Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

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.

arXiv commentAccepted for 60th IEEE Conference on Decision and Control (CDC)

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Cited by in corpus (2)

• Linear tracking MPC for nonlinear systems Part II: The data-driven case
• Robust data-driven control for nonlinear systems using the Koopman operator