Tracking control for a ten-ring chaotic system with an exponential nonlinear term

Deng, Kuibiao; Wang, Ruixia; Li, Chunlai; Fan, Yongqing

doi:10.1016/j.ijleo.2016.10.088

Cited by 9 publications

(5 citation statements)

References 24 publications

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“…As mentioned in the introduction, the optimization of chaotic systems is usually made by the following three easy modifications to the nonlinear term of the existing system. In the first approach, the nonlinear term is modified to a higher order nonlinear term, such as changing the product term to an exponential or logarithmic function [12][13][14][15], while in the second approach, simple adjustments to the nonlinear terms without affecting its order [16,17] are made. As a third approach, more nonlinear terms can be added to the system.…”

Section: The Proposed Dynamical Systemmentioning

confidence: 99%

Analysis, Synchronization, and Robotic Application of a Modified Hyperjerk Chaotic System

et al. 2020

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In this work, a novel hyperjerk system, with hyperbolic sine function as the only nonlinear term, is proposed, as a modification of a hyperjerk system proposed by Leutcho et al. First, a dynamical analysis on the system is performed and interesting phenomena concerning chaos theory, such as route to chaos, antimonotonicity, crisis, and coexisting attractors, are studied. For this reason, the system’s bifurcation diagrams with respect to different parameter values are plotted and its Lyapunov exponents are computed. Afterwards, the synchronization of the system is considered, using active control. The proposed system is then applied, as a chaotic generator, to the problem of chaotic path planning, using a combination of sampling and a modulo tactic technique.

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Section: The Proposed Dynamical Systemmentioning

confidence: 99%

Analysis, Synchronization, and Robotic Application of a Modified Hyperjerk Chaotic System

et al. 2020

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“…, and are selected in such a way that inequality (42) is verified, and control law (26) with learning law (35) is applied to uncertain Zhang system (25), then It is worth mentioning that Theorem 4 only guarantees the asymptotic convergence to a bounded zone around zero for , , and . Thus, rigorously speaking, the convergence time could be infinite and consequently this result does not provide any procedure to determine it.…”

Section: Theorem 4 If Assumption 3 Is Satisfied the Constantsmentioning

confidence: 99%

“…In technical literature, various strategies have been proposed for control of chaotic systems [41][42][43][44][45][46][47][48]. Three approaches have commonly been used when both the structure and the parameters of the system are known: linear feedback control [49][50][51][52][53], nonlinear control [54][55][56][57][58], and active control [59][60][61][62][63][64][65][66][67][68].…”

Section: Introductionmentioning

confidence: 99%

Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control

Pérez-Cruz

2018

Complexity

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Standard adaptive control is the preferred approach for stabilization and synchronization of chaotic systems when the structure of such systems is a priori known but the parameters are unknown. However, in the presence of unmodeled dynamics and/or disturbance, this approach is not effective anymore due to the drift of the parameter estimations, which eventually causes the instability of the closed-loop system. In this paper, a robustifying term, which consists of a saturation function, is used to avoid this problem. The robustifying term is added to the adaptive control law. Consequently, the learning law is also modified. The boundedness of the states and the parameter estimations is rigorously and thoroughly proven by means of Lyapunov like analysis based on Barbalat’s lemma. On these new conditions, the convergence to zero cannot be achieved due to the presence of unmodeled dynamics and/or disturbance. However, it is still possible to guarantee the asymptotic convergence to a bounded zone around zero. The width of this zone can be adjusted by the designer. The performance of this robust approach is verified by numerical simulations. Although, for simplicity, this strategy is only applied to the stabilization and synchronization of Zhang system, the procedure can easily be generalized to a broad class of chaotic systems.

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“…In recent decades, many new continuous chaotic systems have been discovered in three-dimensional differential systems by using various chaotic construction methods, such as chaotic systems with only five terms [10], chaotic systems with linear terms [11], chaotic systems with only noequilibrium point [12], chaotic systems with signum nonlinearity [13], chaotic systems with absolute nonlinearity [14], chaotic systems with exponential nonlinearity [15], chaotic systems with hyperbolic tangent nonlinearity [16], chaotic systems with exponential nonlinear term [15,[17][18][19][20], etc. Generally, At least how many terms are required for a 3D dynamical system to produce chaotic characteristics?…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Bound Synchronization of the New Chaotic System With Energy Consumption Estimation

Wei¹,

Xie

Tong

et al. 2022

IEEE Access

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As chaotic systems are widely used in many fields, the study of them is becoming more and more in-depth. This paper first presents a new single-equilibrium chaotic system which is only three terms, and some fundamental dynamical feature of the new chaotic system are discussed, such as equilibria, dissipativity, Poincaré diagram, bifurcation graph, etc. Secondly, a new finite-time controllers is designed by using Lyapunov stability theory, and it can be used for bound synchronization of the general chaotic systems. In contrast to the current finite time controller of the chaotic system, the designed controller in this paper does not contain exponential term, it can be simple and eliminate the chattering phenomenon during synchronizationis, which may be easier to implement in practical application. In addition, under the finite time controller, the bound of control energy consumption of the chaotic system is estimated. Finally, the finite-time controllers for the new chaotic system are advanced using the design method of finite-time controller of the general chaotic system, and the result of numerical simulation is given to check its validity by the designed method.

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Tracking control for a ten-ring chaotic system with an exponential nonlinear term

Cited by 9 publications

References 24 publications

Analysis, Synchronization, and Robotic Application of a Modified Hyperjerk Chaotic System

Analysis, Synchronization, and Robotic Application of a Modified Hyperjerk Chaotic System

Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control

Finite-Time Bound Synchronization of the New Chaotic System With Energy Consumption Estimation

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