Distributed parameter differential games: A dynamic programming approach†
ROBERT J. LANDY‡ · International Journal of Control · 1971
This paper extends certain results known for lumped parameter differential games to differential games which involve distributed systems described by partial differentia] equations. In particular the distributed system is described by a linear second-order vector partial differential equation with appropriate boundary conditions. Simultaneous distributed and boundary controls are considered and all performance criteria involved are quadratic. Three types of solutions are sought for the non-zero sum game: The Nash equilibrium, the non-inferior and the minimax. Closed-loop strategies are found using techniques of dynamic programming. Finally, the solution of certain partial differential equations which arise in this method is considered using the normal modes approach.