SFU Discrete Math Seminar: Mehdi Salimi

What is a game? Mathematically speaking, a game has players, strategies and scores to explain why the players win or lose. Games which are modelled with differential equations are called differential games. Common examples are pursuit-evasion games that are abstract models for pursuers who try to catch evaders who are running away.

In this research, we consider a pursuit-evasion differential game in plane with geometric or integral constraints on the control functions of players. We use parallel strategy and show that pursuit can be completed. We also consider a pursuit-evasion discrete game of one pursuer and one evader. Position of the evader satisfies phase constraint and controls of the players satisfy geometric constraints. We show that pursuit can be completed in finite time interval and construct a control for the pursuer in explicit form.