平均法在几类非线性微分系统中的应用

发布时间：2018-07-04 16:00

本文选题：不确定系统 + 集值微分方程　；参考：《河北大学》2017年硕士论文

【摘要】：平均法理论被广泛使用在工程应用中,在研究力学、控制等许多领域的众多问题上起着重要的作用.但是平均法理论的研究仍然处于发展阶段,其后续还需要大量的研究工作.本文主要利用平均法,研究了几类非线性微分系统初值问题及边值问题解的性质.主要内容共分为四大部分.第一部分阐述了所研究问题的历史背景与发展现状,总结了当前学者在这些方面已经取得的成果,并简要陈述了本文的研究内容.第二部分利用平均法研究了不确定系统稳定性问题,得到了该系统的渐近稳定性的判别准则,并给出了实例验证.第三部分研究了集值微分方程边值问题,应用平均法得出了集值微分方程的解与平均方程的解是渐近的,通过一个例子验证了所得结论的适用性.第四部分利用平均法研究了带有小参数的模糊集值控制微分系统中解的性质,证明了模糊集值控制微分系统与平均系统解之间的渐近关系。
[Abstract]:The averaging theory is widely used in engineering applications and plays an important role in studying many problems in mechanics, control and many other fields. However, the study of average method theory is still in the developing stage, and a great deal of research work is needed for its follow-up. In this paper, we study the solutions of initial value problems and boundary value problems for some nonlinear differential systems by means of averaging method. The main content is divided into four parts. The first part describes the historical background and development of the problems, summarizes the current achievements of scholars in these areas, and briefly describes the research content of this paper. In the second part, the stability problem of uncertain systems is studied by means of averaging method, and the criterion of asymptotic stability of the system is obtained, and an example is given to verify it. In the third part, the boundary value problem of set-valued differential equation is studied. The solution of set-valued differential equation and the solution of average equation are obtained by using the averaging method. The applicability of the obtained conclusion is verified by an example. In the fourth part, we use the averaging method to study the properties of solutions in fuzzy set-valued control differential systems with small parameters, and prove the asymptotic relationship between the solutions of fuzzy set-valued control differential systems and average systems.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.8

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