This thesis explores the use of a learning algorithm in the "guarding a territory" game. The game occurs in continuous time, where a learning invader tries to get as close as possible to a territory before being captured by a guard. Previous research has let only the guard learn. We will examine the other possibility of the game, in which only the invader is learning. Furthermore, the guard is superior to the invader. We will also consider using models with non-holonomic constraints. A control system is designed and optimized for the invader to play the game. The thesis shows how the learning system is able to adapt to an unknown environment. We evaluated our system's performance through different simulations. We conducted experiments at the Royal Military College of Canada using real robots in a real-life environment. Our results show that our learning invader behaved rationally in different circumstances.