D-SIORHC, Distributed MPC with Stability Constraints Based on a Game Approach

  • J. M. LemosEmail author
  • J. M. Igreja
Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA, volume 69)


This chapter describes D-SIORHC, a distributed MPC algorithm with stability constraints based on a game approach. This controller is designed for chained linear systems, in which each local subsystem interacts only with their neighbors. At the beginning of each sampling interval, each local controller agent computes the value of the corresponding manipulated variable in an iterative process where, in each iteration, it optimizes a quadratic cost by assuming that the neighbor controllers will use for their manipulated variables the value which they have computed in the previous iteration. Therefore, in a game theory framework, if this coordination procedure converges, a Nash equilibrium is reached. The use of linear plant models and the absence of inequality operational constraints allows to compute the manipulated variables in an explicit way, in each iteration of the coordination procedure, thereby reducing the computational load. This approach differs from other distributed MPC algorithms based on linear models in the inclusion of stability constraints in the local controllers that leads to a different control law. The controller usage is illustrated through its application to a water delivery canal.


Nash Equilibrium Tracking Error Coincidence Point Prediction Horizon Stability Constraint 
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.



This work was supported by FCT—Fundação para a Ciência e a Tecnologia, Portugal, under project AQUANET: Decentralized and reconfigurable control for water delivery multipurpose canal systems, contract PTDC/EEA-CRO/102102/2008, and INESC-ID multi-annual funding through PEst-OE/EEI/LA0021/2011.


  1. 1.
    T. Başar, G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd edn. (SIAM, Philadelphia, 1999)zbMATHGoogle Scholar
  2. 2.
    D. Georges, Decentralized adaptive control for a water distribution system, in Proceedings of the 3rd IEEE Conference on Control Applications, pp. 1411–1416 (1994)Google Scholar
  3. 3.
    J.M. Igreja, J.M. Lemos, F.M. Cadete, L.M. Rato, M. Rijo, Control of a water delivery canal with cooperative distributed mpc, in Proceedings of the 2012 Americain Control Conference, pp. 1961–1966, Montreal, Canada (2012)Google Scholar
  4. 4.
    J.M. Lemos, F. Machado, N. Nogueira, L. Rato, M. Rijo, Adaptive and non-adaptive model predictive control of an irrigation channel. Netw. Heterog. Media 4(2), 303–324 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    J.M. Lemos, L.F. Pinto, Distributed linear-quadratic control of serially chained systems: application to a water delivery canal. IEEE Control Syst. 32(6) (2012)Google Scholar
  6. 6.
    J.M. Maestre, D. Munoz de la Peña, E.F. Camacho, T. Alamo, Distributed model predictive control based on agent negotiation. J. Proc. Control 21, 685–697 (2011)CrossRefGoogle Scholar
  7. 7.
    E. Mosca, Optimal, Predictive, and Adaptive Control (Prentice Hall, Englewood Cliffs, 1995)Google Scholar
  8. 8.
    E. Mosca, J.M. Lemos, J. Zhang, Stabilizing i/o receding horizon control, in Proceedings of the 29th Conference on Decision and Control, pp. 2518–2523, Honolulu, Hawai (1990)Google Scholar
  9. 9.
    E. Mosca, J. Zhang, Stable redesign of predictive control. Automatica 28(6), 1229–1233 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    I. Necoara, V. Nedelcu, I. Dumitrache, Parallel and distributed optimization methods for estimation and control in networks. J. Proc. Control 21, 756–766 (2011)CrossRefGoogle Scholar
  11. 11.
    A.N. Venkat, I.A. Hiskens, J.B. Rawlings, S.J. Wright, Distributed mpc strategies with application to powet system generation control. IEEE Trans. Control Syst. Technol. 16, 1192–1206 (2008)CrossRefGoogle Scholar
  12. 12.
    Y. Zhang, S.Y. Li, Networked model predictive control based on neighbourhood optimization for serially connected large-scale processes. J. Process Control 17(1), 37–50 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.INESC-ID/IST/UTLLisboaPortugal
  2. 2.INESC-ID/ISEL/IPLLisboaPortugal

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