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

• Published in: Applied mathematics and computation 2022-05, Vol.421, p.126958, Article 126958
• Main Authors: Tian, Jiayue, Zhao, Xueyan, Deng, Feiqi
• Format: Article
• Language: English
• Subjects: Newton’s method; Optimal control; Stochastic algebraic Riccati equation; Stochastic systems
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.126958

•For optimal control, the stochastic information with current iterative results is used to solve the stochastic algebraic Riccati equation, which has stochastic characteristics.•Calculate the increment instead of the value itself to improve the calculation accuracy.•Newton’s method with line search solve the potentially disastrous problem of the first Newton step.•The convergence and even quadratic convergence of the proposed incremental Newton’s iterative algorithm have been discussed. 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.