Advertisement

Distributed MPC of Interconnected Nonlinear Systems by Dynamic Dual Decomposition

  • A. GrancharovaEmail author
  • T. A. Johansen
Chapter
Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA, volume 69)

Abstract

A suboptimal approach to distributed Nonlinear Model Predictive Control (NMPC) for systems consisting of nonlinear subsystems with nonlinearly coupled dynamics subject to both state and input constraints is proposed. The approach applies a dynamic dual decomposition method to reformulate the original centralized NMPC problem into a distributed quasi-NMPC problem by linearization of the nonlinear system dynamics and taking into account the couplings between the subsystems. The developed approach is based entirely on distributed on-line optimization (by gradient iterations) and can be applied to large-scale nonlinear systems. The theoretical results related to the application of the distributed MPC approach to both linear and nonlinear systems are outlined and some simulation results are provided.

Keywords

Input Constraint Linear Subsystem Nonlinear Model Predictive Control Price Sequence Nonlinear Subsystem 
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.

References

  1. 1.
    S. Boyd, L. Vandenberghe, in Convex Optimization (Cambridge University Press, Cambridge, 2004)Google Scholar
  2. 2.
    A. Bryson, Y. Ho, Applied Optimal Control: Optimization Estimation and Control (Blaisdell, Waltham, 1969)Google Scholar
  3. 3.
    G. Cohen, B. Miara, Optimization with an auxiliary constraint and decomposition. SIAM J. Control Optim. 28, 137–157 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    G.A. Constantinides. Parallel architectures for model predictive control, in Proceedings of the European Control Conference, pp 138–143, Budapest, Hungary, 2009Google Scholar
  5. 5.
    G.B. Dantzig, P. Wolfe, The decomposition algorithm for linear programs. Econometrica 29, 767–778 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    W.B. Dunbar, R.M. Murray, Distributed receding horizon control for multi-vehicle formation stabilization. Automatica 42, 549–558 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    P. Giselsson, A. Rantzer, Distributed model predictive control with suboptimality and stability guarantees, in Proceedings of the IEEE Conference on Decision and Control, pp. 7272–7277, Atlanta, GA, (2010)Google Scholar
  8. 8.
    A. Grancharova, E.I. Grøtli, T.A. Johansen, Distributed path planning for a UAV communication chain by dual decomposition, in Proceedings of the 2nd IFAC Workshop on Multivehicle Systems, Espoo, Finland, (2012)Google Scholar
  9. 9.
    A. Grancharova, T.A. Johansen, Distributed quasi-nonlinear model predictive control by dual decomposition, in Proceedings of the 18-th IFAC World Congress, pp. 1429–1434, Milano, Italy, (2011)Google Scholar
  10. 10.
    A. Grancharova, T.A. Johansen, Suboptimality analysis of distributed quasi-nonlinear model predictive control, in Proceedings of the IFAC Conference on Nonlinear Model Predictive Control, NMPC’12 (Noordwijkerhout, Netherlands, 2012)Google Scholar
  11. 11.
    T. Keviczky, F. Borrelli, G.J. Balas, Decentralized receding horizon control for large scale dynamically decoupled systems. Automatica 42, 2105–2115 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    T.H. Kim, T. Sugie, Robust decentralized MPC algorithm for a class of dynamically interconnected constrained systems, in Proceedings of the IEEE Conference on Decision and Control, pp. 290–295, Seville, Spain, (2005)Google Scholar
  13. 13.
    W.C. Li, L.T. Biegler, Multistep, Newton-type control strategies for constrained nonlinear processes. Chem. Eng. Res. Des. 67, 562–577 (1989)Google Scholar
  14. 14.
    L. Magni, R. Scattolini, Stabilizing decentralized model predictive control of nonlinear systems. Automatica 42, 1231–1236 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    R.R. Negenborn, Multi-Agent Model Predictive Control with Applications to Power Networks. PhD thesis, Delft University of Technology, Delft, Netherlands, December 2007Google Scholar
  16. 16.
    N.M.C. Oliveira, L.T. Biegler, An extension of Newton-type algorithms for nonlinear process control. Automatica 31, 281–286 (1995)CrossRefzbMATHGoogle Scholar
  17. 17.
    A. Rantzer, Dynamic dual decomposition for distributed control, in Proceedings of the American Control Conference, pp. 884–888, St. Louis, MO, USA, (2009)Google Scholar
  18. 18.
    R. Scattolini, Architectures for distributed and hierarchical model predictive control: a review. J. Process Control 19, 723–731 (2009)CrossRefGoogle Scholar
  19. 19.
    A.N. Venkat, J.B. Rawlings, S.J. Wright, Plant-wide optimal control with decentralized MPC, in Proceedings of the IFAC Conference on Dynamics and Control of Process Systems, Boston, MA, (2004)Google Scholar
  20. 20.
    Y. Zhang, S. Li, Networked model predictive control based on neighbourhood optimization for serially connected large-scale processes. J. Process Control 17, 37–50 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Institute of System Engineering and RoboticsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Department of Industrial AutomationUniversity of Chemical Technology and MetallurgySofiaBulgaria
  3. 3.Department of Engineering CyberneticsNorwegian University of Science and TechnologyTrondheimNorway

Personalised recommendations