Differential games on Lie groups

A new concept for nonlinear differential games on Lie groups is presented. This concept is a direct generalization of several topics, including right-invariant control systems on Lie groups, geodesic variational problems and of course linear-quadratic differential games on IRⁿ. Besides introducing several definitions for games with and without boundary value problems, we discuss the well-posedness of the variational problem and show (in a special case) how to derive the optimal control laws of the players.