  This work considers the stability of nonlinear stochastic receding horizon
control when the optimal controller is only computed approximately. A number of
general classes of controller approximation error are analysed including
deterministic and probabilistic errors and even controller sample and hold
errors. In each case, it is shown that the controller approximation errors do
not accumulate (even over an infinite time frame) and the process converges
exponentially fast to a small neighbourhood of the origin. In addition to this
analysis, an approximation method for receding horizon optimal control is
proposed based on Monte Carlo simulation. This method is derived via the
Feynman-Kac formula which gives a stochastic interpretation for the solution of
a Hamilton-Jacobi-Bellman equation associated with the true optimal controller.
It is shown, and it is a prime motivation for this study, that this particular
controller approximation method practically stabilises the underlying nonlinear
process.
