Nash and Minimax Bi-Cumulant Games

Abstract

Cumulants have been gaining interest in control lately. This paper applies cumulants to the area of game theory and gives sufficient conditions for nonzero and zero sum games to a class of nonlinear systems. With a linear system and quadratic costs, Nash and minimax equilibrium solutions are found. The games consider the finite time horizon, state feedback problem. Special cases of these methods reduce to the H 2/H∞ and H∞ control problems, so that a generalization is achieved.