Controlling chaos in a high dimensional system with periodic parametric perturbations

Mirus, K. A.; Sprott, Julien Clinton

doi:10.1016/s0375-9601(99)00068-7

Cited by 24 publications

(8 citation statements)

References 29 publications

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“…Theorem 2. The Pan chaotic system (18) is globally asymptotically stabilized for all initial conditions with the sliding mode controller u defined by (25).…”

Section: Theoretical Resultsmentioning

confidence: 99%

“…Chaos theory has been applied to a variety of fields such as physical systems [7], chemical systems [8], ecological systems [9], secure communications [10][11][12], etc. Chaos in control systems and control of chaotic dynamical systems have both received rapid attention in the recent decades [13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

“…the controlled Pan system (18) with the sliding mode controller u given by(25) using MATLAB.In the chaotic case, the parameter values are given byThe initial values of the Pan system (18) are taken as illustrates the chaos control of the Pan system(18).…”

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confidence: 99%

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Analysis and Control of the Pan System via Sliding Mode Control

Vaidyanathan¹

2012

SIPIJ

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In this paper, we obtain new results for the analysis and control of the Pan system (2010) using sliding mode control (SMC). The stability results derived in this paper for the control of the Pan system to stabilize about its unstable equilibrium at the origin have been derived using sliding mode control and Lyapunov stability theory. Numerical simulations are depicted to demonstrate the control results derived in this paper.

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“…Theorem 2. The Pan chaotic system (18) is globally asymptotically stabilized for all initial conditions with the sliding mode controller u defined by (25).…”

Section: Theoretical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis and Control of the Pan System via Sliding Mode Control

Vaidyanathan¹

2012

SIPIJ

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“…This observation is further strengthened by its Fast Fourier Transform (FFT) Spectrum shown in Figure 4 where narrowband, discontinuous and isolated frequency harmonics can be seen. As for the trajectory or the phase portrait when V in is equal 20V in Figure 5, a normal period-1 loop is noticed [16][17][18][19][20][21][22][23][24].…”

Section: Let and And Given Thatmentioning

confidence: 89%

Bifurcation Behaviour of the Buck Converter

Chiang¹,

Lin²,

Tien³

2014

TJIEM

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The bifurcation and chaos phenomena appeared in power system have become a focus subject at present. It has become apparent about a decade ago that power converters exhibit various types of non-linear behaviour which includes all kinds of bifurcations and chaos. Even basic DC/DC converters exhibit bifurcation and chaos phenomena as well as parallel-connected DC/DC converters and PFC system. The main source of such non-linearity is the switching mechanism of the converters. Non-linear components of the converter circuit and control scheme such as the use of naturally-sampled, constant-frequency PWM further contribute to the non-linear behaviour of converters such as a DC-to-DC buck converter. Thus, all feedback controlled power converters exhibit certain non-linear phenomena over a specific breadth of parameter values. Despite being commonly encountered by power electronics engineers, these non-linear phenomena are by and large not thoroughly understood by engineers. This paper examines the bifurcation behaviour of the buck converter in an ideal case when the input voltage is varied. The computer simulation scheme, PSPICE is employed to model the behaviour of the ideal buck converter. For certain values of the input voltage, Vin instability occurs. The analysis and conclusion presented in this paper will provide an overview of the bifurcation behaviour of the DC-to-DC buck converter, aspiring to draw attention of the power electronics and the circuits and systems communities to a field that is not often researched and examined.

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“…It is widely used in many fields of physics, engineering and secure communications [2,29,31]. Currently, more works have been done in the study of chaos and hyperchaos synchronization and many different kinds of synchronizations have been discovered such as completed synchronization, generalized synchronization, phase synchronization, projective synchronization, lag synchronization and impulsive synchronization [5,9,10,12,16,25,36], of most important, chaotic synchronization can be described as hybrid [14,30], high-dimension [4,19], fractional order [34], coupled complex system [17,18,35], and neural network [6,7].…”

Section: Introductionmentioning

confidence: 99%

Scaling Synchronization of a 6D Hyperchaotic System

Osman¹,

Zhu²,

Yang³

2018

dtcse

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Abstract. This paper focuses on the scaling synchronization issue of a 6D hyperchaotic system with one or three equilibria which is obtained by controlling a 5D hyperchaotic system that is formed by adding a linear feedback controller and a nonlinear feedback controller to the Lorenz system. When the parameters are known in advance, applying the one-way linear coupling approach to synchronize the 6D hyperchaotic system up to a scaling factor. When the parameters are fully unknown, utilizing the adaptive method to synchronize the uncertain 6D hyperchaotic system up to a scaling factor. Finally, many numerical simulations have been carried out to verify the validation and efficiency of the proposed schemes.

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Controlling chaos in a high dimensional system with periodic parametric perturbations

Cited by 24 publications

References 29 publications

Analysis and Control of the Pan System via Sliding Mode Control

Analysis and Control of the Pan System via Sliding Mode Control

Bifurcation Behaviour of the Buck Converter

Scaling Synchronization of a 6D Hyperchaotic System

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