非线性系统的递推最小二乘自适应模糊控制

Recursive Least Square Adaptive Fuzzy Control for Nonlinear Systems

提出了一种可有效消除被控系统不确定性的自适应模糊控制方法.该方法采用模糊逻辑系统(FLS)来辨识系统的未知函数,并采用连续形式的递推最小二乘算法作为自适应律调节FLS权参数.该自适应律可保证FLS权参数稳定收敛,最终收敛至最佳值的一个很小邻域中,同时保证跟踪误差指数衰减趋于0.倒立摆仿真结果表明,采用该方法时,辨识的归一化平方误差小于2%,其相对跟踪误差较混合自适应控制方法减少了58%.

A new approach to adaptive fuzzy control was proposed to efficiently eliminate uncertainties in controlled systems, in which fuzzy logical systems （FLS） were utilized to identify unknown functions in the system, and continuous recursive least square （RLS） algorithm was used as an adaptive law to adjust FI.S weight parameters. The properties of RLS ensure that the weight parameters of FLS would converge asymptotically. Finally, these weight parameters converge to a tiny neighborhood of their optimal values. Meanwhile it ensures that the tracking error exponentially approximates to zero. Simulation results using an inverted pendulum system show that the normalized squared-error of identification of unknown functions is less than 2G, and the relative tracking error decreases by 58 % compared with that using hybrid adaptive controller.