This project is concerned with optimal control of nonlinear stochastic
systems with noisy dynamics and observations. The pay-off function is of
an exponential-of-integral form which leads to robust controllers with
respect to unknown noise statistics. This type of pay-off function minimizes
in addition to the average value of the integral sample cost, its standard
deviation. A series of results are introduced concerning the explicit computation
of optimal control laws, for systems with nonlinear dynamics and observations.
The result extends the separation theorem of Linear-Gaussian Systems to
nonlinear systems. Lie algebraic methods are also introduced to decide
a priori whether there exists finite-dimensional optimal control laws.
In addition, connections to deterministic disturbance attenuation problems