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

作者：

Highlights：

• 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.

摘要

•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.

论文关键词：Stochastic systems,Optimal control,Stochastic algebraic Riccati equation,Newton’s method

论文评审过程：Received 13 June 2021, Revised 19 October 2021, Accepted 16 January 2022, Available online 26 January 2022, Version of Record 26 January 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.126958