||Applying nonlinear programming to pursuit-evasion games
Systems Analysis Laboratory
Helsinki University of Technology
P.O. Box 1100, 02015 HUT, FINLAND
||Accepted for publication in Journal of Optimization Theory and Algorithms under the title "On Applied Nonlinear and Bilevel Programming for Some Pursuit-Evasion Games"
||Motivated by the benefits of discretization in optimal control problems we consider possibilities to discretize pursuit-evasion games. Two approaches are introduced. In the first one, the solution of the necessary conditions of the continuous-time game is decomposed into ordinary optimal control problems that can be solved using discretization and nonlinear programming techniques. In the second approach, the game is discretized and transformed into a bilevel programming problem which is solved using a first order feasible direction method. Although the starting point of the approaches is different, they lead in practice to the same solution algorithm. We demonstrate the usability of the discretization by solving some open-loop representations of feedback solutions for a complex pursuit-evasion game between a realistically modeled aircraft and a missile with terminal time as the payoff. The solutions are compared with solutions obtained by an indirect method.
||Pursuit-evasion games, optimal control, bilevel programming, aerospace applications.