集值微分系統的幾類穩(wěn)定性問題
發(fā)布時間：2018-09-18 12:50
【摘要】：集值微分系統作為常微分系統最為方便的推廣形式之一,在物理學、工程學、控制理論、計算機與信息處理等領域有著重要應用,這使得帶有控制項的集值微分系統也備受關注.雖然目前關于集值微分系統的解的存在性和穩(wěn)定性的結果已有不少,但是關于帶有控制項的集值微分系統的討論多是關于存在性的結果.另外,這些結果多是在含經典Hukuhara導數的情形下研究得到的,其缺陷主要是該情形下得到的解的直徑隨時間的推移而增長,這在含不確定性參數且不確定性是由解的直徑所代替的模型中使用是不方便的.而在含第二型Hukuhara導數的情形下可以得到其解直徑隨時間的推移而遞減的解.因此,在含第二型Hukuhara導數的情形下研究集值微分系統是有意義的,值得深入研究.本文主要利用Lyapunov函數方法并通過構建新的比較原理,討論帶有控制項的集值微分系統及含第二型Hukuhara導數的集值微分系統的穩(wěn)定性問題.全文主要內容分為四大部分:前兩部分在引入上擬單調增的情況下,分別研究一類集值控制微分系統的積分0-穩(wěn)定性、兩度量積分0-穩(wěn)定性和一類集值控制積分微分方程的等度0-穩(wěn)定性、兩度量實用0-穩(wěn)定性;后兩部分將第二型Hukuhara導數的概念引入到集值微分系統,分別研究含第二型Hukuhara導數的集值微分方程的等度穩(wěn)定性和時標上含第二型Hukuhara導數的模糊動力方程的實用穩(wěn)定性及兩度量實用穩(wěn)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.
【學位授予單位】：河北大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175
本文編號：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.
【學位授予單位】：河北大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175
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