---
_id: '13879'
abstract:
- lang: eng
  text: Model Predictive Control evolved as the state of the art paradigm for safety
    critical control tasks. Control-as-Inference approaches thereof model the constrained
    optimization problem as a probabilistic inference problem. The constraints have
    to be implemented into the inference model. A recently introduced physics-informed
    Gaussian Process method uses Control-as-Inference with a Gaussian likelihood for
    state constraint modeling, but lacks guarantees of open-loop constraint satisfaction.
    We mitigate the lack of guarantees via an additional sampling step using Hamiltonian
    Monte Carlo sampling in order to obtain safe rollouts of the open-loop dynamics
    which are then used to obtain an approximation of the truncated normal distribution
    which has full probability mass in the safe area. We provide formal guarantees
    of constraint satisfaction while maintaining the ODE structure of the Gaussian
    Process on a discretized grid. Moreover, we show that we are able to perform optimization
    of a quadratic cost function by closed form Gaussian Process computations only
    and introduce the Matérn kernel into the inference model.
article_number: '101600'
author:
- first_name: Jörn
  full_name: Tebbe, Jörn
  id: '85958'
  last_name: Tebbe
- first_name: Andreas
  full_name: Besginow, Andreas
  id: '61743'
  last_name: Besginow
- first_name: Markus
  full_name: Lange-Hegermann, Markus
  id: '71761'
  last_name: Lange-Hegermann
citation:
  ama: Tebbe J, Besginow A, Lange-Hegermann M. Physics-informed Gaussian Processes
    as Linear Model Predictive Controller with Constraint Satisfaction. <i>European
    Journal of Control</i>. Published online 2026. doi:<a href="https://doi.org/10.1016/j.ejcon.2026.101600">10.1016/j.ejcon.2026.101600</a>
  apa: Tebbe, J., Besginow, A., &#38; Lange-Hegermann, M. (2026). Physics-informed
    Gaussian Processes as Linear Model Predictive Controller with Constraint Satisfaction.
    <i>European Journal of Control</i>, Article 101600. <a href="https://doi.org/10.1016/j.ejcon.2026.101600">https://doi.org/10.1016/j.ejcon.2026.101600</a>
  bjps: <b>Tebbe J, Besginow A and Lange-Hegermann M</b> (2026) Physics-Informed Gaussian
    Processes as Linear Model Predictive Controller with Constraint Satisfaction.
    <i>European Journal of Control</i>.
  chicago: Tebbe, Jörn, Andreas Besginow, and Markus Lange-Hegermann. “Physics-Informed
    Gaussian Processes as Linear Model Predictive Controller with Constraint Satisfaction.”
    <i>European Journal of Control</i>, 2026. <a href="https://doi.org/10.1016/j.ejcon.2026.101600">https://doi.org/10.1016/j.ejcon.2026.101600</a>.
  chicago-de: Tebbe, Jörn, Andreas Besginow und Markus Lange-Hegermann. 2026. Physics-informed
    Gaussian Processes as Linear Model Predictive Controller with Constraint Satisfaction.
    <i>European Journal of Control</i>. doi:<a href="https://doi.org/10.1016/j.ejcon.2026.101600">10.1016/j.ejcon.2026.101600</a>,
    .
  din1505-2-1: '<span style="font-variant:small-caps;">Tebbe, Jörn</span> ; <span
    style="font-variant:small-caps;">Besginow, Andreas</span> ; <span style="font-variant:small-caps;">Lange-Hegermann,
    Markus</span>: Physics-informed Gaussian Processes as Linear Model Predictive
    Controller with Constraint Satisfaction. In: <i>European Journal of Control</i>.
    Oxford [u.a.], Elsevier BV (2026)'
  havard: J. Tebbe, A. Besginow, M. Lange-Hegermann, Physics-informed Gaussian Processes
    as Linear Model Predictive Controller with Constraint Satisfaction, European Journal
    of Control. (2026).
  ieee: 'J. Tebbe, A. Besginow, and M. Lange-Hegermann, “Physics-informed Gaussian
    Processes as Linear Model Predictive Controller with Constraint Satisfaction,”
    <i>European Journal of Control</i>, Art. no. 101600, 2026, doi: <a href="https://doi.org/10.1016/j.ejcon.2026.101600">10.1016/j.ejcon.2026.101600</a>.'
  mla: Tebbe, Jörn, et al. “Physics-Informed Gaussian Processes as Linear Model Predictive
    Controller with Constraint Satisfaction.” <i>European Journal of Control</i>,
    101600, 2026, <a href="https://doi.org/10.1016/j.ejcon.2026.101600">https://doi.org/10.1016/j.ejcon.2026.101600</a>.
  short: J. Tebbe, A. Besginow, M. Lange-Hegermann, European Journal of Control (2026).
  ufg: '<b>Tebbe, Jörn/Besginow, Andreas/Lange-Hegermann, Markus</b>: Physics-informed
    Gaussian Processes as Linear Model Predictive Controller with Constraint Satisfaction,
    in: <i>European Journal of Control</i> (2026).'
  van: Tebbe J, Besginow A, Lange-Hegermann M. Physics-informed Gaussian Processes
    as Linear Model Predictive Controller with Constraint Satisfaction. European Journal
    of Control. 2026;
date_created: 2026-07-28T07:07:24Z
date_updated: 2026-07-28T07:12:38Z
department:
- _id: DEP5015
doi: 10.1016/j.ejcon.2026.101600
language:
- iso: eng
place: Oxford [u.a.]
publication: European Journal of Control
publication_identifier:
  eissn:
  - 1435-5671
  issn:
  - 0947-3580
publication_status: published
publisher: Elsevier BV
quality_controlled: '1'
status: public
title: Physics-informed Gaussian Processes as Linear Model Predictive Controller with
  Constraint Satisfaction
type: scientific_journal_article
user_id: '83781'
year: '2026'
...