一类随机Riccati矩阵代数方程的线性迭代解法

An iterative method for sloving stochastic riccati algebralc equations

针对无穷区间随机线性二次最优控制问题对应的随机代数Riccati方程提出了线性迭代解法.算法中得到Liapunov线性代数方程解的序列,该序列收敛于随机Riccati代数方程的解.已有的理论算法针对该SARE得到的是非线性的常规Riccati代数方程解的序列,而通常每一次运用经典的Kleinman迭代方法求解常规Riccati代数方程,都是反复迭代求解Lia-punov线性代数方程的过程.这就使得本文算法相较于已有理论算法在针对特定类型SARE时,具有较好的性能.

This paper develops an iterative method for solving stochastic Riccati algebraic equations（SARE） for indefinite stochastic linear quadratic problem. We obtain a sequence of solutions of Liapunov algebraic equations which converges to the solution of a SARE. The known algorithm gives a sequence of solutions of classical riccati algebraic equations which require another algorithm （Kleimn-Newton iterative algorithm） to obtain.