系统辨识的互补变分法

Tikhonov正则化是近似解决病态最小二乘参数辨识的一个有效的方法。然而,直接求解由此得到的极小元素所满足的方程有较大的困难。这里应用互补变分原理,对此极小元素进行近似估计。此外,此近似估计的逼近程度能够利用相应的泛函上下界的误差表征。

System Identification Using Complementary Variational Principles

The identification of system parameter from noisy data is an ill-posed problem and cannot be done directly by means of approximation method. It is now showed that with the aid of the so-called Tikhoaov regularization usable approximation method, one can solve these ill-posed problems. It is well known that for a smoothing functional there exists a unique minimizing solution determined by a minimal function equation. In this paper, instead of dealing directly with the solution of the minimal function equation, the complementary variational principle is applied to direct both upper and lower bounds to the solution of the variational problem as well as the approximation solutions to the original system identification problem. Finally, an example is given using the complementary variational method.