The problem of closed-loop control of coupled systems under state constraints is considered. A new method for generating an approximate feedback policy is used in which the gradient of the value function is replaced by a vector-valued kernel surrogate. This is built up from samples from open-loop control problems. Here, additional information about the system originating from the Pontryagin Maximum Principle is exploited. Furthermore, a multi-stage approach and the vectorial kernel orthogonal greedy algorithm are used. With this procedure we can overcome the curse of dimensionality that occurs in the determination of the value function via Hamilton-Jacobi-Bellman equation. Nevertheless, the resulting feedback control is very accurate, robust and real-time capable.
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