractional-order chaotic system with different fractional orders. Two examples are presented to demonstrate the effectiveness of the proposed method.

Passivity-Based Tracking Control for Uncertain Nonlinear Feedback Systems

2016 ◽  
Vol 28 (6) ◽  
pp. 837-841 ◽  
Author(s):  
Ni Bu ◽  
◽  
Mingcong Deng ◽  
Keyword(s):  
Control Problem ◽  
Tracking Control ◽  
Feedback System ◽  
Factorization Method ◽  
Tracking Performance ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Control Scheme ◽  
Asymptotic Tracking ◽  
Nonlinear Feedback Systems

[abstFig src='/00280006/07.jpg' width='300' text='The asymptotic tracking performance and the passivity property' ] The tracking control problem for the uncertain nonlinear feedback systems is considered in this paper by using passivity-based robust right coprime factorization method. Concerned with the passivity for the nonlinear feedback system, two stable controllers are designed such that the nonlinear feedback system is robust stable and the plant output asymptotically tracks to the reference output. A numerical example is given to show the validity of the control scheme as well as the tracking performance.

NEW METHOD FOR STABILIZATION OF UNSTABLE PERIODIC ORBITS IN CHAOTIC SYSTEMS

1995 ◽  
Vol 05 (01) ◽  
pp. 281-295 ◽  
Author(s):  
ZBIGNIEW GALIAS
Keyword(s):  
Periodic Orbits ◽  
Chaotic System ◽  
System Parameter ◽  
Chaotic Systems ◽  
New Method ◽  
Unstable Periodic Orbits ◽  
Numerical Example ◽  
Element Set

In this paper we present a new method of controlling periodic orbits in chaotic systems. This method can be applied in situations when the chaotic system depends on one system parameter, which can be changed over a continuous interval or over a discrete, two-element set. We compare the new method to other ones, discuss its properties, and illustrate our approach with a numerical example.

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.

Soft Computing Simulations of Chaotic Systems

2019 ◽  
Vol 29 (08) ◽  
pp. 1950112 ◽  
Author(s):  
Erivelton G. Nepomuceno ◽  
Priscila F. S. Guedes ◽  
Alípio M. Barbosa ◽  
Matjaž Perc ◽  
Robert Repnik
Keyword(s):  
Lower Bound ◽  
Soft Computing ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Logistic Map ◽  
Largest Lyapunov Exponent ◽  
Lower And Upper Bounds ◽  
Finite Precision ◽  
Chua Circuit ◽  
Widespread Interest

Soft computing strategies are drawing widespread interest in engineering and science fields, particularly so because of their capacity to reason and learn in a domain of inherent uncertainty, approximation, and unpredictability. However, soft computing research devoted to finite precision effects in chaotic system simulations is still in a nascent stage, and there are ample opportunities for new discoveries. In this paper, we consider the error that is due to finite precision in the simulation of chaotic systems. We present a generalized version of the lower bound error using an arbitrary number of natural interval extensions. The lower bound error has been used to simulate a chaotic system with lower and upper bounds. The width of this interval does not diverge, which is an advantage compared to other techniques. We illustrate our approach on three systems, namely the logistic map, the Singer map and the Chua circuit. Moreover, we validate the method by calculating the largest Lyapunov exponent.

On the Potential for Entangled States Between Chaotic Systems

2014 ◽  
Vol 24 (06) ◽  
pp. 1450077 ◽  
Author(s):  
Matthew A. Morena ◽  
Kevin M. Short
Keyword(s):  
Dynamical System ◽  
Periodic Orbits ◽  
Chaotic Systems ◽  
Entangled States ◽  
Future Research ◽  
Unstable Periodic Orbits ◽  
Qualitative Information ◽  
Chaotic Dynamical System ◽  
Naturally Occurring ◽  
External Intervention

We report on the tendency of chaotic systems to be controlled onto their unstable periodic orbits in such a way that these orbits are stabilized. The resulting orbits are known as cupolets and collectively provide a rich source of qualitative information on the associated chaotic dynamical system. We show that pairs of interacting cupolets may be induced into a state of mutually sustained stabilization that requires no external intervention in order to be maintained and is thus considered bound or entangled. A number of properties of this sort of entanglement are discussed. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. Based on certain properties of chaotic systems and on examples which we present, there is further potential for chaotic entanglement to be naturally occurring. A discussion of this and of the implications of chaotic entanglement in future research investigations is also presented.

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