一类参数失配主从非自治混沌系统的正弦反馈同步
Synchronization of a class of master-slave non-autonomous chaotic systems with parameter mismatch via sinusoidal feedback control
摘要：
研究了两个n维非自治混沌系统在正弦状态误差反馈控制下的主从同步方案，其中主系统和从系统的外部谐波激励之间存在参数失配.由于参数失配，引入了带误差界的同步概念，并给出了同步误差界的解析估计。首先利用李雅普诺夫直接法得到了一些以矩阵不等式形式表示的同步判据，然后利用Gerschgorin圆盘定理将其简化为一些代数不等式.估计的同步误差界和系统参数之间的关系表明，同步误差可以控制尽可能小，通过增加耦合强度或降低失配的幅度。以一个三维陀螺体系统为例，验证了该方法的有效性，并将估计的同步误差界与数值误差界进行了比较。理论和数值结果都表明，本文提出的正弦状态误差反馈控制对同步是有效的。数值算例验证了该控制器对幅值或相位失配具有较强的鲁棒性。
英文摘要：
In this paper we investigate a master-slave synchronization scheme of two n-dimensional non-autonomous chaotic systems coupled by sinusoidal state error feedback control, where parameter mismatch exists between the external harmonic excitation of master system and that of slave one. A concept of synchronization with error bound is introduced due to parameter mismatch, and then the bounds of synchronization error are estimated analytically. Some synchronization criteria are firstly obtained in the form of matrix inequalities by the Lyapunov direct method, and then simplified into some algebraic inequalities by the Gerschgorin disc theorem. The relationship between the estimated synchronization error bound and system parameters reveals that the synchronization error can be controlled as small as possible by increasing the coupling strength or decreasing the magnitude of mismatch. A three-dimensional gyrostat system is chosen as an example to verify the effectiveness of these criteria, and the estimated synchronization error bounds are compared with the numerical error bounds. Both the theoretical and numerical results show that the present sinusoidal state error feedback control is effective for the synchronization. Numerical examples verify that the present control is robust against amplitude or phase mismatch.
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