The Researches On Control Problems Of Differential Equations

The control problems of phase-field system and Boussinesq systems are studied in this dissertation. We obtain the stabilization of phase-field system via inner feedback control and establish the Pontryagin's maximum principle for the controlled Boussinesq system with state constricted. We establish the Pontryagin's maximum principle for the time optimal control problem governed by the 2-dimensional Boussinesq system as well.This dissertation has five chapters. In the first chapter, we review the beginning of cybernetics, some of famous scholars and works of our country in this field are introduced. The backgrounds of our systems and main results are introduced as well. In the second chapter, we recall some definitions and theorems. In the third chapter, we get the stabilization of phase-field system via inner feedback control and two types of boundary conditions are studied respectively. In the fourth chapter, we obtain the maximum principle for the controlled Boussinesq system, some special cases of cost functional and state constraint are given as examples. In the last chapter, we establish the Pontryagin's maximum principle for the time optimal control problems governed by 2-dimensional Boussinesq system.