Control of Chaos Using Sampled-Data Feedback Control

In this paper we present a theory for control of chaotic systems using sampled data. The output of the chaotic system is sampled at a given sampling rate and the sampled output is used by a feedback subsystem to construct a control signal, which is held constant by a holding subsystem. Hence, during each control iteration, the control input remains unchanged. Theoretical results on the asymptotic stability of the resulting controlled chaotic systems are presented. Numerical experimental results via Chua's circuit are used to verify the theoretical results.

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Iterative learning control with sampled-data feedback for robot manipulators

Archives of Control Sciences ◽

10.2478/acsc-2014-0018 ◽

2014 ◽

Vol 24 (3) ◽

pp. 299-319 ◽

Cited By ~ 4

Author(s):

Kamen Delchev ◽

George Boiadjiev ◽

Haruhisa Kawasaki ◽

Tetsuya Mouri

Keyword(s):

Feedback Control ◽

Iterative Learning Control ◽

Feedforward Control ◽

Robotic Manipulators ◽

Learning Control ◽

Iterative Learning ◽

Control Input ◽

Sampled Data ◽

Model Based ◽

Data Feedback

Abstract This paper deals with the improvement of the stability of sampled-data (SD) feedback control for nonlinear multiple-input multiple-output time varying systems, such as robotic manipulators, by incorporating an off-line model based nonlinear iterative learning controller. The proposed scheme of nonlinear iterative learning control (NILC) with SD feedback is applicable to a large class of robots because the sampled-data feedback is required for model based feedback controllers, especially for robotic manipulators with complicated dynamics (6 or 7 DOF, or more), while the feedforward control from the off-line iterative learning controller should be assumed as a continuous one. The robustness and convergence of the proposed NILC law with SD feedback is proven, and the derived sufficient condition for convergence is the same as the condition for a NILC with a continuous feedback control input. With respect to the presented NILC algorithm applied to a virtual PUMA 560 robot, simulation results are presented in order to verify convergence and applicability of the proposed learning controller with SD feedback controller attached

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SAMPLED-DATA FEEDBACK CONTROL FOR CHEN'S CHAOTIC SYSTEM

Acta Physica Sinica ◽

10.7498/aps.49.1039 ◽

2000 ◽

Vol 49 (6) ◽

pp. 1039

Author(s):

YANG LIN-BAO

Keyword(s):

Feedback Control ◽

Chaotic System ◽

Sampled Data ◽

Data Feedback

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Output-feedback control for sampled-data systems with variable sampling rate

International Journal of Control ◽

10.1080/00207179.2017.1299942 ◽

2017 ◽

Vol 91 (4) ◽

pp. 897-906 ◽

Cited By ~ 1

Author(s):

Hojin Lee ◽

Yasumasa Fujisaki

Keyword(s):

Feedback Control ◽

Output Feedback ◽

Sampling Rate ◽

Output Feedback Control ◽

Data Systems ◽

Sampled Data ◽

Variable Sampling

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A relation between overshoot and sampling period in sampled data feedback control systems

IEEE Transactions on Automatic Control ◽

10.1109/tac.1980.1102334 ◽

1980 ◽

Vol 25 (3) ◽

pp. 603-604 ◽

Cited By ~ 7

Author(s):

T. Mita

Keyword(s):

Feedback Control ◽

Control Systems ◽

Sampling Period ◽

Sampled Data ◽

Data Feedback ◽

Feedback Control Systems

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Hybrid Passivity Based and Fuzzy Type-2 Controller for Chaotic and Hyper-Chaotic Systems

Acta Mechanica et Automatica ◽

10.1515/ama-2017-0015 ◽

2017 ◽

Vol 11 (2) ◽

pp. 96-103 ◽

Cited By ~ 1

Author(s):

Fernando Serrano ◽

Josep M. Rossell

Keyword(s):

Lyapunov Exponents ◽

Chaotic System ◽

Control Strategy ◽

Chaotic Systems ◽

Control Law ◽

Four Dimensions ◽

Design Requirements ◽

The Stability ◽

Theoretical Results

AbstractIn this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.

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STABILIZATION OF CHAOTIC SYSTEMS USING LINEAR SAMPLED-DATA CONTROLLER

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407018191 ◽

2007 ◽

Vol 17 (06) ◽

pp. 2021-2031 ◽

Cited By ~ 20

Author(s):

H. K. LAM ◽

F. H. F. LEUNG

Keyword(s):

Chaotic System ◽

Chaotic Systems ◽

Lorenz System ◽

Design Procedure ◽

Sampling Period ◽

Feedback Gain ◽

Sampled Data ◽

Lyapunov Approach ◽

And Performance ◽

Data Controller

This paper proposes a linear sampled-data controller for the stabilization of chaotic system. The system stabilization and performance issues will be investigated. Stability conditions will be derived based on the Lyapunov approach. The findings of the maximum sampling period and the feedback gain of controller, and the optimization of system performance will be formulated as a generalized eigenvalue minimization problem. Based on the analysis result, a stable linear sampled-data controller can be realized systematically to stabilize a chaotic system. An example of stabilizing a Lorenz system will be given to illustrate the design procedure and effectiveness of the proposed approach.

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Time-Delayed Sampled-Data Feedback Control of Differential Systems Undergoing Hopf Bifurcation

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421500048 ◽

2021 ◽

Vol 31 (01) ◽

pp. 2150004

Author(s):

Huan Su ◽

Jing Xu

Keyword(s):

Hopf Bifurcation ◽

Feedback Control ◽

Blood Transfusion ◽

Sampling Period ◽

Delayed Feedback Control ◽

Control Technique ◽

Blood Collection ◽

Sampled Data ◽

Differential Systems ◽

Data Feedback

In this paper, time-delayed sampled-data feedback control technique is used to asymptotically stabilize a class of unstable delayed differential systems. Through the analysis for the distribution change of eigenvalues, an effective interval of the control parameter is obtained for a given sampling period. Here an indirect strategy is taken. Specifically, the system of continuous-time delayed feedback control is studied first by Hopf bifurcation theory. And then, the result and implicit function theorem are used to analyze the system of time-delayed sampled-data feedback control with a sufficiently small sampling period. Considering the practical criterion for the size of sampling period, the upper bound of sampling period is estimated. Finally, an application example, an unstable Mackey–Glass model, is asymptotically stabilized by introducing a blood transfusion item with time-delayed sampled-data feedback control. The blood transfusion speed and blood collection test period are derived from the main results. Some simulations and comparisons show the correctness and advantages of the main theoretical results.

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