Data-based Control of Feedback Linearizable Systems

TL;DR

This paper extends Willems' Fundamental Lemma to feedback linearizable nonlinear systems, enabling data-based input-output trajectory representation despite uncertainties and noise, with practical bounds demonstrated on a double inverted pendulum.

Contribution

It introduces a novel data-driven framework for feedback linearizable systems, accounting for uncertainties and noise, and provides bounded approximation solutions.

Findings

Bounded difference between approximate and true solutions

Effective data-based representation of nonlinear systems

Successful application to a double inverted pendulum

Abstract

We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems, thus providing a data-based representation of their input-output trajectories. Two sources of uncertainty are considered. First, the unknown linearizing input is inexactly approximated by a set of basis functions. Second, the measured output data is contaminated by additive noise. Further, we propose an approach to approximate the solution of the data-based simulation and output matching problems, and show that the difference from the true solution is bounded. Finally, the results are illustrated on an example of a fully-actuated double inverted pendulum.