%0 Journal Article %T 概率论与随机过程融入现代控制理论分析的研究
The Research on Integrating Probability Theory and Stochastic Processes into Modern Control Theory Analysis %A 陈孟申 %A 梁琨 %J Pure Mathematics %P 1-8 %@ 2160-7605 %D 2025 %I Hans Publishing %R 10.12677/pm.2025.156183 %X 随着人工智能技术的快速发展，机器学习、强化学习与深度学习等前沿领域均依赖概率论与随机过程的数学基础，这一学科发展趋势为现代控制理论的研究提供了重要启示：本文基于概率论与随机过程知识框架，融合现代数据分析技术，从多角度对系统动力学行为及矩阵统计特性进行了深入且更为精准的研究与分析。通过这一方法，提升了对复杂系统演化规律和随机结构特性理解的准确性和系统性。此外基于统计学理论，结合神经网络算法的强大拟合与泛化能力，对随机非线性动态系统进行了精确的辨识与建模。通过融合传统统计方法与现代智能计算技术，进一步提升了对复杂动态行为的捕捉能力与建模精度。所提出的方法不仅有助于系统深入理解现代控制理论的基本框架与核心思想，同时也显著提升了应用控制理论分析复杂问题和提出解决方案的能力。
With the rapid development of artificial intelligence technology, many frontier fields such as machine learning, reinforcement learning, and deep learning all rely on the mathematical basis of probability theory and stochastic processes. This disciplinary development trend provides important inspirations for the research of modern control theory: Based on the knowledge framework of probability theory and stochastic processes, and integrating modern data analysis techniques, this paper conducts in-depth and more precise research and analysis on the dynamic behavior of the system and the statistical characteristics of matrices from multiple perspectives. Through this method, the accuracy and systematicness of understanding the evolution laws and random structural characteristics of complex systems have been enhanced. Furthermore, based on statistical theory and combined with the powerful fitting and generalization capabilities of neural network algorithms, precise identification and modeling of stochastic nonlinear dynamic systems have been carried out. By integrating traditional statistical methods with modern intelligent computing technologies, the ability to capture complex dynamic behaviors and the modeling accuracy have been further enhanced. The proposed method not only helps the system to deeply understand the basic framework and core ideas of modern control theory, but also significantly improves the ability to apply control theory to analyze complex problems and propose solutions. %K 概率论， %K 随机过程， %K 现代控制
Probability Theory %K Random Process %K Modern Control %U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=116860