In this paper we mainly propose efficient and reliable numerical algorithms for solving stochastic continuous-time algebraic Riccati equations (SCARE) typically arising from the differential statedependent Riccati equation technique from the 3D missile/target engagement, the F16 aircraft flight control and the quadrotor optimal control etc. To this end, we develop a fixed point (FP)-type iteration with solving a CARE by the structure-preserving doubling algorithm (SDA) at each iterative step, called FP-CARE SDA. We prove that either the FP-CARE SDA is monotonically nondecreasing or nonincreasing, and is R-linearly convergent, with the zero initial matrix or a special initial matrix satisfying some assumptions. The FP-CARE SDA (FPC) algorithm can be regarded as a robust initial step to produce a good initial matrix, and then the modified Newton (mNT) method can be used by solving the corresponding Lyapunov equation with SDA (FPC-mNT-Lyap SDA). Numerical experiments show that the FPC-mNT-Lyap SDA algorithm outperforms the other existing algorithms.

翻译：本文主要针对由三维导弹/目标拦截、F16飞行器控制及四旋翼最优控制等场景中微分状态相关Riccati方程技术所导出的随机连续时间代数Riccati方程(SCARE)，提出高效可靠的数值算法。为此，我们开发了一种不动点(FP)型迭代方法，在每个迭代步中利用结构保持加倍算法(SDA)求解CARE，称为FP-CARE SDA。我们证明了FP-CARE SDA要么单调非减要么单调非增，且当零初始矩阵或满足特定假设的特殊初始矩阵时，该算法具有R线性收敛性。FP-CARE SDA(FPC)算法可作为稳健的初始化步骤，生成优良的初始矩阵，随后可采用修正牛顿(mNT)方法，通过SDA求解对应的Lyapunov方程(FPC-mNT-Lyap SDA)。数值实验表明，FPC-mNT-Lyap SDA算法优于现有其他算法。