数学分析方法在现代控制理论中的应用

Application of Mathematical Analysis Method in Modern Control Theory

数学分析是高校数学专业学生的一门基础专业课,其蕴涵的丰富内容和精深的思想方法为后续各学科理论学习提供了坚实的基础.在数学分析教材中,言语精炼、概念抽象、推理严密的理论证明和繁杂的计算无处不在,在证明和计算过程中使用到的思想、方法和知识为其他自然科学和工程科学提供了研究方法和手段,也在理论和应用之间架起了桥梁.数学分析的学习既有助于加深对数学理论和内容本质的规律性认识,又对将数学理论应用于实际工业生产生活中起到了促进作用.此外,现代控制理论是利用现代数学方法和计算机来分析、综合复杂控制系统的新理论,其发展离不开数学理论的推动,多种数学工具结合来解决控制与系统科学中的一些问题已成为一种规律.本文将着重探讨数学分析方法在现代控制理论中的相关应用.

Mathematical analysis is a basic professional course for students majoring in Mathematics in Colleges and universities. Its rich contents and profound thinking methods provide a solid foundation for the follow-up theoretical study of various disciplines. In the teaching materials of mathematical analysis, theoretical proof and complicated calculation with refined language, abstract concept and strict reasoning are everywhere. The ideas, methods and knowledge used in the process of proof and calculation provide research methods and means for other natural and engineering sciences, and also build a bridge between theory and application. The study of mathematical analysis not only helps to deepen the understanding of the regularity of mathematical theory and content essence, but also promotes the application of mathematical theory in actual industrial production and life. In addition, modern control theory is a new theory that uses modern mathematical methods and computers to analyze and synthesize complex control systems. Its development is inseparable from the promotion of mathematical theory.It has become a rule to solve some problems in control and system science by combining various mathematical tools. This paper will focus on the application of mathematical analysis method in modern control theory.