串级系统的自适应设计

利用反演法，对一类串级系统进行了自适应的控制设计。本文利用了关于串级系统的研究结果，将反演法推广到更一般形式的串级系统。设计的主要技术思想是：对每个子系统，引入中间虚拟控制变量，通过建立和推导各阶段的Lyapunov函数，设计出每个阶段的虚拟控制和调整函数，逐步实现各个阶段的镇定，利用递归设计方法，逐步修正算法，在设计的最终阶段，得到参数估计的实际更新法则和系统反馈控制律，从而实现系统的自适应设计。

Adaptive design of cascaded systems

In this paper, the backstepping method is introduced to deal with the adaptive control design for a class of cascadedsystems. Basedontheresultshave beenobtained on cascadedsystem, the presentednew method extendedthe backstepping methodto the system which is more generally. The main idea of the design is as follow. For each subsystem, a virtual control is introduced,a Lyapunov function for each step is structured, and then the virtual control and tuning function of each step are designed. The al-gorithm is modified step by step in the recursive design approach. In the final step, the actual update law for parameter estimateand the actual feedback control law are designed. Then The Adaptive Design of Cascaded Systems is achieved.