Application Of Impulsive Control To Therapy Of Tumor

In recent years, science and technology change rapidly and information disciplines such as control, computer and system engineering develop dramatically. Impulsive control as an important part of system control theory and system engineering attracts more and more interests of scientists who study control and system engineering. Many impulsive phenomena are in natural science and science and social science such as physics, chemistry, biology, economic, sociology, more attention focus on impulsive system and impulsive differential equation and lots of excellent books and papers come out. Nowadays, impulsive control applies to a lot of realma. In this thesis impulsive control is apply to therapy of tumor.At first, the stability is studied for a class of systems with impulse effects. We introduce of impulsive system in brief, by employing Lyapunov function and Riccati inequality, we analyze the sufficient conditions of common impulsive systems,linear impulsive systems and nonlinear impulsive systems, and introduce the definitions and theories of existing stability.Impulsive control is apply to therapy of single tumor. Supposed the body of tumor sufferers have only single tumor cells, we can establish the tumor impulsive control system by using the single tumor model, and develop the sufficient conditions of this system's stability. A simulation example is presented to demonstrate the effectiveness of the proposed method by Matlab.Because of the complexity of the tumor, tumor system not only contains the tumor cells, and also contains immune cells. The tumor system of immunity cell is studied. By employing existing stability, we discuss this tumor system and get the sufficient conditions of tumor system's stability, numerical simulation is given.A general model for ontogenetic growth is studied. From the stability of linear impulsive systems, we can get the stability of a general mode for ontogenetic growth.Finally, a summary has been done for all research work in the thesis. The research work is further study is presented.