  Following the recently developed algorithms for fully probabilistic control
design for general dynamic stochastic systems [15], [18], this paper presents
the solution to the probabilistic dual heuristic programming (DHP) adaptive
critic method [15] and randomized control algorithm for stochastic nonlinear
dynamical systems. The purpose of the randomized control input design is to
make the joint probability density function of the closed loop system as close
as possible to a predetermined ideal joint probability density function. This
paper completes the previous work [15], [18] by formulating and solving the
fully probabilistic control design problem on the more general case of
nonlinear stochastic discrete time systems. A simulated example is used to
demonstrate the use of the algorithm and encouraging results have been
obtained.
