Pursuit and evasion games have garnered much research attention since the class of problems was first posed over a half century ago. With wide applicability to both civilian and military problems, the study of pursuit and evasion games showed much early promise. Early work generally focused on analytical solutions to games involving a single pursuer and a single evader. These solutions generally assumed simple system dynamics to facilitate convergence to a solution. More recently, numerical techniques have been utilized to solve more difficult problems. While many sophisticated numerical tools exist for standard optimization and optimal control problems, developing a more complete set of numerical tools for pursuit and evasion games is still a developing topic of research. This thesis extends the current body of numeric solution tools in two ways. First, an existing approach that modifies sophisticated optimization tools to solve two player pursuer and evasion games is extended to incorporate a class of state inequality constraints. Several classical problems are solved to illustrate the e±cacy of the new approach. Second, a new cooperation metric is introduced into the system objective function for multi-player pursuit and evasion games. This new cooperation metric encourages multiple pursuers to surround and then proceed to capture an evader. Several examples are provided to demonstrate this new cooperation metric.

We study single-pursuer, line-of-sight Pursuit and Evasion games in polytopes in $\mathbb{R}^n$. We develop winning Pursuer strategies for simple classes of polytopes (monotone prisms) in Rn, using proven algorithms for polygons as inspiration and as subroutines. More generally, we show that any Pursuer-win polytope can be extended to a new Pursuer-win polytope in more dimensions. We also show that some more general classes of polytopes (monotone products) do not admit a deterministic winning Pursuer strategy. Though we provide bounds on which polytopes are Pursuer-win, these bounds are not tight. Closing the gap between those polytopes known to be Pursuer-win and those known not to be remains an problem for future researchers.