Multi-player Qualitative Differential Games With Single Superior Evader

The theory and applications of differential games have been increasingly concerned by researchers in recent years,and become a research frontier of systems and control science.Inspired by the hunting and foraging behaviors of group predators in nature,this thesis addresses a class of multi-player qualitative differential games with single superior evader,so as to offer decision support for the cooperative besiegement,tracking and interception of multi-agent systems to some faster targets.The theory and solution techniques of two-player pursuit-evasion game of kind,the environment,rules and artificial barriers of the game of kind,the barrier and optimal strategies of three-player fishing game,and the multi-player qualitative pursuit-evasion games with superior evader,are studied systematically and deeply,which mainly include the following aspects and results:Firstly,the fundamental theory of two-player pursuit-evasion game of kind is elaborated,and the method and procedure of state reversal to construct natural barrier are also provided,which lay the theoretical foundations for the analytical solution of barrier.Take the classic Homicidal Chauffeur game as examples,the procedure of its complete solution is presented in detail,including the construction of natural barrier,the analysis and delineation of singular surfaces(involving universal surfaces,equivocal surfaces,dispersal surfaces,switch envelope and focal surfaces),and a necessary condition of existing escape zone.Secondly,the barrier is defined as four types: natural barrier,transferred barrier,envelope barrier and semi-barrier,where the latter three are collectively called artificial barrier.The distinctions among them and the relations of artificial barriers with the environment and rules of differential game are expounded clearly.Take the lifeline game,the deadline game and the game of three cars as examples,the influences of different environments and rules to the outcome of the game are discussed,meanwhile,the solution procedures of corresponding artificial barriers are also derived.Furthermore,the construction methods and analytical procedures of artificial barriers for general pursuit-evasion game of kind are concluded.Thirdly,a novel multi-player pursuit-evasion game,fishing game,is proposed and its complete solution is solved,which provide theoretical directions for practical applications.In the case of discrete time,the non-escape angle of the evader and the optimal strategies of all the players are solved by using a geometric method for straight line motion and sinuous movement of the evader,respectively.Along with these,three equivalent capture conditions are attained.In the case of continuous time,the method of explicit policy is proposed.The fishing game is divided into two sub-games which are related to the relative distances and the included angle.For each sub-game,the possibility of capture or escape is demonstrated and the analytical forms of winning regions for the players are obtained.Then a precise description of the artificial barrier is ascertained by synthesizing these winning regions.Furthermore,the games of kind and degree are fused in which each player seeks to achieve success in the minimum time when the initial state lies in their winning regions.Through partitioning the state space into four zones,the trajectories of the players associated with the optimal strategies are delineated and the upper bounds of their winning times are also derived.Finally,for the multi-player pursuit-evasion games of kind with more pursuers and one superior evader,the capture condition and optimal strategies of the players are solved.Based on the complete solution of the fishing game,the surrounding condition,combined barrier and optimal strategies are determined for multi-player fishing games.While for multi-player pursuit-evasion games with a more agile evader,the concepts of natural cooperation and artificial cooperation are defined,and a set of cooperative pursuit scheme,besiege-shrink-capture,is presented,which is inspired by the hunting and foraging behaviors of group predators.Accordingly,the besieged status and capturing status of the game are defined originally,and the besieging condition,transition condition and suitable pursuit strategies are provided to ensure that the game can reach these statuses.Meanwhile,the minimum number of the pursuers is also determined,which is one of the great concerns of multi-player pursuit-evasion games of kind,and reveal the laws of nature in wolves hunting.