物理学报Issue(24)：1-8,8.DOI:10.7498/aps.63.240508
随机系统的概率密度函数形状调节∗
The shap e regulation of probability density function for sto chastic systems
摘要
Abstract
For nonlinear stochastic systems which are excited by Gaussian white noise, an innovational regulation method is proposed to control the shape of the probability density function of state response to track a desired shape. Firstly, a polynomial feedback scheme is established, and the nonlinear part is replaced by polynomials expansion. Then the recursive equations of the moments which are related to control gain are derived under Fokker-Planck-Kolmogorov theory framework. Meanwhile, regarding the tracking requirement, an optimization problem about the moment approximation is constructed, and the gain of regulation function is obtained by solving this optimization problem using the gradient method. Furthermore, the probability density function of state response is reconstructed from the relationship of the Fourier transform pairs between the characteristic function and probability density function. Finally, two examples are given to demonstrate the effectiveness of the method developed in this paper.关键词
非线性随机系统/概率密度函数/Fokker-Planck-Kolmogorov方程/矩Key words
nonlinear stochastic systems/probability density function/Fokker-Planck-Kolmogorov equation/moment引用本文复制引用
杨恒占,钱富才,高韵,谢国..随机系统的概率密度函数形状调节∗[J].物理学报,2014,(24):1-8,8.基金项目
国家自然科学基金(批准号:61273127,61304204)和高等学校博士点专项科研基金(批准号:20116118110008)资助的课题.@@@@* Project supported by the National Natural Science Foundation of China (Grant Nos.61273127,61304204), and the Spe-cialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20116118110008) （批准号:61273127,61304204）
