A qualitative account is given of a differential pursuit/evasion game. A criterion for the existence of an intercept solution is obtained using future cones that contain all attainable trajectories of target or interceptor originating from an initial position. A sufficient and necessary conditon that an opportunity to intercept always exists is that, after some initial time, the future cone of ...

We investigate a pursuit-evasion differential game of countably many pursuers and one evader. Integral constraints are imposed on control functions of the players. Duration of the game is fixed and the payoff of the game is infimum of the distances between the evader and pursuers when the game is completed. Purpose of the pursuers is to minimize the payoff and that of the evader is to maximize ...

Aiming at intercepting a hypersonic weapon in a hypersonic pursuit-evasion game, this paper presents a fractional calculus guidance algorithm based on a nonlinear proportional and differential guidance law. First, under the premise of without increasing the complexity degree of the guidance system against a hypersonic manoeuvering target, the principle that the differential signal of the line-o...

This paper considers a pursuit-evasion game for non-holonomic systems where a number of pursuers attempt to capture a single evader in a bounded connected domain. The problem is challenging because all vehicles have the same manoeuvring capability and are subject to turn radius constraints making them non-holonomic systems. The paper initially presents simple and alternate proofs for results ex...

Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of incomplete information and that this value is uniform, i.e. there are ǫ-optimal strategies for both players that are ǫ-optimal in any long enough prefix of the game. ...

A well-known differential game in the theory of differential games is the “homicidal chauffeur” problem which was introduced by Isaacs [7]. It is a pursuit-evasion game. In the paper, a variant of this problem proposed by Bernhard [3] is considered. The computation of level sets of the value function in this variant becomes difficult since holes in the “victory domains” of the pursuer can appea...

We study zero-sum dynamic games with deterministic transitions and alternating moves of the players. Player 1 aims at reaching a terminal set and minimising a running and final cost. We propose and analyse an algorithm that computes the value function of these games extending Dijkstra’s algorithm for shortest paths on graphs. We also show the connection of these games with numerical schemes for...

A classical and a modified (acoustic) variants of the differential game “homicidal chauffeur” are considered. An interesting peculiarity of the letter variant consists, in particular, in the presence of holes located strictly inside the victory domain of the pursuit-evasion game. In the paper, an explanation to this phenomenon is given. The explanation is based on an analysis of families of sem...

Tag is a children’s game based on symmetrical pursuit and evasion. In the experiments described here, control programs for mobile agents (simulated vehicles) are evolved based on their skill at the game of tag. A player’s fitness is determined by how well it performs when placed in competition with several opponents chosen randomly from the coevolving population of players. In the beginning, th...