Optimality and Tractability in Stochastic Nonlinear Control

We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman's infamous "curse of dimensionality". We present a result that shows that repeatedly solving an open-loop deterministic problem from the current state, as in the so-called Model Predictive Control (MPC) approach, results in the true global stochastic optimal policy. This result holds irrespective of the attendant uncertainty.