Observer-based optimal control for delta-domain LQ games with disturbances in finite/infinite time horizon

This paper addresses the observer-based composite control problem for a class of delta-domain LQ games with disturbances in both finite- and infinite-time horizon. In the presence of the disturbances, the Nash Equilibrium (NE) is revisited, and the scalar ϵ is proposed to describe the deviation of NE in such noise environment. A composite control strategy integrating the observer-based control and the feedback Nash strategies are developed such that NE can be achieved while compensating the matched disturbances. Sufficient conditions are given to ensure the existence of both the desired observer and the feedback Nash strategies in the delta-domain, and then the explicit expressions of such observer gain and Nash strategies are provided. An upper bound for the scalar ϵ is derived explicitly, and the corresponding convex optimization method is given to compute such epsilon level.