非线性系统同步的反向设计
Backstepping Design in Synchronizing Nonlinear Systems
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摘要: 反向设计是将Lyapunov函数的选取与控制的设计相结合的一种回归设计方法。将该方法用于同步系 统的设计,给出了一个具体可行的同步设计过程。在同步设计中,不管是几阶系统均只需一个控制项。不仅适 用于一般的非线性系统的同步,还适用于一些混沌系统(如有外激励的van der Pol系统、Duffing系统、Chua电 路、R¨ossler系统等)的同步。控制项中不出现求导项,便于该方法的实施。作为算例,给出了van der Pol系统及 Chua电路的同步设计。Abstract: Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. In this paper, a practical backstepping design scheme is proposed for synchronizing nonlinear systems. In the scheme, only one feedback control is required regardless of the order of the system. It can be applied not only to ordinary nonlinear systems, but also to a variety of chaotic systems, such as van der Pol system and Duffing system with external excitation, Chua s circuit and system,etc. It is easy to be carried out since its feedback control has no derivatives. Examples of van der Pol system and Chua s circuit designs are presented.
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Key words:
- nonlinear system /
- control /
- chaotic synchronization
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