A Trajectory-Based Framework for Data-Driven System Analysis and Control

Authors

Julian Berberich, Frank Allgower

Year

2019

Conference Paper

Algorithm

Trajectory-Based Data-driven Control

Source

European Control Conference

Identifiers

arXiv 1903.10723 DOI 10.23919/ECC51009.2020.9143608

Abstract¶

The vector space of all input-output trajectories of a discrete-time linear time-invariant (LTI) system is spanned by time-shifts of a single measured trajectory, given that the respective input signal is persistently exciting. This fact, which was proven in the behavioral control framework, shows that a single measured trajectory can capture the full behavior of an LTI system and might therefore be used directly for system analysis and controller design, without explicitly identifying a model. In this paper, we translate the result from the behavioral context to the classical state-space control framework and we extend it to certain classes of nonlinear systems, which are linear in suitable input-output coordinates. Moreover, we show how this extension can be applied to the data-driven simulation problem, where we introduce kernel-methods to obtain a rich set of basis functions.

Summary¶

Recasts behavioral trajectory spanning in state-space language and extends the idea toward nonlinear systems that admit linear input-output coordinates. It helps connect classical control intuition, data-driven simulation, and later kernelized or nonlinear fundamental-lemma variants.