分布参数系统边界控制的Haar小波算法

HAAR WAVELET TRANSFORM ALGORITHM FOR OPTIMAL BOUNDARY CONTROL OF DISTRIBUTED PARAMETER SYSTEMS

由于分布参数系统通常由偏微分方程描述,采用解析法求解分布参数系统最优边界控制问题,是非常难以解决的。正交函数逼近的方法在分布参数系统控制方面,已经取得了较好的效果。Haar小波作为正交基函数,利用小波的一些运算及变换矩阵,将分布参数系统转化为集总参数系统,再求其逼近解。仿真示例验证了所提出的算法是非常有效的。该方法为分布参数系统的控制算法提出了一条新的解决方案。

It＇s difficult to solve the optimal boundary control problems of distributed parameter systems （ DPS）, which are described by partial differential equations（ PEDs）. The orthogonal function approximation method is very effective for the optimal boundary control of distribu- ted parameter systems. Orthogonal Haar wavelet bases are applied to solve the optimal boundary control problems of distributed parameter systems. With the help of characteristics of Haar wavelets transforms and their operational matrices, optimal boundary control problems of distributed parameter systems are converted into optimal control problems of lumped parameter system. The simulation results verify the effectiveness of the presented algorithm. The proposed method is a new way to solve the optimal boundary control problems of distributed parameter systems.