On dynamic programming for sequential decision problems under a general form of uncertainty

We study the applicability of the method of Dynamic Programming (DP) for the solution of a general class of sequential decision problems under uncertainty, that may more commonly be referred to as discrete-time control problems under uncertainty. The uncertainty is due to the fact that the evolution of the state of the controlled system is affected by disturbances that are only known to belong to random sets, whose distributions are given a-priori. This includes as special cases the well known stochastic control problem and the robust min-max problem.