切换系统基于反演递推法的鲁棒自适应控制

摘要

切换系统的稳定控制问题是一个重要的研究问题.基于李雅普诺夫函数的方法是研究切换系统稳定性的重要手段,但是有约束非线性系统的李亚普诺夫函数构造仍是一个难题(特别是对带有不确定性的非线性系统).针对一类带有不确定性的严格反馈型切换非线性系统,利用反演递推法(backstepping)设计了子系统的基于李亚普诺夫函数的鲁棒自适应控制器,并证明了子闭环系统的稳定性,同时设计适当的切换律保证了整个闭环系统的稳定性.其中系统的未知不确定性及外界干扰不要求线性增长速度,并由模糊系统在线逼近.结果表明所提出方法的有效性.%Stabilization of the switched systems is an attractive research subject. The methods of multiple Lyapunov functions are main tools for switched system's stability analysis. But construction of the constrained Lyapunov funetions remains a difficult problem (especially for nonlinear systems with uncertainty). In this paper, for a kind of switched systems whose subsystems are strict- feedback system with uncertainties, a robust and adaptive control approach based on backstepping and Lyapunov functions is presented to ensure the stability of the closed - loop subsystem. Also a suitable switched law is given to ensure the stability of whole closed - loop system. Finally, the simulation results for a numerical example show the effectiveness of designed strategy in this paper.