基于微分算子小波显式表示的分布参数系统最优逼近控制

基于微分算子在紧支撑正交小波基下的精确显式表示，给出了一种分布参数系统最优控制的逼近计算方法．将微分算子投影到小波空间，利用其矩阵表示形式，将分布参数系统的最优控制转化为集中参数系统最优控制问题．该方法不需要为边界条件重新构造基函数，在将偏微分方程转化为其常微分方程近似形式的过程中，不需要考虑边界条件的影响，因此计算方便、适用范围广，同时具有很高的精度和计算效率,可以对计算误差进行预测．利用该方法进行了基于Daubechies (db1)小波的仿真计算，并对计算结果进行了验证．

Optimal Approximate Control for Distributed Parameter Systems Based on Wavelet Explicit Representations of Differential Operators

This paper presents an approximate computation method of optimal control for distributed parameter systems(DPSs),based on the exact and explicit representations of differential operators in the bases of compactly supported orthogonal wavelets.The proposed method translates the computation of optimal control for DPSs into that for lumped parameter systems with the matrix representations obtained by projecting the differential operators into wavelet space.The method need not construct new basis functions for boundary conditions nor consider the effect of boundary conditions when partial differential equation is approximated with differential equation,so the computation is convenient and its application scope is wider.The method is exact and efficient and the error can be estimated.Numerical experiments with the proposed method have been performed based on the wavelet of Daubechies(db1),and the results are verified.