Numerical integration of the differential Riccati equation and some related issues
Numerical integration of the differential Riccati equation and some related issues
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DOI：
10.1137/0729049
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发表时间：
1992-06
影响因子：
2.9
通讯作者：
L. Dieci
中科院分区：
文献类型：
--
作者：
L. Dieci
抽象。本文研究了微分Riccati方程的直接数值积分问题及其相关问题。DRE是常微分方程的线性系统的变量的特定变化的表达式。考虑了DRE近似解对系统原始变量的误差，它与系统本身的几何性质有关。根据原系统的局部误差和几何性质，给出了计算解的全局误差的精确界。考虑了非对称型和对称型的非刚性和刚性DRE。一个有用的矩阵解释给出了许多积分计划（如向后微分公式，BDF），当应用到DRE。这允许利用问题的矩阵结构。特别是，对于严格的销毁去除率，由此产生的战略相对于标准的改革可节省三个数量级.。
Abstract. In this paper the problem of direct numerical integration of differential Riccati equations (DREs) and some related issues are considered. The DRE is an expression of a particular change of variables for a linear system of ordinary differential equations. The error that an approximate solution of the DRE induces on the original variables of the system is considered, and it is related to geometrical properties of the system itself. Sharp bounds on the global error for the computed solution are also given in terms of local errors and geometrical properties of the original system. Nonstiff and stiff DREs of unsymmetric and symmetric type are considered. A useful matrix interpretation is given for many integration schemes (such as the backward differentiation formulas, BDF), when applied to the DRE. This allows the matrix structure of the problem to be exploited. In particular, for stiff DREs, the resulting strategy allows for a saving of three orders of magnitude with respect to the standard reform...