离散线性随机系统输入-输出关系的数学描述(英文)

Mathematical Description for the Input output Relationship of the Discrete Linear Stochastic Systems

研究离散线性随机系统输入－ 输出间的关系，证明了任何线性随机系统输出方差与其输入无关．因此在任何意义下由方差极小化而得最优控制是不可能的，且已证明，输出与其集点间的期望差依赖于控制信号的选择，得到了最小偏差控制器，考虑了与线性随机系统输入－ 输出关系有关的所谓完全ｉ－ 步输出可达性这一重要概念，并给出了以输入－ 输出随机差分方程所描述的多变量随机系统的完全ｉ－ 步输出可达性的充要条件。

This paper studies the relationship between the input and the output of discrete linear stochastic systems.It is proven that the variance of the output of any linear stochastic system is independent of its control input.This implies that it is impossible to get optimal control in any sense by minimizing the variance of the output.However,it is shown that the expected difference between the output and its setpoint,defined herein as the bias in the output,does depend on the choice of the control signal.Based on this observation,a minimum bias(MB)controller that minimizes the bias in the output is obtained.Another important concept regarding the input output relationship is the complete i- step output reachability of linear stochastic systems,which is the natural extension of the output reachability of linear deterministic systems. The nesessary and sufficient condition for the complete i- step output reachability of multivariable stochastic systems described by input output stochastic difference equations is given,which also leads to a direct easy to use method to check the output reachability.