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Incremental Newton’s iterative algorithm for optimal control of Itô stochastic systems

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  • Tian, Jiayue
  • Zhao, Xueyan
  • Deng, Feiqi

Abstract

In this paper, a novel incremental Newton’s iterative algorithm for investigating the optimal control problem of Itô stochastic systems is presented. Newton’s method is employed under the Fréchet derivative framework to iteratively solve a stochastic algebraic Riccati equation. Under moderate conditions, the convergence and even quadratic convergence of the proposed incremental Newton’s iterative algorithm are discussed, respectively. In addition, the Newton’s method is extended to the one with linear search. In the end, numerical results are given to demonstrate the effectiveness and superiority of the proposed algorithms.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000443
    DOI: 10.1016/j.amc.2022.126958
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    References listed on IDEAS

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    1. 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.
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