Near-nash equilibrium strategies for LQ differential games with inaccurate state information

Abstract

ε-Nash equilibrium or "near equilibrium" for alinear quadratic cost game is considered. Due to inaccurate stateinformation, the standard solution for feedback Nash equilibriumcannot be applied. Instead, an estimation of the players' statesis substituted into the optimal control strategies equationobtained for perfect state information. The magnitude of theε in the ε-Nash equilibrium will dependon the quality of the estimation process. To illustrate thisapproach, a Luenberger-type observer is used in the numericalexample to generate the players' state estimates in a two-playernon-zero-sum LQ differential game.