一类Riccati方程组对称自反解的两种迭代算法

针对源于Markov跳变线性二次控制问题中的一类对偶代数Riccati方程组,分别采用修正共轭梯度算法和正交投影算法作为非精确Newton算法的内迭代方法,建立求其对称自反解的非精确Newton-MCG算法和非精确Newton-OGP算法.两种迭代算法仅要求Riccati方程组存在对称自反解,对系数矩阵等没有附加限定.数值算例表明,两种迭代算法是有效的.

TWO ITERATIVE ALGORITHMS FOR THE SYMMETRIC REFLEXIVE SOLUTION OF A CLASS OF RICCATI EQUATIONS

Concerning coupled algebraic Riccati equations arising from Markov jump linear-quadratic control problems, two iterative methods called the inexact Newton-MCG algorithm and the inexact Newton-OGP algorithm are proposed for the symmetric reflexive solution of those equations by making use of modified conjugate gradient algorithm and orthogonal projection algorithm as the inner iterative method, respectively. These two iterative algorithms have no other limits to the coefficient matrix except for the existence of symmetric reflexive solution. Numerical experiments confirm these two algorithms are effective.