Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations

TL;DR

This paper extends data-enabled predictive control to nonlinear systems using basis functions, providing consistent, computationally efficient formulations with theoretical guarantees and practical validation on a nonlinear pendulum model.

Contribution

It introduces a basis functions DeePC framework with necessary and sufficient conditions for equivalence, and develops two efficient formulations for nonlinear predictive control.

Findings

The basis functions DeePC is consistent under certain conditions.

The proposed formulations improve computational efficiency.

Validated on a nonlinear pendulum with noise and noise-free data.

Abstract

This paper considers the extension of data-enabled predictive control (DeePC) to nonlinear systems via general basis functions. Firstly, we formulate a basis functions DeePC behavioral predictor and we identify necessary and sufficient conditions for equivalence with a corresponding basis functions multi-step identified predictor. The derived conditions yield a dynamic regularization cost function that enables a well-posed (i.e., consistent) basis functions formulation of nonlinear DeePC. To optimize computational efficiency of basis functions DeePC we further develop two alternative formulations that use a simpler, sparse regularization cost function and ridge regression, respectively. Consistency implications for Koopman DeePC as well as several methods for constructing the basis functions representation are also indicated. The effectiveness of the developed consistent basis functions DeePC formulations is illustrated on a benchmark nonlinear pendulum state-space model, for both noise free and noisy data.