End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data

TL;DR

This paper introduces an end-to-end indirect data-driven control method for bilinear systems, providing stability guarantees and finite sample error bounds even with noisy, unbounded data, and explores connections to nonlinear system control via Koopman theory.

Contribution

It presents a novel algorithm for bilinear system control with probabilistic stability guarantees and finite sample bounds, integrating identification errors into robust controller design.

Findings

Finite sample identification error bounds derived.

Stable closed-loop control achieved with structured error bounds.

Numerical studies demonstrate the effectiveness of the approach.

Abstract

In this paper we propose an end-to-end algorithm for indirect data-driven control for bilinear systems with stability guarantees. We consider the case where the collected i.i.d. data is affected by probabilistic noise with possibly unbounded support and leverage tools from statistical learning theory to derive finite sample identification error bounds. To this end, we solve the bilinear identification problem by solving a set of linear and affine identification problems, by a particular choice of a control input during the data collection phase. We provide a priori as well as data-dependent finite sample identification error bounds on the individual matrices as well as ellipsoidal bounds, both of which are structurally suitable for control. Further, we integrate the structure of the derived identification error bounds in a robust controller design to obtain an exponentially stable closed-loop. By means of an extensive numerical study we showcase the interplay between the controller design and the derived identification error bounds. Moreover, we note appealing connections of our results to indirect data-driven control of general nonlinear systems through Koopman operator theory and discuss how our results may be applied in this setup.