离散非线性系统Worst-Case辨识——小波逼近法

THE WORST CASE IDENTIFICATION OF DISCREET TIME NONLINEAR SYSTEMS:A WAVELET APPROXIMATION APPROACH

利用小波逼近的软阈（Ｓｏｆｔ－Ｔｈｒｅｓｈｏｌｄｉｎｇ）方法，研究了离散非线性系统的Ｗｏｒｓｔ－Ｃａｓｅ辨识问题．证明了该算法在Ｗｏｒｓｔ－Ｃａｓｅ误差下的拟最优性和光滑性；估计了该算法的Ｗｏｒｓｔ－Ｃａｓｅ误差：给出了存在鲁棒收敛的辨识算法的充要条件；最后，证明了小波网逼近算法是鲁棒收敛的．

In this paper the problem of robust identification of nonlinear discrete time systems via wavelet networks is studied. An identification algorithm is proposed. It is shown that the algorithm has the properties of smoothness and near minimaxity. In addition, for some input, the necessary and sufficient condition on the existence of a robustly convergent identification algorithm is given. With that the wavelet approximation algorithm is shown to be robustly convergent.