变论域模糊控制器的万能逼近性及其逼近条件  

Universal approximation properties of fuzzy controllers with variable universe of discourse and their approximation conditions

作　　者：龙祖强[1,2] 梁昔明[2] 阎纲[2] 

机构地区：[1]衡阳师范学院物理与电子信息科学系,湖南衡阳421008 [2]中南大学信息科学与工程学院,湖南长沙410083

出　　处：《中南大学学报（自然科学版）》2012年第8期3046-3052,共7页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(61074069);湖南省科技计划项目(2011FJ309);衡阳师范学院科学基金启动项目(11B40)

摘　　要：通过一组非线性伸缩因子实时地调节论域,变论域模糊控制器显著减少初始规则的数量,在期望控制点有效地提高控制精度。首先,证明这类模糊控制器的逼近误差具有收敛性,从而证明它在整个时域上是一种万能逼近器,即它能以任意精度逼近紧集上的任意非线性实函数;并指出它是一种二阶精度的逼近器;在预定精度条件下,给出它作为逼近器的充分条件。最后,通过1个数值实例验证变论域模糊控制器逼近非线性函数的实际效果。研究结果表明:逼近精度完全满足给定的要求,相对常规模糊控制器,变论域模糊控制器的逼近精度提高87.4%。By tuning universe of discourse online using a set of contraction-expansion nonlinear factors, the amount of initial rules was reduced greatly on fuzzy controllers with variable universe of discourse, and the control accuracy was improved significantly at the control points of expectation. First, the approximation error of these fuzzy controllers was proved to be convergent, which suggested that they were universal approximators in the whole time domain. At the same time, they were pointed out to be approximators with second order accuracy. Next, a sufficient condition was given to use these fuzzy controllers as approximators under the prearranged accuracy. Finally, a numerical example was also given to illustrate the real effect of these fuzzy controllers on the approximation of nonlinear functions. The results show that the given requirements are met fully, and that fuzzy controllers based on variable universe of discourse increases by 87.4%, compared with conventional fuzzy controllers on approximation accuracy.

关 键 词：模糊控制器 变论域 万能逼近器 充分逼近条件 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]