Systematic perturbations of discrete-time stochastic dynamical systems

The discrete-time stochastic optimal control problem is approximated by a variation of differential dynamic programming with systematic calculations of the perturbations due to small stochastic noise. This problem is related to the dual control aspects of stochastic optimal control problems. The motivation is to correct prior calculations for missing terms and to examine the foundations of the method. The state vector is properly expanded asymptotically, in addition to the control vector, in contrast to previous solutions. Corrections are given for the small noise expansions of the solution