Multi-player pursuit-evasion differential games

The increasing use of autonomous assets in modern military operations has led to renewed interest in (multi-player) Pursuit-Evasion (PE) differential games. However, the current differential game theory in the literature is inadequate for dealing with this newly emerging situation. The purpose of this dissertation is to study general PE differential games with multiple pursuers and multiple evaders in continuous time.; The current differential game theory is not applicable mainly because the terminal states of a multi-player PE game are difficult to specify. To circumvent this difficulty, we solve a deterministic problem by an indirect approach starting with a suboptimal solution based on "structured" controls of the pursuers. If the structure is set-time-consistent, the resulting suboptimal solution can be improved by the optimization based on limited look-ahead. When the performance enhancement is applied iteratively, an optimal solution can be approached in the limit. We provide a hierarchical method that can determine a valid initial point for this iterative process.; The method is also extended to the stochastic game case. For a problem where uncertainties only appear in the players' dynamics and the states are perfectly measured, the iterative method is largely valid. For a more general problem where the players's measurement is not perfect, only a special case is studied and a suboptimal approach based on one-step look-ahead is discussed.; In addition to the numerical justification of the iterative method, the theoretical soundness of the method is addressed for deterministic PE games under the framework of viscosity solution theory for Hamilton-Jacobi equations. Conditions are derived for the existence of solutions of a multi-player game. Some issues on capturability are also discussed for the stochastic game case.; The fundamental idea behind the iterative approach is attractive for complicated problems. When a direct solution is difficult, an alternative approach is usually to search for an approximate solution and the possibility of serial improvements based on it. The improvement can be systematic or random. It is expected that an optimal solution can be approached in the long term.