Optimal Data-Driven Prediction and Predictive Control using Signal Matrix Models

TL;DR

This paper introduces a simplified, data-driven predictive control method based on a refined Willems' lemma, offering a closed-form optimal predictor and demonstrating strong control performance without regularisers.

Contribution

It presents a more parsimonious formulation of Willems' lemma that separates initial condition matching from predictive control, eliminating the need for regularisers and providing a closed-form optimal predictor.

Findings

Closed-form optimal predictor derived for future output trajectories

Simulation results show improved control performance

Method avoids regularisers used in other data-driven control approaches

Abstract

Data-driven control uses a past signal trajectory to characterise the input-output behaviour of a system. Willems' lemma provides a data-based prediction model allowing a control designer to bypass the step of identifying a state-space or transfer function model. This paper provides a more parsimonious formulation of Willems' lemma that separates the model into initial condition matching and predictive control design parts. This avoids the need for regularisers in the predictive control problem that are found in other data-driven predictive control methods. It also gives a closed form expression for the optimal (minimum variance) unbiased predictor of the future output trajectory and applies it for predictive control. Simulation comparisons illustrate very good control performance.