离散线性随机系统中的某些问题

研究了离散线性随机系统输入与输出间的关系。证明了任何线性随机系统的输出方差与其控制输入无关,因而在任何意义下,由极小化方差而得最优控制是不可能的。证明了输出与其集点间的期望差,文中定义为输出偏差,依赖于控制信号的选择。基于这种观点,给出了输出偏差极小化的最小偏差(M B)控制器。另一涉及输入输出关系的重要概念是线性随机系统完全i-步输出可达性。给出了由输入-输出随机差分方程所给多变量随机系统完全i-步输出可达的充要条件和检验输出可达性的简易方法。

Some Problems of the Discrete Linear Random System

This paper studies the relationship between the input and output of discrete linear random systems.It is proven that the variance of the output of any linear random systems 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,difined 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 regard the input-output relationship is the complete i-step output reachability of linear random 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 random difference equations is given,which also leads to a direct easy-to-use method to check the output reachability.