Direct data-driven LPV control of nonlinear systems: An experimental result

TL;DR

This paper presents a novel experimental approach for controlling nonlinear systems directly from measurement data using a behavioral LPV framework, successfully stabilizing a real-world system with minimal data.

Contribution

It introduces a data-driven LPV control method for nonlinear systems that requires only measurement data and a scheduling map, validated through real-world experiments.

Findings

Successfully stabilized a nonlinear system with only 7 data points.

Demonstrated the first experimental stabilization of arbitrary equilibria using behavioral data-driven methods.

Validated the approach on a nonlinear unbalanced disc system.

Abstract

We demonstrate that direct data-driven control of nonlinear systems can be successfully accomplished via a behavioral approach that builds on a Linear Parameter-Varying (LPV) system concept. An LPV data-driven representation is used as a surrogate LPV form of the data-driven representation of the original nonlinear system. The LPV data-driven control design that builds on this representation form uses only measurement data from the nonlinear system and a priori information on a scheduling map that can lead to an LPV embedding of the nonlinear system behavior. Efficiency of the proposed approach is demonstrated experimentally on a nonlinear unbalanced disc system showing for the first time in the literature that behavioral data-driven methods are capable to stabilize arbitrary forced equilibria of a real-world nonlinear system by the use of only 7 data points.