Mean and Entropy of B-spline PDF Models: Analysis and Design

Authors:	Zhou Jinglin, Institute of Automation, Chinese Academy of Sciences, China Yue Hong, The University of Manchester, United Kingdom Wang Hong, The University of Manchester, United Kingdom
Topic:	1.4 Stochastic Systems
Session:	Control, Estimation and Analysis of Stochastic Systems
Keywords:	Dynamic stochastic systems; Probability density function (PDF);B-spline neural network; Minimum entropy; Mean constraint

Abstract

For continuous probability density functions (PDFs) approximatedby the B-spline basis functions, the relationships between theB-spline weights, the entropy and the mean have been analyzed indetail. It shows the different characteristics of the entropy withand without mean constraint. A minimum entropy controllersubjected to mean constraint is developed by taking theperformance function as a Lyapunov function and ensuring thenegativeness of its first-order derivative. Simulation examplesare included to validate the analysis results and evaluate theclosed-loop control performance.