使用曲線尺函數於漢彌司頓系統鑑別

Abstract

漢彌司頓系統是由一個非線性無記憶的子系統接著一個線性子系統所構成。傳統的係數確認方法用高階多項式模擬非線性子系統，這種方法在訓練序列短的情況下表現不佳。為了克服此問題，我們提出線性和二次的曲線尺函數來模擬非線性子系統。我們考慮兩種確認演算法。第一種是限制性最小平方演算法，適用於批次處理。第二種演算法是限制性最小均方適應性演算法，適用於線上處理。提出的限制是為了要確保非線性函數的連續性及平滑性。電腦模擬顯示所提出的方法表現優於現存的演算法，包括係數性或非係數性方法。

A Hammerstein system is a cascade of a nonlinear memoryless subsystem and a linear subsystem. Conventional parametric identification methods model the nonlinear subsystem using high-order polynomials, which performs poorly for a short training sequence. To overcome the problem, we propose to model the nonlinear subsystem using linear and quadratic spline functions. Two types of identification algorithms are considered. The first one is a constrained least-squares algorithm which is suitable for batch processing. The second one is a constrained least mean square (CLMS) adaptive algorithm that is suitable for online processing. Constraints are imposed to ensure the continuity and smoothness of the nonlinear function. Simulations show that the proposed method outperform the existing algorithms including parametric or non-parametric one.