Speaker
Description
The synthesis of optimal feedback-laws for optimal control problems is a challenging topic. Classical approaches consist in constructing an optimal feedback-law by approximating the value function of the problem. However, these types of methods suffer from the curse of dimensionality, namely, its computational cost increases exponentially with the dimension of the underlaying control problem. For this reason, machine learning based methods have been proposed for remedy this problem. Although there are promising results from the practical point of view, performance guarantees of feedback laws produced by these methods are still necessary. Recently, performance guarantees have been provided by controlling the semi-concavity and the H¹ error of the approximation. Nevertheless, this is not possible for usual machine learning models. This talk is focused on a machine learning based approach for approximating semi-concave functions. The main novelty of this approach lies in preserving the semi-concavity of the approximation, which is crucial for ensuring performance guarantees of the synthesis of optimal feedback-laws. Further, we demonstrate that any semi-concave function can be approximated by this method. The performance of this approach will be illustrated by numerical examples, where the approximated function is known to be semi-concave.
