Performance of NMPC Schemes without Stabilizing Terminal Constraints

  • Nils AltmüllerEmail author
  • Lars Grüne
  • Karl Worthmann
Conference paper


In this paper we investigate the performance of unconstrained nonlinear model predictive control (NMPC) schemes, i.e., schemes in which no additional terminal constraints or terminal costs are added to the finite horizon problem in order to enforce stability properties. The contribution of this paper is twofold: on the one hand in Section 3 we give a concise summary of recent results from [7, 3, 4] in a simplified setting. On the other hand, in Section 4 we present a numerical case study for a control system governed by a semilinear parabolic PDE which illustrates how our theoretical results can be used in order to explain the differences in the performance of NMPC schemes for distributed and boundary control.


Model Predictive Control Horizon Problem Numerical Case Study Terminal Constraint Terminal Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Allgöwer F, Zheng A, eds. (2000), Nonlinear model predictive control,Birkhäuser, BaselzbMATHGoogle Scholar
  2. 2.
    Altmüller N, Grüne L,Worthmann K (2010), Instantaneous control of the linear wave equation, Proceedings of MTNS 2010, Budapest, Hungary, to appearGoogle Scholar
  3. 3.
    Grüne L (2009) Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems, SIAM J. Control Optim., 48, pp. 1206–1228zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Grüne L, Pannek J, Seehafer M, Worthmann K (2009), Analysis of unconstrained nonlinear MPC schemes with time varying control horizon, Preprint, Universität Bayreuth; submittedGoogle Scholar
  5. 5.
    Grüne L, Pannek J, Worthmann K (2009), A networked unconstrained nonlinear MPC scheme, Proceedings of ECC 2009, Budapest, Hungary, pp. 371–376Google Scholar
  6. 6.
    Grüne L, Nešić D (2003), Optimization based stabilization of sampled–data nonlinear systems via their approximate discrete-time models, SIAM J. Control Optim., 42, pp. 98–122zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Grüne L, Rantzer A (2008), On the infinite horizon performance of receding horizon controllers, IEEE Trans. Automat. Control, 53, pp. 2100–2111CrossRefMathSciNetGoogle Scholar
  8. 8.
    Qin S, Badgwell T (2003), A survey of industrial model predictive control technology, Control Engineering Practice, 11, pp. 733–764CrossRefGoogle Scholar
  9. 9.
    Rawlings JB, Mayne DQ (2009), Model Predictive Control: Theory and Design, Nob Hill Publishing, MadisonGoogle Scholar

Copyright information

© Springer -Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Mathematical Institute, University of BayreuthBayreuthGermany

Personalised recommendations