里卡提微分方程解的奇异性分析

SINGULAR ANALYSIS TO THE SOLUTION OF THE RICCATIDIFFERENTIAL EQUATION

本文处理有限长时间的里卡提微分方程。指出可以用区段混合能合并消元之法来得出它的解,在t_f处边界条件可以放在最后一步进行处理。这样就可以避免从奇点开始数值积分的困难。还可以据此分析t_f处的奇性。

The Riccati differential equation of finite duration is considered in thipaper. The solution is closely related to the variational principle and the correspondent interval mixed energy. Instead of the numerical integration method, the assembling and condensation method to the interval mixed energy can be used to the solution. The boundary condition at t can be processed at the last step, such that the difficulty of beginning integration from the singular point can be avoided. And the singular property at tj can be analysed by the present method. It is pointed out here, that the requirement of the state variables at tf be controlled zero causes the singular property of the solution of the Riccati differential equation, but the control variables are usually still finite. And now the number q of the state variables to be controlled zero versus the number m of the control variables influences the singular property of the solution.