Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

TL;DR

This paper introduces a data-driven control method for nonlinear systems with rational or non-polynomial dynamics, providing stability and performance guarantees without requiring explicit model knowledge.

Contribution

It extends data-driven control to non-polynomial nonlinear systems using a new parametrization and sum-of-squares techniques, surpassing polynomial-only approaches.

Findings

Successfully controls systems with rational dynamics

Provides robust stability guarantees based on measured data

Demonstrates effectiveness through numerical examples

Abstract

In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial dynamics, our approach allows to design controllers for unknown systems with rational or general non-polynomial dynamics. We first derive a data-driven parametrization of unknown nonlinear systems with rational dynamics. By applying robust control techniques to this parametrization, we obtain sum-of-squares based criteria for designing controllers with closed-loop robust stability and performance guarantees for all systems which are consistent with the measured data and the assumed noise bound. We then apply this approach to control systems whose dynamics are linear in general non-polynomial basis functions by transforming them into polynomial systems. Finally, we apply the developed approaches to numerical examples.