A Distributed NMPC Scheme without Stabilizing Terminal Constraints

  • Lars Grüne
  • Karl Worthmann
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 417)


We consider a distributed NMPC scheme in which the individual systems are coupled via state constraints. In order to avoid violation of the constraints, the subsystems communicate their individual predictions to the other subsystems once in each sampling period. For this setting, Richards and How have proposed a sequential distributed MPC formulation with stabilizing terminal constraints. In this chapter we show how this scheme can be extended to MPC without stabilizing terminal constraints or costs.We show theoretically and by means of numerical simulations that under a suitable controllability condition stability and feasibility can be ensured even for rather short prediction horizons.


Optimal Control Problem State Constraint Model Predictive Control Control Sequence Nonlinear Model Predictive Control 
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  1. 1.
    Altmüller, N., Grüne, L., Worthmann, K.: Performance of NMPC schemes without stabilizing terminal constraints. In: Diehl, M., et al. (eds.) Recent Advances in Optimization and Its Applications in Engineering, pp. 289–298. Springer, London (2010)CrossRefGoogle Scholar
  2. 2.
    Altmüller, N., Griine, L., Worthmann, K.: Receding horizon optimal control for the wave equation. In: Proc. 49th IEEE Conf. Decision and Control (CDC 2010), Atlanta, GA, pp. 3427–3432 (2010)Google Scholar
  3. 3.
    Dashkovskiy, S., Rüffer, B.S., Wirth, F.R.: An ISS small gain theorem for general networks. Math. Control Signals Systems 19(2), 93–122 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Giselsson, P., Rantzer, A.: Distribited model predictive control with siboptimality and stability giarantees. In: Proc. 49th IEEE Conference on Decision and Control (CDC 2010), Atlanta, GA, pp. 7272–7277 (2010)Google Scholar
  5. 5.
    Grimm, G., Messina, M.J., Tuna, S.E., Teel, A.R.: Model predictive control: For want of a local control Lyapunov finction, all is not lost. IEEE Trans. Automatic Control, 546–558 (2005)Google Scholar
  6. 6.
    Grüne, L., Pannek, J.: Nonlinear Model Predictive Control. Theory and Algorithms. Springer, London (2011)zbMATHCrossRefGoogle Scholar
  7. 7.
    Grüne, L., Pannek, J., Seehafer, M., Worthmann, K.: Analysis of iinconstrained nonlinear MPC schemes with varying control horizon. SIAM J. Control Optimization 48, 4938–4962 (2010)zbMATHCrossRefGoogle Scholar
  8. 8.
    Grüne, L.: Analysis and design of iinconstrained nonlinear MPC schemes for finite and infinite dimensional systems. SIAM J. Control Optimization 48, 1206–1228 (2009)zbMATHCrossRefGoogle Scholar
  9. 9.
    Jadbabaie, A., Hauser, J.: On the stability of receding horizon control with a general terminal cost. IEEE Trans. Aromatic Control 50(5), 674–678 (2005)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: stability and optimality. Automatica 36, 789–814 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Primbs, J., Nevistić, V.: Feasibility and stability of constrained finite receding horizon control. Automatica 36(7), 965–971 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Rawlings, J.B., Mayne, D.Q.: Model Predictive Control: Theory and Design. Nob Hill Pib- lishing, Madison (2009)Google Scholar
  13. 13.
    Richards, A., How, J.P.: Robust distributed model predictive control. Int. J. Control 80(9), 1517–1531 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Richards, A., How, J.P.: A decentralized algorithm for robist constrained model predictive control. In: Proc. American Control Conf. (ACC 2004), Boston, MA, pp. 4261–4266 (2004)Google Scholar
  15. 15.
    Scattolini, R.: Architectires for distribited and hierarchical model predictive control—A review. J. Process Control 19(5), 723–731 (2009)CrossRefGoogle Scholar

Copyright information

© Springer London 2012

Authors and Affiliations

  • Lars Grüne
    • 1
  • Karl Worthmann
    • 1
  1. 1.Mathematical InstituteUniversity of BayreuthBayreuthGermany

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