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Two iterative algorithms for stochastic algebraic Riccati matrix equations

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

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.

Suggested Citation

  • Wu, Ai-Guo & Sun, Hui-Jie & Zhang, Ying, 2018. "Two iterative algorithms for stochastic algebraic Riccati matrix equations," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 410-421.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:410-421
    DOI: 10.1016/j.amc.2018.07.032
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    References listed on IDEAS

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    1. Ying Zhang & Ai-Guo Wu & Hui-Jie Sun, 2018. "An implicit iterative algorithm with a tuning parameter for Itô Lyapunov matrix equations," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(2), pages 425-434, January.
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    Cited by:

    1. Tian, Jiayue & Zhao, Xueyan & Deng, Feiqi, 2022. "Incremental Newton’s iterative algorithm for optimal control of Itô stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 421(C).

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