Dual control based on approximate a posteriori density functions

The problem of control of a nonlinear time discrete stochastic system is considered. The control function is obtained with the help of approximate a posteriori density functions from a set of measurable functions defined on all past controls and measurements. Approximations are chosen to retain the dual (estimator-controller) nature of the truly optimal control The controls obtained from this method can have considerably different structure from those obtained by the more usual use of linearization and application of the "separation theorem" that is invalid for this problem. The possible use of this method to discover the proper structure of an optimal control that may then be implemented in a much simpler fashion for real-time applications is discussed.