Research On The Existence And Controllability Of Solutions Of Measure Evolution Equations

The measure differential equations are also called the measure driven equations,and its concept was first proposed by Das in 1972.Measure differential equations are used in non-smooth mechanics,game theory and other applied mathematics.The concept of controllability was first proposed by Kalman in 1963.Its concept has great significance in the analysis and design of control systems.There have been great developments in the approximate controllability of the fractional control system.In order to improve the research on the theory of measure evolution equations,this article discusses the existence and approximate controllability of the solutions of two types of measure differential equations.The specific distribution of the article is as follows:Chapter 1,briefly introduces the research background,current situation and basic knowledge of measure differential equations.Chapter 2,firstly,under the application of the Schauder fixed point theorem,the existence of a mild solution to the neutral measure evolution equations is obtained;secondly,the approximate controllability of system is obtained by using the Krasnoselskii fixed point theorem;finally,an example proves the validity of the results obtained.Chapter 3,by constructing a control function involving the Gramian controllability operator and applying the Schauder fixed point theorem,a sufficient condition and approximate controllability for the existence of a mild solution to a class of non-autonomous measure evolution equations are given;finally,an example is used to verify the validity of the results obtained.Chapter 4,summarizes the article and makes a prospect for future work.