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

On Novel Fixed-Point-Type Iterations with Structure-Preserving Doubling Algorithms for Stochastic Continuous-time Algebraic Riccati equations