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

TL;DR

This work addresses the challenge of data-efficient, guaranteed data-driven control for nonlinear systems by embedding nonlinear dynamics into an LPV form through a scheduling map $p_k = \psi(x_k,u_k)$. It develops a fully data-driven LPV representation from measurements under a persistency of excitation condition and provides closed-loop state-feedback synthesis procedures that guarantee stability and quadratic performance or bounded $L_2$-gain. The authors demonstrate the approach experimentally on an unbalanced disc, showing that arbitrary forced equilibria can be stabilized and reference tracking achieved using only 7 data points, thereby significantly reducing data requirements. The results highlight the practical potential of LPV-based data-driven control for nonlinear systems and point to future work on robustness to noisy data and conditioning-aware data selection.

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.

Figures (5)

• Figure 1: LPV embedding of a nonlinear system, where $w$ represents the collection of input and output signals.
• Figure 2: The unbalanced disc experimental setup.
• Figure 3: Data-dictionary used for controller synthesis with $N_\mathrm{d}=7$.
• Figure 4: Experimental results with \ref{['controller1']} in a disturbance rejection scenario. The gray areas indicate when we disturbed the experimental setup by hand.
• Figure 5: Experimental results with changing setpoint.