Towards reliable data-based optimal and predictive control using extended DMD

TL;DR

This paper extends the theoretical analysis of Koopman-based extended DMD methods to control applications, providing error bounds for data-driven optimal and predictive control while addressing high-dimensional challenges.

Contribution

It generalizes error estimates to control settings and introduces a bilinear approach to mitigate the curse of dimensionality in data-driven control.

Findings

Established uniform bounds on approximation errors for control-related quantities

Extended rigorous error analysis to optimal and predictive control scenarios

Reduced dimensionality impact using a bilinear approach

Abstract

While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates were only recently established. To this end, both sources of error resulting from a finite dictionary and only finitely-many data points in the generation of the surrogate model have to be taken into account. We generalize the rigorous analysis of the approximation error to the control setting while simultaneously reducing the impact of the curse of dimensionality by using a recently proposed bilinear approach. In particular, we establish uniform bounds on the approximation error of state-dependent quantities like constraints or a performance index enabling data-based optimal and predictive control with guarantees.