Title: Computational methods for dynamic optimization and pursuit-evasion games
Authors: Tuomas Raivio
Systems Analysis Laboratory
Helsinki University of Technology
P.O. Box 1100, 02015 HUT, FINLAND

Date: March 2000
Status: Systems Analysis Laboratory Research Reports A80 March 2000
Abstract: The thesis deals with the numerical solution of deterministic optimal control problems and pursuit-evasion games that emerge in the field of aircraft trajectory optimization. In the optimization framework, the thesis presents a continuation method for minimum time problems and compares the use of discretization and nonlinear programming with indirect approaches through numerical examples. Motivated by the benefits of the discretization and nonlinear programming, the thesis extends the underlying ideas into pursuit-evasion games. The approaches proposed here allow the computation of open-loop representations of feedback saddle point strategies for a class of pursuit-evasion games without explicitly solving the necessary conditions. Numerical results are computed for complex pursuit-evasion problems describing a missile chasing an aircraft and a visual identification of an unknown aircraft. Finally, a way to use the proposed approaches in the numerical solution of a game of kind is presented and applied to the estimation of the capture set of an optimally guided missile. Although the application examples are related to aeronautics, the presented methods are of a general nature and can be applied to different areas as well.
Keywords: optimal control, pursuit-evasion games, multipoint boundary value problems, discretization and nonlinear programming, aerospace applications.