An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

• Published in: Journal of scientific computing Vol. 85; no. 2; p. 51
• Main Authors: Archibald, Richard, Bao, Feng, Yong, Jiongmin, Zhou, Tao
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2020; Springer Nature B.V; Springer
• Subjects: Algorithms; Approximation; Computational Mathematics and Numerical Analysis; Control systems; Data analysis; data driven; Differential equations; Dynamic programming; Dynamical systems; Efficiency; Feedback control; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematics; MATHEMATICS AND COMPUTING; Mathematics and Statistics; maximum principle; Methods; nonlinear filtering; Numerical analysis; Optimal control; Optimization; Partial differential equations; Stochastic models; Stochastic optimal control; stochastic optimization; Theoretical; 93E11; 60G35; Data driven; Stochastic optimal control; Nonlinear filtering; Maximum principle; 65K10; Stochastic optimization
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-020-01358-y

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. We call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.