不确定非线性系统自适应镇定的充要条件

Necessary and sufficient conditions of adaptive robust control for a class of nonlinear systems

中文关键词  非线性系统  自适应控制  非最小相位系统  鲁棒控制

英文关键词  nonlinear systems  adaptive control  non-minimum phase systems  robust control

中文摘要

      研究了一类相当广泛的包含未知参数的非线性控制系统的自适应鲁棒控制问题, 这类系统的标称系统包含一些非最小相位非线性系统和一些不存在相对阶的非线性系统. 其未知定常参数是线性的. 在一定假设条件下,对该类系统给出了存在自适应控制器的充要条件, 并采用backstepping方法给出了控制器的设计步骤. 所得主要结论没有用到增长性假设、最小相位假设和相对阶的假设. 同时, 还给出了不存在相对阶及非最小相位的非线性系统的例子, 对于后者给出了控制器的设计过程.

英文摘要

      The problem of robust adaptive stabilization is discussed for a wide class of uncertain nonlinear control systems, of which the nominal systems include some non-minimum phase nonlinear systems and some systems without relative degree. The uncertainties are time-invariant unknown linear parameters. Firstly, necessary and sufficient conditions are presented for the existence of a robust adaptive controller with some assumptions. The design procedure of the controller is then explicitly given by using the back-stepping approach. The main result does not require any growth conditions, relative degree conditions and minimum phase conditions. Finally, some examples are presented to illustrate the design procedure.