Synchronization of Chaotic Systems Using Sampled-Data Polynomial Controller

Abstract

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 1 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.

Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional‐order chaotic systems

“…8 Many control techniques have been presented for the synchronization purpose of fractional-order systems, for instance, active control, feedback control, fuzzy control, fractional PID control, sliding mode control (SMC), and Laplace transformation theory. 9 Nevertheless, in the most studied research works, the influences of the external disturbances and modeling inexactitudes have been ignored, which cannot be avoided in the practical applications. The SMC approach is recognized as an effective tool to design robust control laws for complex high-order nonlinear systems in the presence of uncertain conditions.…”

Fuzzy‐model‐based sampled‐data chaotic synchronisation under the input constraints consideration

“… Time responses of the performance indices for s of the proposed method (solid line), [7] (dash‐dotted line), and [8] (dashed line)…”

“…However, because chaotic systems are highly non‐linear, its time response is very sensitive to initial conditions or model variations. As a result, synchronising two chaotic systems has been a challenging research topic in the control engineering [7–15].…”

“…Therefore, earlier studies have been conducted based on this non‐diverging characteristic, which causes the degradation of the synchronisation performance (e.g. [7]). Recent studies have eliminated the modelling error term more effectively than the earlier approaches by letting the controller include the modelling error term [9].…”

Synchronisation and anti‐synchronisation of chaotic systems with application to DC–DC boost converter

“…Sampled‐data fuzzy control of chaotic systems is discussed for Takagi–Sugeno (T–S) fuzzy model in [22], where some stability conditions have been derived based on a novel time‐dependent Lyapunov functional approach, and the design technique of the desired sampled‐data controller is also proposed. Lam and Li [23] discussed the synchronisation of two chaotic systems, namely the drive and response chaotic systems using sampled‐data polynomial controllers, where sum‐of‐squares based stability conditions are obtained to guarantee the system stability and realise the chaotic synchronisation subject to performance function. However, in many real‐world applications external disturbances are always persistent bounded with infinite energy.…”