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

Jiayue Tian, Xueyan Zhao and Feiqi Deng

Applied Mathematics and Computation, 2022, vol. 421, issue C

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.

Keywords: Stochastic systems; Optimal control; Stochastic algebraic Riccati equation; Newton’s method (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000443

DOI: 10.1016/j.amc.2022.126958

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