  This paper studies the stochastic optimal control problem for systems with
unknown dynamics. First, an open-loop deterministic trajectory optimization
problem is solved without knowing the explicit form of the dynamical system.
Next, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal
trajectory-dependent linearized system, such that under a small noise
assumption, the actual states remain close to the optimal trajectory. The
trajectory-dependent linearized system is identified using input-output
experimental data consisting of the impulse responses of the nominal system. A
computational example is given to illustrate the performance of the proposed
approach.
