Nonlinear Data-Driven Control Part II: qLPV Predictive Control using Parameter Extrapolation

TL;DR

This paper introduces a novel data-driven MPC approach for nonlinear systems using qLPV embeddings and parameter extrapolation, enabling regulation and constraint satisfaction solely from measured data.

Contribution

It develops a new nonlinear data-driven MPC algorithm based on behavioral theory and qLPV embeddings, incorporating parameter extrapolation without needing scheduling trajectories.

Findings

The proposed method ensures regulation and IO constraints satisfaction.

The extrapolation procedure converges with bounded errors.

The algorithm's effectiveness is demonstrated through a numerical example.

Abstract

We present a novel data-driven Model Predictive Control (MPC) algorithm for nonlinear systems. The method is based on recent extensions of behavioural theory and Willem's Fundamental Lemma for nonlinear systems by the means of adequate Input-Output (IO) quasi-Linear Parameter Varying (qLPV) embeddings. Thus, the MPC is formulated to ensure regulation and IO constraints satisfaction, based only on measured datasets of sufficient length (and under persistent excitation). Instead of requiring the availability of the scheduling trajectories (as in recent papers), we consider an estimate of the function that maps the qLPV realisation. Specifically, we use an extrapolation procedure in order to generate the future scheduling trajectories, at each sample, which is shown to be convergent and generated bounded errors. Accordingly, we discuss the issues of closed-loop IO stability and recursive feasibility certificates of the method. The algorithm is tested and discussed with the aid of a numerical application.