Backward differentiation formula method and random forest method to solve continuous-time differential Riccati equations

In this paper, we explore the utilization of machine learning techniques for solving the numerical solutions of continuous-time differential Riccati equations. Specifically, we focus on generating a reduction matrix capable of transforming a high-order matrix into a low-order matrix. Additionally, we address the issue of differential terms in the continuous-time differential Riccati equation and incorporate the backward differentiation formula of the matrix to improve stability and accuracy. Finally, by training samples through neural networks and machine learning methods, we could predict the solutions for high-order matrix equations.