Data-Driven Multiple Shooting for Stochastic Optimal Control

Abstract

The implementation of data-driven predictive control schemes based on Willems’ fundamental lemma often relies on a single-shooting approach, i.e., it uses one large Hankel matrix to cover the entire optimization horizon. However, the numerical solution is fostered by the use of multiple segmented horizons which require less data in smaller Hankel matrices. This letter extends the segmentation idea towards multiple shooting for data-driven optimal control of stochastic LTI systems. Using a stochastic variant of the fundamental lemma and polynomial chaos expansions, we propose a multiple-shooting formulation which combines trajectory segmentation and moment matching. We show that, for LTI systems subject to Gaussian noise of finite variance, our formulation is without loss of optimality while it allows for a significant reduction of the problem dimension in Gaussian and non-Gaussian settings. We draw upon a numerical example to compare the proposed framework to the usual single-shooting approach.