Greedy sampling and approximation for realizing feedback control for high dimensional nonlinear systems

Abstract

The problem of closed-loop control for high dimensional nonlinear systems is considered. Three different types of kernel interpolation surrogates for the optimal feedback policy are compared. The data for this comes from open-loop controlled solutions. Here, additional information about the system originating from the Pontryagin Maximum Principle is exploited. The starting position for the open-loop control is adaptively selected by a geometric greedy selection criterion, and a so-called vectorial kernel orthogonal greedy algorithm is performed to set up the surrogate. With this procedure we can overcome the curse of dimensionality and still receive a very precise, robust and real-time capable feedback control.