Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity

Lin, Chih‐Hsueh; Hu, Guo-Hsin; Yan, Jun Juh

doi:10.3390/math8030327

Cited by 6 publications

(4 citation statements)

References 17 publications

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“…In [16][17][18][19][20], the authors studied the series expansions of appropriate functionals which is called the Ito-Wiener-Chaos expansion. Our method introduced in Theorem 3 is also a kind of these expansions.…”

Section: Remarkmentioning

confidence: 99%

Generalized Integral Transforms via the Series Expressions

Chung

2020

Mathematics

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From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used, but it is also not possible to calculate for all the functionals. In this paper, we define a generalized integral transform. We then introduce a new method to evaluate the generalized integral transform for functionals using series expressions. Our method can be used to evaluate various functionals that cannot be calculated by conventional methods.

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Section: Remarkmentioning

confidence: 99%

Generalized Integral Transforms via the Series Expressions

Chung

2020

Mathematics

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“…The complex dynamics of Lorenz-Stenflo dynamical systems are analyzed with Lyapunov exponents, bifurcation diagrams, and the 0-1 test by using the Adomian decomposition numerical scheme and fractional-order representation of the model in the sense of the Riemann-Liouville integral [24]. A robust chaos suppression control is designed and applied via sliding mode control to the integer-order Lorenz-Stenflo system constrained to uncertainties and nonlinearities [25].…”

Section: Introductionmentioning

confidence: 99%

Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator

Deressa

Etemad

Kaabar

et al. 2022

Journal of Function Spaces

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The Lorenz-Stenflo mathematical model describes a complex dynamical behavior related to atmospheric acoustic-gravity waves. In this study, qualitative analysis of the four-dimensional hyperchaotic Lorenz-Stenflo system via the Caputo fractional derivative is implemented. By using the Matignon stability criterion, the local stability analysis of the system showed that all the equilibrium points of the system are locally unstable. Calculation of the Lyapunov exponents along with the relevant bifurcation diagrams with respect to different fractional orders exposed the hyperchaotic dynamical behavior for the system. Bifurcation diagrams for all the four parameters in the system also showed the hyperchaotic nature of the Lorenz-Stenflo system. Different phase attractors of the system corresponding to different fractional derivatives and parameters are presented to specify the dynamical nature of the system. The Lorenz-Stenflo system showed sensitivity to initial conditions. The master and slave systems showed a strong correlation among themselves, as verified by graphs of time series solutions of the two systems.

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“…Another approach frequently introduced to suppress the chattering is to modify the designed discontinuous SMC with the boundary layer method. [15][16][17][18] But it can only ensure the sliding motion outside a specified boundary layer, which will affect the control performance. Also, in the recent works, [19][20][21] the adaptive backstepping SMC was proposed to effectively eliminate the chattering and complete the actual engineering system control.…”

Section: Introductionmentioning

confidence: 99%

Robust chaos suppression of uncertain unified chaotic systems based on chattering-free sliding mode control

Lin

et al. 2022

Measurement and Control

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For continuous sliding mode control (SMC) in the unified chaotic systems subjected to matched/unmatched uncertainties, a novel chattering-free SMC design is proposed. First, an augmented state is introduced such that it becomes possible to develop a continuous controller to eliminate the undesired chattering which often appears in the typical SMC. Then by using this chattering-free controller, the chaos behavior in unified chaotic systems with matched uncertainties can be completely suppressed. As for the unmatched uncertainties, every state of controlled systems can be driven and limited to a predictable bound, which is not addressed in the literature. Finally, the effectiveness of the proposed chattering-free controller is verified by the numerical simulations.

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Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity

Cited by 6 publications

References 17 publications

Generalized Integral Transforms via the Series Expressions

Generalized Integral Transforms via the Series Expressions

Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator

Robust chaos suppression of uncertain unified chaotic systems based on chattering-free sliding mode control

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