代数Riccati方程数值解的一种牛顿迭代法

A Newton iteration method for numerical solution of algebraic Riccati equations

代数Riccati方程在优化控制理论中具有十分重要的作用.结合了二次方程的牛顿迭代法与Lya-punov方程的自由参数轮转方向迭代法,提出了一种求代数Riccati方程数值解的一种新方法,并给出了算法的收敛性证明.最后,给出了具体的数值算例.

Algebraic Riccati equations play a very important role in optimal control theory.In this paper,Newton iteration method for quadratic equations and parameter free alternating directions implicit method are combined,and a new method is proposed for numerical solution of algebraic Riccati equations.Then the convergence of this method is proved and the numerical experiment has been done.