一种最优控制数值计算方法

本文为解决非线性微分方程自治系统的周期轨道的数值计算,提出了一种最优控制的数值计算方法。其方法的实质是利用连续的打靶法,在非线性最小二乘公式的监护下,附加惩罚函数进行控制来实现的。并利用该法计算了典型的化学反应模型。

AN OPTIMAL CONTROL METHODS OF THE NUMERICAL COMPUTATION

This paper is in order to solve the numerical computation of the periodic orbits of nonlinear autonomous differential equations. We design an optimal control method of the numerical computation. The solution method is basically a continue shooting method,under the guardianship of nonlinear least squaves that takes advantage of an optimal Central formulation, in which attached to the contral techniques of the penalty function.In this method,we use the Crank-Nicolson discretization schemes and Conjugate Gradient methods.This method has been applied to the solution of nonlinear differential equations modelling chemical reactions,the corresponding numerical results are presented here.