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Research Papers

Synchronization of Chaotic Systems Using Sampled-Data Polynomial Controller

[+] Author and Article Information
H. K. Lam

Department of Informatics,
King's College London, Strand,
London WC2R 2LC, UK
e-mail: hak-keung.lam@kcl.ac.uk

Hongyi Li

College of Information Science and Technology,
Bohai University,
Jinzhou 121013, China
e-mail: lihongyi2009@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 11, 2012; final manuscript received November 30, 2013; published online February 19, 2014. Assoc. Editor: Warren E. Dixon.

J. Dyn. Sys., Meas., Control 136(3), 031006 (Feb 19, 2014) (7 pages) Paper No: DS-12-1105; doi: 10.1115/1.4026304 History: Received April 11, 2012; Revised November 30, 2013

This paper presents the synchronization of two chaotic systems, namely the drive and response chaotic systems, using sampled-data polynomial controllers. The sampled-data polynomial controller is employed to drive the system states of the response chaotic system to follow those of the drive chaotic system. Because of the zero-order-hold unit complicating the system dynamics by introducing discontinuity to the system, it makes the stability analysis difficult. However, the sampled-data polynomial controller can be readily implemented by a digital computer or microcontroller to lower the implementation cost and time. With the sum-of-squares (SOS) approach, the system to be handled can be in the form of nonlinear state-space equations with the system matrix depending on system states. Based on the Lyapunov stability theory, SOS-based stability conditions are obtained to guarantee the system stability and realize the chaotic synchronization subject to an H performance function. The solution to the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. Simulation examples are given to illustrate the merits of the proposed sampled-data polynomial control approach for chaotic synchronization problems.

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Figures

Grahic Jump Location
Fig. 1

Synchronization error e(t) of Lorenz's systems with u(t) = 0 applied for 0s≤t<50s and the sampled-data polynomial controller u(t) applied for 50s≤t≤100s

Grahic Jump Location
Fig. 2

Control signal of the sampled-data polynomial controller for the Lorenz's systems for 50s≤t≤100s

Grahic Jump Location
Fig. 3

Synchronization error e(t) of Rössler's systems with u(t) = 0 applied for 0s≤t<50s and the sampled-data polynomial controller u(t) applied for 50s≤t≤100s

Grahic Jump Location
Fig. 4

Control signal of the sampled-data polynomial controller for the Rössler's systems for 50s≤t≤100s

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