线性时不变系统集员辨识的区间算法

INTERVAL ALGORITHM FOR MEMBERSHIP-SET IDENTIFICATION OF LINEAR TIME-INVARIANT SYSTEM

在不确定但有界(UBB)噪声假设下,提出一种针对线性时不变系统参数集员辨识的区间算法.借助区间数学,寻求与观测数据和噪声相容的参数的最小超长方体(或区间向量),推导了递推列式,并分析了算法的收敛性.此算法不仅可以给出参数估计值,还可以给出参数的不确定性界限.通过数值算例,将此算法与Fogel 椭球算法和最小二乘算法进行了比较,显示了其计算量小和精度高的优点.

Based on the assumption of Unknown-But-Bounded （UBB） noise, an interval algorithm is presented for parameter membership-set estimation of a linear time-invariant system. In virtue of interval mathematics, the algorithm objective is to seek the minimal hyper-rectangle （or interval vector） of parameters which is compatible with the measurements and the bounded noise, and its recursive formula are derived. Convergence of the algorithm is analyzed. The presented algorithm can obtain not only the center estimations of parameters, but also the uncertain bounds on them. Numerical examples illustrate its small computation efforts and higher accuracy in comparison with Fogel＇s algorithm and the least squares algorithm.