Title :
Convexity in zero-sum differential games
Author_Institution :
Dept. of Electr. & Comput. Eng., California Univ., Berkeley, CA, USA
Abstract :
A new approach to two-player zero-sum differential games with convex-concave cost function is presented. It employs the tools of convex and variational analysis. A necessary and sufficient condition on controls to be an open-loop saddle point of the game is given. Explicit formulas for saddle controls are derived in terms of the subdifferential of the function conjugate to the cost. Existence of saddle controls is concluded under very general assumptions, not requiring the compactness of control sets. A Hamiltonian inclusion, new to the field of differential games, is shown to describe equilibrium trajectories of the game.
Keywords :
differential equations; differential games; variational techniques; Hamiltonian inclusion; control sets; convex-concave cost function; convexity; equilibrium trajectories; open loop saddle point; saddle controls; subdifferential function; two players game; variational analysis; zero-sum differential games; Control engineering; Control engineering computing; Cost function; Differential equations; Integral equations; Open loop systems; Sufficient conditions;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1184986