求解连续时微分 Riccati 方程的后向微分公式法和随机森林法

IF 2.7 4区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Asian Journal of Control Pub Date : 2024-09-19 DOI:10.1002/asjc.3494

Juan Zhang, Wenwen Zou, Chenglin Sui

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引用次数: 0

摘要

本文探讨了如何利用机器学习技术求解连续时间微分里卡提方程的数值解。具体来说，我们的重点是生成能够将高阶矩阵转化为低阶矩阵的还原矩阵。此外，我们还解决了连续时间微分 Riccati 方程中的微分项问题，并结合了矩阵的反向微分公式，以提高稳定性和准确性。最后，通过神经网络和机器学习方法训练样本，我们可以预测高阶矩阵方程的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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来源期刊

Asian Journal of Control 工程技术-自动化与控制系统

CiteScore

4.80

自引率

25.00%

发文量

253

审稿时长

7.2 months

期刊介绍： The Asian Journal of Control, an Asian Control Association (ACA) and Chinese Automatic Control Society (CACS) affiliated journal, is the first international journal originating from the Asia Pacific region. The Asian Journal of Control publishes papers on original theoretical and practical research and developments in the areas of control, involving all facets of control theory and its application. Published six times a year, the Journal aims to be a key platform for control communities throughout the world. The Journal provides a forum where control researchers and practitioners can exchange knowledge and experiences on the latest advances in the control areas, and plays an educational role for students and experienced researchers in other disciplines interested in this continually growing field. The scope of the journal is extensive. Topics include: The theory and design of control systems and components, encompassing: Robust and distributed control using geometric, optimal, stochastic and nonlinear methods Game theory and state estimation Adaptive control, including neural networks, learning, parameter estimation and system fault detection Artificial intelligence, fuzzy and expert systems Hierarchical and man-machine systems All parts of systems engineering which consider the reliability of components and systems Emerging application areas, such as: Robotics Mechatronics Computers for computer-aided design, manufacturing, and control of various industrial processes Space vehicles and aircraft, ships, and traffic Biomedical systems National economies Power systems Agriculture Natural resources.