Controllability For A Type Of Integrodifferential Inclusion In Fréchet Space

Differential inclusion, which is named as multi-valued functional differential equa-tion as well, is one of the most important branchs of non-linear analysis theory. Alongwith the continuous improvement of set-valued theory and differential inclusion theory,the research about controllability and control optimization becomes more popular. Onone hand, controllability issues can be solved by converting them to equivalent differ-ential inclusion; on the other hand, control system with uncertainty can be approacheddirectly, i.e. control system with constraint of differential inclusion. Till now, a lot ofcontrollability of mathematical systems have been proposed and proved, however, mostof the proposed systems are based on Banach space, there are few discussion about thedifferential inclusion on Fre′chet space. This paper mainly focus on the research of con-trollability of differential inclusion on Fre′chet space, and the sufficient condition has beenproposed targeting a type of the controllability of differential inclusion on Fre′chet space.This paper includes three parts, the content is as follows:In first chapter, the overview of differential inclusion and set-valued analysis is in-troduced, the achievement of the research of differential inclusion is detailed as well.In second chapter, the fundamental theory related this paper is introduced, as wellas the introduction of notations, definitions and theorems to be used later.In third chapter, the sufficient condition is proposed targeting a type of the con-trollability of Integrodifferential inclusion on Fre′chet space. A mathematical model isproposed, then it is converted to an equivalent fixed-point issue, finally, the controllabili-ty of system is proved through verifying the conditions of fixed-point theory.In the last part, the conclusion of this paper is summarized, the references of thispaper and the published paper are listed as well.