An Online Adaptation Strategy for Direct Data-driven Control

TL;DR

This work strives to extend the applicability of the fundamental lemma from behavioral systems theory to more strongly nonlinear systems by updating the system representation during control by running as an observer parallel to the controller.

Abstract

The fundamental lemma from behavioral systems theory yields a data-driven non-parametric system representation that has shown great potential for the data-efficient control of unknown linear and weakly nonlinear systems, even in the presence of measurement noise. In this work, we strive to extend the applicability of this paradigm to more strongly nonlinear systems by updating the system representation during control. Unlike existing approaches, our method does not impose suitable excitation to the control inputs, but runs as an observer parallel to the controller. Whenever a rank condition is deemed to be fulfilled, the system representation is updated using newly available datapoints. In a reference tracking simulation of a two-link robotic arm, we showcase the performance of the proposed strategy in a predictive control framework.

Figures (4)

• Figure 1: Exemplary comparison of singular values from noisy data matrices whose uncorrupted counterparts satisfy or violate rank condition \ref{['eq:perexc_ext']}. Thresholding the singular values with $\varrho$ recovers the original rank.
• Figure 2: Schematic illustration of the two-link robot.
• Figure 3: Boxplots of the total trajectory costs $J_{\text{tot}}$ for Proposed Method, Always Update, and Never Update.
• Figure 4: Mean trajectories and confidence intervals for Proposed Method, Always Update, and Never Update, and mean updating decisions of the proposed method.