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

TL;DR

A more parsimonious formulation of Willems’ lemma is derived that separates the model into initial condition matching and predictive control design parts, which avoids the need for regularisers in the predictive control problem that are found in other data-driven predictive control methods.

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.

Figures (3)

• Figure 1: Output trajectories, mean value and 1 std. dev. (shaded)
• Figure 2: Input trajectories, mean value and 1 std. dev. (shaded)
• Figure 3: Performance indices over 30 Monte Carlo runs

Theorems & Definitions (3)

• Lemma 2: Willems' Fundamental Lemma
• Lemma 4
• Theorem 6