中文摘要：

反步设计法是通过将一个系统分解为多个低阶子系统，一步步构建Lyapunov函数导出稳定的控制律，获得需要的控制器，实现同步的目的。基于Lyapunov稳定性理论，结合反步法思想为混沌ADVP系统设计了同步控制器。注意到系统参数间量级相差很大，在选择增益矩阵时，通过调节柯西不等式放大参数，使控制中系数的量级差别适当减小。设计出的控制器只需施加于一个子系统，使得控制的实现更加方便，且大大降低了控制成本和难度，可将其应用于保密通信。仿真结果表明了该方法的有效性。

英文摘要：

Backstepping method helps to design a desired controller through a step-by-step process of constructing Lyapunov function. By dividing a system into several subsystems of lower order, the stable controlling law is derived to meet the needs of synchronization. A kind of synchronous controller was designed for a class of chaotic ADVP systems with the backstepping method. Considering great difference in quantity between the coefficients in the system, an adjustment of enlarging parameter in Cauchy inequality was done for narrowing the difference in controller. Such a controller is only needed to act on a subsystem and it is convenient for realizing control in secure communication, meanwhile the controlling cost and difficulty in design are greatly reduced. The simulation verifies the effective- ness of the synchronization method.