Optimal Control Problem For Exact Synchronization Of Ordinary Differential Equations

In this thesis,we consider a kind of optimal problem related to the exact synchronization for a controlled linear ordinary differential system.We give the necessary and sufficient conditions for exact synchronization of this system and prove the existence and uniqueness of the optimal control.By utilizing variational method,Hahn-Banach Theorem and some calculations,we establish a necessary and sufficient conditions for the optimal control.Moreover,we give the numerical simulation of the optimal control.The innovative points of this thesis is that we obtain the necessary and sufficient conditions as well as the numerical simulation for the optimal control.This thesis can be divided into five chapters.In Chapter 1,we introduce the background and definition of exact synchronization,formulate the problem considered in this thesis and give some hypothesis.In Chapter 2,we give some preliminaries.In Chapter 3,we prove the main results of this thesis.In Chapter 4,we design an algorithm to illustrate the optimal control numerically,and present some examples to test the convergence of the algorithm.Finally,we summarize this thesis and present some further comments.