---
_id: '16297'
abstract:
- lang: eng
  text: "In real-world problems, uncertainties (e.g., errors in the measurement,\r\nprecision
    errors) often lead to poor performance of numerical algorithms when\r\nnot explicitly
    taken into account. This is also the case for control problems,\r\nwhere optimal
    solutions can degrade in quality or even become infeasible. Thus,\r\nthere is
    the need to design methods that can handle uncertainty. In this work,\r\nwe consider
    nonlinear multi-objective optimal control problems with uncertainty\r\non the
    initial conditions, and in particular their incorporation into a\r\nfeedback loop
    via model predictive control (MPC). In multi-objective optimal\r\ncontrol, an
    optimal compromise between multiple conflicting criteria has to be\r\nfound. For
    such problems, not much has been reported in terms of uncertainties.\r\nTo address
    this problem class, we design an offline/online framework to compute\r\nan approximation
    of efficient control strategies. This approach is closely\r\nrelated to explicit
    MPC for nonlinear systems, where the potentially expensive\r\noptimization problem
    is solved in an offline phase in order to enable fast\r\nsolutions in the online
    phase. In order to reduce the numerical cost of the\r\noffline phase, we exploit
    symmetries in the control problems. Furthermore, in\r\norder to ensure optimality
    of the solutions, we include an additional online\r\noptimization step, which
    is considerably cheaper than the original\r\nmulti-objective optimization problem.
    We test our framework on a car\r\nmaneuvering problem where safety and speed are
    the objectives. The\r\nmulti-objective framework allows for online adaptations
    of the desired\r\nobjective. Alternatively, an automatic scalarizing procedure
    yields very\r\nefficient feedback controls. Our results show that the method is
    capable of\r\ndesigning driving strategies that deal better with uncertainties
    in the initial\r\nconditions, which translates into potentially safer and faster
    driving\r\nstrategies."
author:
- first_name: Carlos Ignacio
  full_name: Hernández Castellanos, Carlos Ignacio
  last_name: Hernández Castellanos
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
citation:
  ama: Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit Multi-objective
    Model Predictive Control for Nonlinear Systems  Under Uncertainty. <i>International
    Journal of Robust and Nonlinear Control</i>. 2020;30(17):7593-7618. doi:<a href="https://doi.org/10.1002/rnc.5197">10.1002/rnc.5197</a>
  apa: Hernández Castellanos, C. I., Ober-Blöbaum, S., &#38; Peitz, S. (2020). Explicit
    Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.
    <i>International Journal of Robust and Nonlinear Control</i>, <i>30(17)</i>, 7593–7618.
    <a href="https://doi.org/10.1002/rnc.5197">https://doi.org/10.1002/rnc.5197</a>
  bibtex: '@article{Hernández Castellanos_Ober-Blöbaum_Peitz_2020, title={Explicit
    Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty},
    volume={30(17)}, DOI={<a href="https://doi.org/10.1002/rnc.5197">10.1002/rnc.5197</a>},
    journal={International Journal of Robust and Nonlinear Control}, author={Hernández
    Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2020},
    pages={7593–7618} }'
  chicago: 'Hernández Castellanos, Carlos Ignacio, Sina Ober-Blöbaum, and Sebastian
    Peitz. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems 
    Under Uncertainty.” <i>International Journal of Robust and Nonlinear Control</i>
    30(17) (2020): 7593–7618. <a href="https://doi.org/10.1002/rnc.5197">https://doi.org/10.1002/rnc.5197</a>.'
  ieee: 'C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective
    Model Predictive Control for Nonlinear Systems  Under Uncertainty,” <i>International
    Journal of Robust and Nonlinear Control</i>, vol. 30(17), pp. 7593–7618, 2020,
    doi: <a href="https://doi.org/10.1002/rnc.5197">10.1002/rnc.5197</a>.'
  mla: Hernández Castellanos, Carlos Ignacio, et al. “Explicit Multi-Objective Model
    Predictive Control for Nonlinear Systems  Under Uncertainty.” <i>International
    Journal of Robust and Nonlinear Control</i>, vol. 30(17), 2020, pp. 7593–618,
    doi:<a href="https://doi.org/10.1002/rnc.5197">10.1002/rnc.5197</a>.
  short: C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal
    of Robust and Nonlinear Control 30(17) (2020) 7593–7618.
date_created: 2020-03-13T12:45:56Z
date_updated: 2022-01-21T09:55:39Z
department:
- _id: '101'
doi: 10.1002/rnc.5197
language:
- iso: eng
page: 7593-7618
publication: International Journal of Robust and Nonlinear Control
status: public
title: Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under
  Uncertainty
type: journal_article
user_id: '15694'
volume: 30(17)
year: '2020'
...