Due to simplicity and convenience, Model Predictive Control, which consists in optimizing future decisions based on a pessimistic deterministic forecast of the random processes, is one of the main tools for stochastic control. Yet, it suffers from a large computation time, unless the tactical horizon (i.e. the number of future time steps included in the optimization) is strongly reduced, and la...

Max-plus stochastic processes are counterparts of Markov diffusion processes governed by Ito sense stochastic differential equations. In this framework, expectations are linear operations with respect to max-plus arithmetic. Max-plus stochastic control problems are considered, in which a minimizing control enters the state dynamics and running cost. The minimum max-plus expected cost is equal t...