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Research Papers

Identification and Control of Chaos Using Fuzzy Clustering and Sliding Mode Control in Unmodeled Affine Dynamical Systems

[+] Author and Article Information
Aria Alasty1

Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 1458889694, Iranaalasti@sharif.edu

Hassan Salarieh

Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 1458889694, Iransalarieh@mehr.sharif.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 130(1), 011004 (Dec 05, 2007) (8 pages) doi:10.1115/1.2789472 History: Received October 19, 2005; Revised February 26, 2007; Published December 05, 2007

In this paper, a combination of fuzzy clustering estimation and sliding mode control is used to control a chaotic system, which its mathematical model is unknown. It is assumed that the chaotic system has an affine form. At first, the nonlinear noninput part of the chaotic system is estimated by a fuzzy model, without using any input noise signal. Without loss of generality, it is assumed that chaotic behavior is appeared in the absence of input signal. In this case, the recurrent property of chaotic behavior is used for estimating its model. After constructing the fuzzy model, which estimates the noninput part of the chaotic system, control and on-line identification of the input-related section are applied. In this step, the system model will be estimated in normal form, such that the dynamic equations can be used in sliding mode control. Finally, the proposed technique is applied to a Lur’e-like dynamic system and the Lorenz system as two illustrative examples of chaotic systems. The simulation results verify the effectiveness of this approach in controlling an unknown chaotic system.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Identification and control algorithm of chaotic systems

Grahic Jump Location
Figure 2

The chaotic attractor of Lur’e system with a1=−7.4, a2=−4.1, a3=−1, α=3.6, and u=0

Grahic Jump Location
Figure 3

Behavior of Lur’e system with xd=3. For t<100s: f(t,x̱) is being identified and the controller is off. For t>100s: g(t,x̱) is being identified and the controller is on.

Grahic Jump Location
Figure 4

Behavior of Lur’e system, xd=5+2sin(0.4πt). For t<100s: f(t,x̱) is being identified and the controller is off. For t>100s: g(t,x̱) is being identified and the controller is on.

Grahic Jump Location
Figure 5

Chaotic behavior of Lorenz system in phase space for ρ=10, β=8∕3, and R=28

Grahic Jump Location
Figure 6

Behavior of Lorenz system, yd=5. For t<30s: f(x,y,z) is being identified and the controller is off. For t>30s: g(x,y,z) is being identified and the controller is on.

Grahic Jump Location
Figure 7

Behavior of Lorenz system, yd=5+5sin(πt). For t<30s: f(x,y,z) is being identified and the controller is off. For t>30s: g(x,y,z) is being identified and the controller is on.

Grahic Jump Location
Figure 8

Chaotic attractor in the phase plane of nonlinear pendulum, with α=0.5, a0=−3, a1=0.3, δ=0.12, ω=0.75

Grahic Jump Location
Figure 9

Behavior of chaotic pendulum system with xd=a1cosωt+a0. For t<100s: f(t,x̱) is being identified and the controller is off. For t>100s: g(t,x̱) is being identified and the controller is on.

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