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This paper studies the stochastic optimal control problem for systems withunknown dynamics. First, an open-loop deterministic trajectory optimizationproblem is solved without knowing the explicit form of the dynamical system.Next, a Linear Quadratic Gaussian (LQG) controller is designed for the nominaltrajectory-dependent linearized system, such that under a small noiseassumption, the actual states remain close to the optimal trajectory. Thetrajectory-dependent linearized system is identified using input-outputexperimental data consisting of the impulse responses of the nominal system. Acomputational example is given to illustrate the performance of the proposedapproach.

Stochastic Feedback Control of Systems with Unknown Nonlinear Dynamics