state-feedback control problems involving stochastic nonlinear systems. The method avoids solving
partial differential equations and instead requires only the solution of simpler algebraic equations.
Exploiting a dynamic extension, we provide approximate solutions, with an exactly quantifiable level
of approximation, for optimal control problems and min–max zero-sum games, and exact solutions
for the H∞ control problem. Extensive numerical simulations demonstrate improved performances
with respect to the control laws obtained via the corresponding linear quadratic approximations and
deterministic nonlinear approaches.