一类自适应控制系统的稳定性分析

对一类模型参考自适应控制映射进行了稳定性分析,通过使用中心流形简化和范式方法以及计算机辅助计算讨论了该类系统在参数空间内的所有1-余维和2-余维分岔行为及其性质,全面了解了系统在不同参数区域内的动态.从而为如何选取此类控制系统的参数以避免导致控制失效的多吸引子共存或长期存在的瞬态等动力学行为提供了方法和理论依据,并为在线调整参数以避免控制失效指明了方向.

Stability Analysis of an Adaptive Control System

By using the center manifold reduction and normal form method,the stability of a map which appears in the model-reference adaptive control system is analyzed.This map possesses a lot of codim 1 and codim 2 bifurcations,including Flip,Neimark-Sacker,resonance bifurcations etc.With the help of software Content,all these bifurcations are detected and located in the parameter space,and their properties are obtained via the sign of the critical normal form coefficients.Meanwhile,the dynamic behavior of this map in different parameter regions is demonstrated,which is important for choosing and adjusting the parameters in order to get an effective control.