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

Abstract

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.