Two iterative algorithms for stochastic algebraic Riccati matrix equations

Ai-Guo Wu, Hui-Jie Sun and Ying Zhang

Applied Mathematics and Computation, 2018, vol. 339, issue C, 410-421

Abstract: In this paper, two iterative algorithms are proposed to solve stochastic algebraic Riccati matrix equations arising in the linear quadratic optimal control problem of linear stochastic systems with state-dependent noise. In the first algorithm, a standard Riccati matrix equation needs to be solved at each iteration step, and in the second algorithm a standard Lyapunov matrix equation needs to be solved at each iteration step. In the proposed algorithms, a weighted average of the estimates in the last and the previous steps is used to update the estimate of the unknown variable at each iteration step. Some properties of the sequences generated by these algorithms under appropriate initial conditions are presented, and the convergence properties of the proposed algorithms are analyzed. Finally, two numerical examples are employed to show the effectiveness of the proposed algorithms.

Keywords: Stochastic Riccati matrix equations; Iterative algorithms; linear stochastic systems (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:410-421

DOI: 10.1016/j.amc.2018.07.032

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