Optimal control algorithm of multivariate second-order distributed parameter systems based on fourier transform

Abstract

This article gives the differential properties of the multi-function fourier transform and integrating nature as well as its corollaries. Also, it gives the corresponding proof. For homogeneous second-order distributed parameter systems, first, this artical uses the fourier transform of the nature to chang the system model, transforms the partial differential equation into the ordinary differential equations in the domain time and obtains the solution of the transformed equation, then, change the solution into the inverse fourier transform to calculate the state variables and optimal control indicators accurately. For non-homogeneous second-order control system whose input is not zero of distributed parameter system's models, first, this artical transforms fourier transform on the model as well as the optimal control indicators, transforms the partial differential equation into the ordinary differential equations to get the solution, then, chang the solution into the inverse fourier transform to calculate the state variables and optimal control indicators accurately. For n-ary of distributed parameter systems model, this article regards the n-1 space parameter variable as vector then uses the same mathed to obtain the exact optimal solution.