HAVOK Model Predictive Control for Time-Delay Systems with Applications to District Heating

TL;DR

This work tackles controlling district heating systems with unknown, flow-dependent transport delays by introducing a data-driven HAVOK-MPC that leverages delay-embedded Koopman representations. By applying the Hankel Alternative View of Koopman on time-delay coordinates and enforcing causality through a downshift-based input construction, the method achieves a low-dimensional, causally consistent MPC despite large delay horizons. The authors validate the approach on a lab-scale DHS, showing accurate prediction and robust tracking with a modest data requirement (less than ~1000 samples) and a computationally bounded QP formulation. The results highlight the practical potential of HAVOK-MPC for real-time control of time-delay systems under parameter uncertainty, with avenues for extension to LPV and Bilinear DMD frameworks.

Abstract

A computationally efficient Model-Predictive Control (MPC) approach is proposed for systems with unknown delay using only input/output data. We use the Koopman operator framework and the related Hankel Alternative View of Koopman (HAVOK) algorithm to identify a model in a basis of projected time-delay coordinates and demonstrate a novel MPC structure that reduces and bounds the computational complexity. The proposed HAVOK-MPC approach is validated experimentally on a laboratory-scale District Heating System (DHS), demonstrating excellent prediction and tracking performance while only requiring knowledge of a conservative upper bound on the system delay.

Figures (4)

• Figure 1: Schematic of the AAU SWIL laboratory setup
• Figure 2: Smart Water Infrastructure Laboratory (AAU-SWIL)
• Figure 3: HAVOK model predictive performance
• Figure 4: HAVOK-MPC reference-tracking performance