CoChat
Sign Up
Cited by 115Advanced Control Systems OptimizationStability and Control of Uncertain SystemsAdvanced Optimization Algorithms Research

Nonlinear Reference Tracking: An Economic Model Predictive Control Perspective

Kohler, Johannes, Muller, Matthias A., Allgower, Frank·2019·IEEE Transactions on Automatic Control
DOI 10.1109/tac.2018.2800789
Open this paper in CoChat — free account

Abstract

In this paper, we study the system theoretic properties of a reference tracking model predictive control (MPC) scheme for general reference trajectories and nonlinear discrete-time systems subject to input and state constraints. Contrary to other existing theoretical results for reference tracking MPC, we do not modify the optimization problem with artificial references or terminal ingredients. Instead, we consider a simple, intuitive implementation and derive theoretical guarantees under a stabilizability condition on the system and suitable conditions on the reference trajectory. We provide sufficient conditions for exponential reference tracking for reachable reference trajectories. In addition, we study unreachable reference trajectories and derive sufficient conditions to ensure practical stability of the unknown optimal reachable reference trajectory. For both cases, we characterize the region of attraction. The results build on the notion of incremental stabilizability, strict dissipativity, and results in (economic) MPC without terminal constraints.

Integrity signals

Registry

Crossref · 10.1109/tac.2018.2800789

Cites

45 of 45 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • In existing MPC without terminal ingredients, prediction is based on a nominal model requiring identification of the nominal model with high precision, whereas the proposed IMPC employs the incremental model based on TDE and thus it is not necessary to identify the model of f(x) and g(x).

    “In existing MPC without terminal ingredients, comparing [17] and [18], the prediction is based on a nominal model. This requires to first identify the nominal model of the plant with high precision, whereas the proposed IMPC approach employs the incremental model based on TDE and, thus, it is not necessary to identify the model of f ( x ) and g ( x ) in (2b).”

    From Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator (2022) · cites this paper as [18]

  • Due to the zooming technique, the minimal N is very conservative.

    “Due to the zooming technique, this minimal N is very conservative (normally overestimated, compare [18]).”

    From Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator (2022) · cites this paper as [18]

  • Due to uncertainties and/or disturbances, the Lyapunov stability established for the nominal system is not simply transferable, and input-to-state stability is required to be considered.

    “Due to uncertainties and/or disturbances, the Lyapunov stability that was established for the nominal system is not simply transferable [17], [18], and input-to-state stability (ISS), also known as practical Lyapunov stability, is required to be considered.”

    From Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator (2022) · cites this paper as [18]

Cites

Flagged first, then by citations

Cited by

Sorted by citations

Related

Authors
Kohler, J., Muller, M. A., & Allgower, F.
ORCID
Venue
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2019-01
Volume
64
Issue
1
Pages
254-269
ISSN
  • 0018-9286 (ISSN-L)
  • 1558-2523
  • 2334-3303
DOI
10.1109/tac.2018.2800789
OpenAlex
W2794065691
Cited by
115
References
45
Citations by year
2026: 4 · 2025: 19 · 2024: 17 · 2023: 19 · 2022: 10 · 2021: 11 · 2020: 18 · 2019: 10 · 2018: 7
FWCI
7.12
Type
journal article
Language
en
Open access
closed
Licence
Locations
IEEE Transactions on Automatic Control (publishedVersion)
Funders
  • German Research Foundation through the project within the International Research Training Group Soft Tissue Robotics (GRK 2198/1)
  • Baden-Württemberg Stiftung through the Eliteprogramme for Postdocs
Topics
  • Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
  • Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
  • Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
Keywords
reference tracking, economic model predictive control, discrete-time nonlinear systems, state and input constraints, exponential tracking, practical stability, domain of attraction, strict dissipativity

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review