基于Haar尺度变换的连续分片线性逼近

Continuous piecewise linear approximation based on Haar scale transform

为了获得非线性系统的连续逼近,提出一种基于Haar尺度变换的连续分片线性逼近算法。由非线性函数的Haar尺度变换获得尺度系数,用紧支撑连续分片线性基函数重构出非线性函数的连续分片线性逼近。理论分析证明这种逼近可以达到任意精度。仿真试验表明:相对于Haar小波逼近,连续分片线性逼近的误差收敛得更均匀。算法的一个显著优势是可以给出逼近的解析表达式。因为Haar尺度变换的计算复杂度低(相当于算术平均),紧支撑连续分片线性基函数的结构简单,所以算法易于推广。

In order to achieve continuous approximation on nonlinear systems,this paper presents an algorithm for continuous piecewise linear approximation based on Haar wavelet transform.The scaling coefficients are obtained using the Haar scaling transformation of a nonlinear function,and then the continuous piecewise linear approximation of the nonlinear function is reconstructed using the compactly supported continuous piecewise linear basis functions.Theoretical analysis proves that the approximation can achieve any accuracy.The simulation demonstrates that the error convergence of the continuous piecewise linear approximation is more uniform than that of the Haar wavelet approximation.It is an obvious advantage that the algorithm provides an analytical expression of approximation.Since the computational complexity of the Haar scale transform（correspond to arithmetic average） is low and the structure of the compactly supported continuous piecewise linear basis functions is simple,it is ease for a wide application of proposed algorithm.