变论域模糊控制的自适应机理及其相关理论问题

Variable universe fuzzy control was created by H.X. Li in 1995, which can solve "rule explosion" problem, so the precision of fuzzy control is highly improved. Besides,it was found that variable universe fuzzy control has some adaptive property。This project mainly researches 5 subjects: 1) it will be proved that a group of fuzzy inference rules is equivalent to a group of experiment data so that getting fuzzy inference rules can be of standardization; 2) the inner relationship between defuzzier based on barycenter and conditional mathematical expectation will be revealed so that the input space and the output space can be transformed two probability spaces. Thus, the relation between iuput variable and output variable will be able to become the relation between two random variables on the two probability spaces respectively; 3) considering the relationship between dynamic systems and time, it will be researched how to construct and deal with dynamic fuzzy inference rules; 4) based on a group of dynamic fuzzy inference rules, the relationship between input variable and output variable of a control system will be described by the conditional mathematical expectation of a group of stochastic processes; 5) based on the conditional mathematical expectation coming from a group of stochastic processes, the adaptive mechanism of variable universe fuzzy control can be showed, so that a basic theoretical frame will be formed.

变论域模糊控制是李洪兴于1995年提出，在控制系统建模中解决了熟知的规则爆炸问题，从而提高了控制精度；还发现这种控制方法具有自适应性。本项目旨在揭示变论域模糊控制的自适应机理，由此探索出自适应模糊控制的基本理论体系，并设计出自适应模糊控制的有效方法，为提高模糊控制的品质作出实质性贡献。该项目有5个研究内容：1）论证一组推理规则与一组数据是等效的，使得推理规则组的获取规范化；2） 揭示基于重心法的解模糊公式与条件数学期望的内在联系，从而把系统的输入空间与输出空间转化为两个概率空间，输入输出变量之间的联系变为随机变量之间的关系；3）考虑到动态系统与时间有关，要研究动态推理规则组的构造和处理；4）基于动态推理规则组，模糊控制系统的输入输出关系将要用若干随机过程的条件数学期望来描述；5）根据一族随机过程形成的条件数学期望来刻画变论域模糊控制的自适应机理，进而获得自适应模糊控制的基本理论体系。

本项目围绕模糊控制和模糊系统建模等开展了相应的理论与应用研究。针对不同类型的非线性系统，建立了若干变论域自适应模糊控制器设计方法，开展了基于自适应模糊滑模控制器、张量积变论域自适应模糊控制器等理论与应用研究，研究了基于数据和规则的模糊系统构造方法和逼近性能分析，同时将变论域自适应理论引入机器学习，建立了基于变论域的参数辨识方法，有效降低了学习结果对初值的依赖性，提高了学习效率。在此基础上，本项目将研究成果应用于多级倒立摆、视觉转台等典型的欠驱动装置控制，取得了良好的控制效果。本项课题的研究成果进一步丰富了模糊控制理论的研究，为解决复杂系统建模和控制积累了一定的研究经验和技术基础。