Disturbance Attenuation Analysis of State Feedback Nash Strategy for Two-Player Linear Quadratic Sequential Games

There is limited formal mathematical analysis of one type of games — dynamic sequential games with large, or even infinitely large, planning horizons, from the point view of system controls. In this paper, we use a zero-sum game theoretical approach to address the disturbance attenuation analysis of state feedback Nash strategies for Dynamic Linear Quadratic Sequential Games (LQSGs) with uncertainties or disturbances. Based on the assumption that the disturbance will do the worst to the normal game players, we provide a simultaneous zero-sum game formulation between nature and each player, and a non-zero sum formulation among the players. For finite-horizon LQSGs, we first provide state feedback Nash strategies with optimal attenuation levels. Then we extend the approach to infinitehorizon LQSGs. We prove that the feedback system is Bounded Input Bounded Output (BIBO) stable with respect to the disturbances.