Infinite-horizon minimax control with pointwise cost functional

This paper is devoted to the discussion of a minimax optimal control problem over an infinite-time horizon, where the functional to be minimized is the highest instantaneous cost that may occur under the worst combination of disturbances. The problem is formulated for a general stationary discrete-time dynamic system, and a dynamic programming algorithm is proposed for its solution. The relationship existing between the cost functional associated to a control law and the reachability properties of the resulting controlled system is discussed.