Infinite horizon robust linear Minkowski regulator

This article considers the infinite horizon robust linear Minkowski regulator through the analysis of the Bellman equation arising from the corresponding infinite horizon minimax optimal control of parametrically uncertain linear discrete time systems with stage cost functions specified in terms of Minkowski functions of convex compact sets that contain the origin in their interior.The existence and uniqueness of the fixed point of the associated Bellman equation, in terms of the minimax value function, over the space of Minkowski functions of compact convex sets that contain the origin in their interior is established under natural conditions.The characterizations of the fixed point minimax value function and its minimax optimizer map are also derived.