非线性连续混沌系统的模糊自适应控制

摘要

This paper presents a direct method of fuzzy adaptive control for a class of nonlinear continuous chaotic systems.The method is established by using a fuzzy system in which parameters are adjusted by gradient descent to approximate an ideal controller,i.e.by minimizing the quadratic cost function of the deviation between the fuzzy controller and the ideal controller.The stability of closed-loop system and the convergence of tracking errors are analyzed by using Lyapunov stability theory.Numerical examples,including Arneodo system and Duffing oscillator,are given to illustrate the validity of the proposed adaptive fuzzy approach.%本文针对一类非线性连续混沌系统,提出了一种直接的模糊自适应控制方法.该方法通过利用模糊系统逼近某个理想控制器来实现,而模糊控制器中参数的调整是使用梯度下降法设计的,即通过最小化理想控制器与模糊控制器之间误差的二次成本函数来实现.根据Lyapunov稳定性理论,分析了闭环系统的稳定性及跟踪误差的收敛性.最后,通过对Arneodo混沌系统Duffing混沌系统的数值仿真验证了该方法的有效性.