Speed feedback control of chaotic system

Tao, Chaohai; Yang, Ce; Luo, Yan; Xiong, Hao; Hu, Feng

doi:10.1016/j.chaos.2004.04.009

Cited by 43 publications

(14 citation statements)

References 5 publications

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“…Based on the Lyapunov stabilization theory and matrix measure, the strategies of speed feed back control of chaotic system to the unsteady equilibrium points S− and S+ were achieved [52]. However, the state of system (1) cannot converge to the unsteady equilibrium point S ( , , ).…”

Section: Remarkmentioning

confidence: 99%

“…First, partly improving and extending the previous chaos control techniques (see [43,[51][52][53][54][55][56][57][58][59]), the single state feedback control is designed, some stabilization conditions will be derived, some simpler controllers are developed. Then, the robust performance of controlled unied chaotic systems with uncertain parameters will be investigated based on maximum and minimum analysis of the uncertain parameter, and the present controller only contains a single state feedback.…”

Section: Introductionmentioning

confidence: 99%

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Single state feedback stabilization of unified chaotic systems and circuit implementation

Jing

Fan

et al. 2014

Open Physics

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This paper focuses on the single state feedback stabilization problem of uni ed chaotic system and circuit implementation. Some stabilization conditions will be derived via the single state feedback control scheme. The robust performance of controlled uni ed chaotic systems with uncertain parameter will be investigated based on maximum and minimum analysis of uncertain parameter, the robust controller which only requires information of a state of the system is proposed and the controller is linear. Both the uni ed chaotic system and the designed controller are synthesized and implemented by an analog electronic circuit which is simpler because only three variable resistors are required to be adjusted. The numerical simulation and control in MATLAB/Simulink is then provided to show the e ectiveness and feasibility of the proposed method which is robust against some uncertainties. The results presented in this paper improve and generalize the corresponding results of recent works.

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Single state feedback stabilization of unified chaotic systems and circuit implementation

Jing

Fan

et al. 2014

Open Physics

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“…Similarly, if the derivative of an independent variable is multiplied by a coefficient as the feedback gain (Tao, Yang, Luo, Xiong & Hu 2005;Zhuang, 2012;Yan, 2005;Zhu & Chen 2008).…”

Section: Definition 3 Speed Feedback Controlmentioning

confidence: 99%

“…However, in a feedback control strategies the necessary condition for suppressing the dynamical system is that the feedback coefficient must be positive. Most of the previous work on chaos control was mostly focused on classical dynamical systems under this condition such as the Liu system (Dou, Sun, Duan, & Lü, 2009;Zhu & Chen 2008), L̈ system (Pang & Liu 2011), Unified system (Tao, Yang, Luo, Xiong, & Hu 2005), Lorenz system (Zhu, 2010), Chen system (Yan, 2005), and et al But in works (Aziz, & AL-Azzawi 2015;Zhu, 2010) founded some cases it can't be controlled, although with positive feedback coefficients. This paper answer this equation and it focused on these problems and we suggest a new method which includes four cases: two cases have at least two positive feedback coefficients and other cases have only one positive feedback coefficient.…”

Section: Introductionmentioning

confidence: 99%

“…and its play a very important role in the study of dynamical systems and has great significance in the application of chaos. Since Ott et al,1990, first introduced in the notation of chaos control (AL-Azzawi, 2012;Pang & Liu 2011).Various kinds of control schemes and techniques such as OGY method, time-delay feedback, Lyapunov method, impulsive control, sliding method control, differential geometric,  H control, adaptive control, chaos suppression method, and so on have been successfully applied to achieve chaos control (Aziz & AL-Azzawi 2016;Tao, Yang, Luo, Xiong & Hu 2005). Among them, the feedback control is especially attractive and has been commonly applied to practical implementation due to its simplicity in configuration and implementation (Tao & Yang, 2008).…”

Section: Introductionmentioning

confidence: 99%

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Some Problems of Feedback Control Strategies and It’s Treatment

Aziz¹,

Al-Azzawi²

2017

JMR

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This paper extends and improves the feedback control strategies. In detailed, the ordinary feedback, dislocated feedback, speed feedback and enhancing feedback control for a several dynamical systems are discussed here. It is noticed that there some problems by these strategies. For this reason, this Letter proposes a novel approach for treating these problems. The results obtained in this paper show that the strategies with positive feedback coefficients can be controlled in two cases and failed in another two cases. Theoretical and numerical simulations are given to illustrate and verify the results.

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Feedback control strategies for a cerium‐catalyzed Belousov–Zhabotinsky chemical reaction system

et al. 2015

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A number of control schemes including nonlinear feedback, dislocated feedback, and speed feedback have been proposed and assessed for a bromate-malonic acid-cerium Belousov-Zhabotinsky batch reaction process. The tuning parameters of the Oregonator model were firstly adjusted based on a UV-vis spectrophotometric analysis in the experimental part of the research. The adjusted Oregonator model successfully reproduced the innate induction time and periodicity of the BZ-batch system. Subsequently, the controllers were implemented and numerical simulations were carried out by employing the multi-stage Adomian decomposition method. The nominal analysis method was used to study the linear stability of each design. All the controlled systems were found to be linearly stable for certain continuous regions of controller gain. The performance of the proposed control laws was assessed and the dislocated feedback control strategy was shown to be able to drive the system states toward desired setpoints quickly. Furthermore, the validity of the dislocated feedback control design was doubly ensured by the sliding mode control theory. It was found that those feedback schemes which manipulate cerium ion concentration can be practically realized by means of electrochemical oxidation or oxygen aeration. Our results were confirmed by the Simulink software package and the block diagram representations are included in the paper.

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Speed feedback control of chaotic system

Cited by 43 publications

References 5 publications

Single state feedback stabilization of unified chaotic systems and circuit implementation

Single state feedback stabilization of unified chaotic systems and circuit implementation

Some Problems of Feedback Control Strategies and It’s Treatment

Feedback control strategies for a cerium‐catalyzed Belousov–Zhabotinsky chemical reaction system

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