Stochastic Optimal Open-Loop Feedback Control

In this chapter a second procedure for an approximate determination of stochastic optimal feedback controls is based on the stochastic open-loop feedback method. This very efficient approximation method is also the basis of the model predictive control procedures. Using the methods mentioned in Chap. 3 , stochastic optimal open-loop feedback controls are constructed by computing next to stochastic optimal open-loop controls on the remaining time intervals \(t_b \le t \le t_f\) with \(t_0 \le t_b \le t_f\) . Having stochastic optimal open-loop feedback controls on each remaining time interval \(t_b \le t \le t_f\) with \(t_0 \le t_b \le t_f\) , a stochastic optimal open-loop feedback control law follows then immediately by evaluating each of the stochastic optimal open-loop controls on \(t_b \le t \le t_f\) at the corresponding initial time point \(t=t_b\) . The efficiency of this method has been proved already by applications to the stochastic optimization of regulators for robots.