Learning explicit predictive controllers: theory and applications

TL;DR

This paper introduces a novel data-driven approach to learn explicit predictive controllers for linear systems directly from data, bypassing system identification, and proves their effectiveness both theoretically and through simulations.

Contribution

It presents the first method to learn explicit predictive laws directly from data using Willems' lemma, avoiding system identification.

Findings

Explicit predictive controllers can be learned directly from data.

The method is asymptotically equivalent to model-based control with noisy data.

Numerical simulations validate the approach on benchmark examples.

Abstract

In this paper, we deal with data-driven predictive control of linear time-invariant (LTI) systems. Specifically, we show for the first time how explicit predictive laws can be learnt directly from data, without needing to identify the system to control. To this aim, we resort to the Willems' fundamental lemma and we derive the explicit formulas by suitably elaborating the constrained optimization problem under investigation. The resulting optimal controller turns out to be a piecewise affine system coinciding with the solution of the original model-based problem in case of noiseless data. Such an equivalence is proven to hold asymptotically also in presence of measurement noise, thus making the proposed method a computationally efficient (but model-free) alternative to the state of the art predictive controls. The above statements are further supported by numerical simulations on three benchmark examples.