| Pursuit-evasion differential game problem is an important component of differential game theory, who plays a key position in the whole game theory. This problem contains two kind of situations. One is how to set up strategy for the pursuer and guide one or a set of pursuers to capture a moving target. The other is how to establish strategy for the evader to escape from all pursuers.In the present thesis, we firstly consider a simple motion pursuit-evasion differen-tial game of many pursuers and one evader on control functions of players with integral constraints in R2, we solve the game by presenting explicit and admissible strategy for the pursuer and evade. And then we consider a pursuit-evasion differential game of many pursuers and one evader on control functions of players with integral constraints in the space of l2. Our main purpose is to put forward new pursuer’s and evader’s strategies to obtain the sufficient conditions for the pursuits completeness and the evasion possibility, respectively.The full text is divided into four chapters, the main content is roughly arranged as follows:Part one is an introduction part, the development of the pursuit-evasion differential game and research status at home and abroad are simply introduced, then the main prob-lem to be resolved are put forward.Part two, we mainly introduce a simple motion pursuit-evasion differential game of many pursuers and one evader in R2, we solve the game by presenting explicit the pursuer’s and evade’s strategies to guarantee the pursuits completeness and the evasion possibility, respectively, which laid the foundation for the following of the research work in the space of l2.Part three introduced a simple motion pursuit-evasion differential game of many pur-suers and one evader described by first-order differential equations in l2, which is expand-ed to a pursuit-evasion differential game of many pursuers and one evader described by second-order differential equations. Under their control functions of players with integral constraints conditions, we put forward new pursuer’s and evader’s strategies to obtain the sufficient conditions for the pursuits completeness and the evasion possibility, respective- ly. This chapter can be thought as the infinite-dimensional expansion of the content in part two.Part four makes a brief summary for the main content of this article, and then presents some prospects for further studies. |
