We show how the use of a parallel between the ordinary $(+, \times)$ and the $(\max, +)$ algebras, Maslov measures that exploit this parallel, and more specifically their specialization to probabilities and the corresponding {\em cost measures} of Quadrat, offer a completely parallel treatment of stochastic and minimax control of disturbed nonlinear discrete time systems with partial information. This paper is based upon, and improves, the discrete time part of the earlier paper \cite{ber95}.