二维随机双线性系统状态估计的降阶

Degree Reduction of State Estimation in Two Dimensional Stochastic Bilinear System

关注的是一类双线性不确定受估计误差协方差配置的随机离散时间系统的降阶状态估计.通过使用逐次逼近法,将原来的最优控制问题转化成一个非齐次线性两个序列点边值问题(两点边值问题).本文提出估计误差协方差的不确定双线性误差动态过程可能具有参数化,且所有降阶状态估计值的误差协方差的特征值可明确取得,并讨论配置条件的可解性.一个简单有效的矩阵不等式方法用来解决此问题.进一步用数值算例证明了该设计过程的有效性.

We will focus on the degree reduction of state estimation in a bilinear uncertatin stochastic discrete-time system with estimation error covariance assignment. The original optimization control problem is transformed to a non- homogenous boundary value problem with two sequence points （two-point boundary problem） by applying successive approximation method. We claim that the uncertain bilinear error dynamic process of estimation on covariance of error may have parametrization and all the eigenvalues of the covariance of the error about the degree reduction state estimation can be obtained explicitly. And we will discuss the solvability of assignment condition. A simple but effective matrix inequality method will give the solution of the problem. Further, we design a numerical experiment to prove the effectivity of the process discussed in this paper.