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 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.
Synchronization of Chaotic Systems Using Sampled-Data Polynomial Controller
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.
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Lam, H. K., and Li, H. (February 19, 2014). "Synchronization of Chaotic Systems Using Sampled-Data Polynomial Controller." ASME. J. Dyn. Sys., Meas., Control. May 2014; 136(3): 031006. https://doi.org/10.1115/1.4026304
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