集值微分系统的几类稳定性问题
发布时间：2018-09-18 12:50
【摘要】：集值微分系统作为常微分系统最为方便的推广形式之一,在物理学、工程学、控制理论、计算机与信息处理等领域有着重要应用,这使得带有控制项的集值微分系统也备受关注.虽然目前关于集值微分系统的解的存在性和稳定性的结果已有不少,但是关于带有控制项的集值微分系统的讨论多是关于存在性的结果.另外,这些结果多是在含经典Hukuhara导数的情形下研究得到的,其缺陷主要是该情形下得到的解的直径随时间的推移而增长,这在含不确定性参数且不确定性是由解的直径所代替的模型中使用是不方便的.而在含第二型Hukuhara导数的情形下可以得到其解直径随时间的推移而递减的解.因此,在含第二型Hukuhara导数的情形下研究集值微分系统是有意义的,值得深入研究.本文主要利用Lyapunov函数方法并通过构建新的比较原理,讨论带有控制项的集值微分系统及含第二型Hukuhara导数的集值微分系统的稳定性问题.全文主要内容分为四大部分:前两部分在引入上拟单调增的情况下,分别研究一类集值控制微分系统的积分0-稳定性、两度量积分0-稳定性和一类集值控制积分微分方程的等度0-稳定性、两度量实用0-稳定性;后两部分将第二型Hukuhara导数的概念引入到集值微分系统,分别研究含第二型Hukuhara导数的集值微分方程的等度稳定性和时标上含第二型Hukuhara导数的模糊动力方程的实用稳定性及两度量实用稳定性.
[Abstract]:As one of the most convenient extension forms of ordinary differential systems, set-valued differential systems have important applications in the fields of physics, engineering, control theory, computer and information processing, etc. Therefore, set-valued differential systems with controls are also concerned. Although there are many results on the existence and stability of solutions for set-valued differential systems, the discussion of set-valued differential systems with controls is mostly about existence. In addition, most of these results are studied in the case of classical Hukuhara derivatives, and the defects are that the diameter of the solutions obtained in this case increases with the passage of time. This is inconvenient to use in a model with uncertain parameters and where uncertainty is replaced by the diameter of the solution. In the case of Hukuhara derivative of the second type, the solution whose solution diameter decreases with the passage of time can be obtained. Therefore, it is meaningful to study set-valued differential systems with Hukuhara derivatives of the second type, which is worthy of further study. In this paper, the stability of set-valued differential systems with control terms and set-valued differential systems with second type Hukuhara derivatives are discussed by using the Lyapunov function method and by constructing a new comparison principle. The main content of this paper is divided into four parts: in the first two parts, we study the integral 0-stability of a class of set-valued control differential systems under the condition of introducing the upper quasi monotone increase. In the last two parts, the concept of the second type Hukuhara derivative is introduced to the set-valued differential system. The equalization stability of set-valued differential equations with second type Hukuhara derivatives and the practical stability and two-metric practical stability of fuzzy dynamic equations with second type Hukuhara derivatives on time scales are studied respectively.
【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
本文编号：2247976
[Abstract]:As one of the most convenient extension forms of ordinary differential systems, set-valued differential systems have important applications in the fields of physics, engineering, control theory, computer and information processing, etc. Therefore, set-valued differential systems with controls are also concerned. Although there are many results on the existence and stability of solutions for set-valued differential systems, the discussion of set-valued differential systems with controls is mostly about existence. In addition, most of these results are studied in the case of classical Hukuhara derivatives, and the defects are that the diameter of the solutions obtained in this case increases with the passage of time. This is inconvenient to use in a model with uncertain parameters and where uncertainty is replaced by the diameter of the solution. In the case of Hukuhara derivative of the second type, the solution whose solution diameter decreases with the passage of time can be obtained. Therefore, it is meaningful to study set-valued differential systems with Hukuhara derivatives of the second type, which is worthy of further study. In this paper, the stability of set-valued differential systems with control terms and set-valued differential systems with second type Hukuhara derivatives are discussed by using the Lyapunov function method and by constructing a new comparison principle. The main content of this paper is divided into four parts: in the first two parts, we study the integral 0-stability of a class of set-valued control differential systems under the condition of introducing the upper quasi monotone increase. In the last two parts, the concept of the second type Hukuhara derivative is introduced to the set-valued differential system. The equalization stability of set-valued differential equations with second type Hukuhara derivatives and the practical stability and two-metric practical stability of fuzzy dynamic equations with second type Hukuhara derivatives on time scales are studied respectively.
【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
【参考文献】
相关期刊论文 前1条
1 王培光;孙维维;;向量Lyapunov函数与集值微分系统的稳定性[J];黑龙江大学自然科学学报;2012年05期
相关硕士学位论文 前2条
1 许青;几类非线性微分系统的相对稳定性分析[D];河北大学;2015年
2 孙维维;关于集值微分系统的稳定性分析[D];河北大学;2013年
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