Explicit model predictive control for PDEs: The case of a heat equation

Stevan Dubljevic, Jukka Pekka Humaloja, Mikael Kurula

Research output: Contribution to journalConference articleScientificpeer-review

1 Citation (Scopus)
52 Downloads (Pure)


Explicit model predictive control design is carefully developed for discrete-time linear plants on Hilbert spaces, and we highlight the role of the so-called Slater condition in the reliable explicit solution of the MPC optimization. We then proceed to present an explicit MPC algorithm that accounts for the stabilization and input constraints satisfaction. We do structure preserving temporal discretization of the infinite-dimensional parabolic PDE system by application of the Cayley transformation. The salient feature of explicit MPC design is the realization of the region-free approach in explicit MPC design with identification of active constraint sets to realize optimal stabilization and constraints satisfaction. Finally, the resulting design is illustrated by the application to the PDE model given by an unstable heat equation with boundary actuation and Neumann boundary conditions. The example demonstrates simultaneous stabilization and input constraints satisfaction on the one hand, and on the ability to deal with a relatively high plant dimension and a long optimization horizon on the other hand.

Original languageEnglish
Pages (from-to)460-465
Number of pages6
Issue number30
Publication statusPublished - 2022
MoE publication typeA4 Article in a conference publication
Event25th IFAC Symposium on Mathematical Theory of Networks and Systems, MTNS 2022 - Bayreuthl, Germany
Duration: 12 Sept 202216 Sept 2022


  • Boundary Control
  • Distributed Parameter Systems
  • Explicit MPC
  • Heat Equation


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