微分代数控制问题的数值计算方法

Some Numerical Methods for the Control Problem of Differential Algebraic System

描述许多轨道控制问题的方程通常构成非线性半显式的微分代数系统。本文提出一些数值方法来计算这些控制问题的控制规律。对于一个模型问题,本文进行了稳定性分析,并且给出了稳定性区域。文中估计了这些方法的全局误差,它们给出控制误差与计算步长的关系。

The equations which describe many trajectory control problems naturally form nonlinear semiexplicit differential algebraic systems. This paper presents some numerical methods to calculate the control laws for these control problems. The asymptotic expansions of the global errors of these methods are constructed which give the relation between the stepsize and the controlled errors. This paper also deals with the stability analysis for a model problem and gives the stability regions.