Stochastic optimal feedback controls are determined for dynamic control systems with random model parameters by means of the stochastic optimal open-loop feedback method, which is also the basis of model predictive control. Based on the stochastic Hamiltonian of the optimum control problem with random parameters, the class of H-minimal controls is determined by solving a finite-dimensional stochastic program for the minimization of the expected Hamiltonian with respect to the input at each time point. Having a H-minimal control, a two-point boundary value problem (BVP) with random parameters is formulated for the computation of optimal state and co-state trajectories. Inserting then these trajectories into the H-minimal control, stochastic optimal open-loop controls are found for each remaining time interval with an arbitrary intermediate starting time point. Evaluating the stochastic optimal open-loop controls at the corresponding intermediate starting time point only, a stochastic optimal open-loop feedback control is obtained. For the numerical solution of the two-point boundary value with random parameters the following techniques are considered: i) Linearizing the basic two-point (BVP); ii) Transformation of the linearized two-point (BVP) into a fixed point condition for the adjoint trajectory and applying then iterative methods; iii) Approximation of the variables on the remaining time interval by constant ones to obtain a system of linear equations for the required values at the intermediate starting time points; iv) Taylor expansion of the variables with respect to the underlying parameter vector at its conditional mean value and reducing the twopoint (BVP) to a linear two-point (BVP) for the trajectories and their sensitivities. v) Solving this two-point (BVP) by using a matrix Riccati differential equation.

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