引用本文:杨恒占,钱富才,黄娇茹,高嵩.一类随机系统完全统计特征控制[J].控制理论与应用,2016,33(5):669~675.[点击复制]
YANG Heng-zhan,QIAN Fu-cai,HUANG Jiao-ru,GAO Song.The complete statistical characterization control for a class of stochastic systems[J].Control Theory and Technology,2016,33(5):669~675.[点击复制]
一类随机系统完全统计特征控制
The complete statistical characterization control for a class of stochastic systems
摘要点击 2708  全文点击 1759  投稿时间：2015-07-04  修订日期：2016-06-14
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DOI编号  10.7641/CTA.2016.50587
  2016,33(5):669-675
中文关键词  非线性  随机系统  完全统计特征  FPK方程
英文关键词  nonlinear  stochastic systems  complete statistical characteristics  FPK equation
基金项目  国家自然科学基金项目(61273127, U1534208), 航天器在轨故障诊断与维修实验室开放课题(SDML–OF2015004), 陕西省科技攻关项目(2016GY– 108), 陕西省国际科技合作重点项目(2015KW–024)资助.
作者单位E-mail
杨恒占 西安理工大学 yanghengzhan@126.com 
钱富才* 西安理工大学 qianfc@xaut.edu.cn 
黄娇茹 西安工业大学  
高嵩 西安工业大学  
中文摘要
      非线性随机系统完全统计特征控制优于低阶矩控制, 但往往因为算法的复杂性难以实际应用. 本文针对受 高斯白噪声激励的标量非线性随机系统, 针对状态响应提出了一种完全统计特征控制方法. 首先将刻画完全统计 特征的概率密度函数表示成指数函数, 利用FPK(Fokker-Planck-Kolmogorov)方程求出概率密度函数的各阶导数, 进 而建立指数函数Taylor展开的系数与待求反馈控制增益间的关系. 然后, 依据控制目标给出了求解反馈增益的优化 问题. 针对目标概率密度函数的不同情况, 分别给出了跟踪控制策略: 对于指数函数Taylor展开为有限项形式的情 况, 能够直接得到控制增益并完全跟踪目标概率密度函数; 其他情况下, 也能够达到较好的控制效果. 仿真验证了本 文方法的有效性.
英文摘要
      For nonlinear stochastic systems, although the complete statistical characterization control method is superior to the traditional low moment control methods, it is difficult to apply the control law into the real system due to its complexity. A complete statistical characteristics control algorithm is presented for nonlinear stochastic systems excited by Gaussian white noise in this paper. Firstly, an exponential function is used to represent the probability density function which characterizes the statistical characteristics completely. Subsequently, the relationship between the Taylor series expansion coefficients of the exponential function and the feedback control gain is derived by the derivation of FPK (Fokker-Planck-Kolmogorov) equation constantly. Then, on the basis of the control objective, an optimization problem is given to obtain the feedback gain. And different tracking control strategies are given for different target probability density function: for the condition that the exponential expansion is finite terms, the control gains can be obtained directly, and completely track-target probability density function; under other conditions, a nearly track-target probability density could be got. The examples show the effectiveness of the proposed method.