一类抛物型分布参数系统最优控制问题的数值方法

Finite Element and Conjugate Gradient Methods for A Parabolic Distributed Parameter System Optimal Control Problem

本文在综合前人结果的基础上,讨论了一类具有非线性边界条件的一维热传导方程所描述的分布参数系统的最优边界控制问题。对于所给模型用有限元方法将空间变量离散化,对一般边界条件进行了有效地处理。并对简化后的系统应用数学规划的共轭梯度方法求出了最优控制及状态的数值解。整个计算用 FORTRAN77语言编写程序,在 IBM-PC 微型机上实现。本文处理问题的方法可供有关实际工作者参考。

This paper has attacked theoretically the optimal control for a parabolic distributed parameter system described by one dimensional heatconduction eg- nation with nonlinear boundary condition,The DPS can be reduced to the lumped parameter system by finite element method,The boundary condition can also be dealt well.Finally,the numerical solution has been obtained by the conjugate gradient method of mathematical programming technigues,with a common computer(IBM-PC)