复杂控制系统随机参量的广义自相关性研究

研究泛逻辑推理中广义自相关系数k值的求解方法,提出了基于泛逻辑的复杂控制系统不确定性推理模型,给出了求解k值的一般步骤和相关定理.研究了3种连续型随机参量的广义自相关性:均匀分布的k值恒等于0.5,是一种理想的精确估计模型;没有基变换时的指数分布和标准正态分布的k值均小于0.5,它们对随机参量的逻辑值呈偏小估计.推导出了求解N范数和k值的通用公式,建立起泛逻辑理论和不确定性推理与控制之间的实用性桥梁.

On the Generalized Self-correlation of Random Parameter in Complex Control Systems

The issue of finding the value of generalized self-correlation coefficient k in universal logic reasoning is addressed. A model of uncertainty reasoning in a complex control system based on universal logic is proposed. General proceedure of finding the value of k and related theorems are given. The generalized self-correlation of three kinds of continuous random parameters are studied. The results indicate that k is identically 0.5 for proportional distributions which gives a precise model; and k is smaller than 0.5 for exponential distributions and normal distributions without radix conversion, which means the smaller logic values of random parameters. The general formula for expressing N-norms and coefficient k are derived. This sets up a practical bridge between universal logic theories and uncertainty reasoning and control.