Cooperative Tube-based Distributed MPC for Linear Uncertain Systems Coupled Via Constraints

  • P. A. TroddenEmail author
  • A. G. Richards
Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA, volume 69)


This chapter presents a robust form of distributed model predictive control for multiple, dynamically decoupled subsystems subject to bounded, persistent disturbances. Control agents make decisions locally and exchange plans; satisfaction of coupling constraints is ensured by permitting only non-coupled subsystems to update simultaneously. Robustness to disturbances is achieved by use of the tube MPC concept, in which a local control agent designs a tube, rather than a trajectory, for its subsystem to follow. Cooperation between agents is promoted by a local agent, in its optimization, designing hypothetical tubes for other subsystems, and trading local performance for global. Uniquely, robust feasibility and stability are maintained without the need for negotiation or bargaining between agents.


Model Predictive Control Constraint Satisfaction Local Constraint Nash Solution Terminal Cost 
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  1. 1.
    W.B. Dunbar, Distributed receding horizon control of dynamically coupled nonlinear systems. IEEE Trans. Autom. Control 52 (7), 1249–1263 (2007)Google Scholar
  2. 2.
    T. Keviczky, F. Borrelli, G.J. Balas, Decentralized receding horizon control for large scale dynamically decoupled systems. Automatica 42(12), 2105–2115 (2006)Google Scholar
  3. 3.
    I. Kolmanovsky, E.G. Gilbert, Theory and computation of disturbance invariant sets for discrete-time linear systems. Mathematical Problems in Engineering 4, 317–367 (1998)Google Scholar
  4. 4.
    Y. Kuwata, J.P. How, Cooperative distributed robust trajectory optimization using receding horizon MILP. IEEE Transactions on Control Systems Technology 19(2), 423–431 (2011)Google Scholar
  5. 5.
    D.Q. Mayne, J.B. Rawlings, C.V. Rao, P.O.M. Scokaert, Constrained model predictive control: Stability and optimality. Automatica 36, 789–814 (2000)Google Scholar
  6. 6.
    D.Q. Mayne, M.M. Seron, S.V. Raković, Robust model predictive control of constrained linear systems with bounded disturbances. Automatica 41(2), 219–224 (2005)Google Scholar
  7. 7.
    A.G. Richards, J.P. How, Robust distributed model predictive control. International Journal of Control 80(9), 1517–1531 (2007)Google Scholar
  8. 8.
    B.T. Stewart, A.N. Venkat, J.B. Rawlings, S.J. Wright, G. Pannocchia, Cooperative distributed model predictive control. Systems & Control Letters 59, 460–469 (2010)Google Scholar
  9. 9.
    P. A. Trodden, D. Nicholson, A. G. Richards, Distributed model predictive control as a game with coupled constraints, In Proceedings of the European Control Conference, pp. 2996–3001, 2009Google Scholar
  10. 10.
    P. A. Trodden, A. G. Richards, Robust distributed model predictive control using tubes. In Proceedings of the American Control Conference, pp. 2034–2039, 2006Google Scholar
  11. 11.
    P. A. Trodden, A. G. Richards. Robust distributed model predictive control with cooperation. In Proceedings of the European Control Conference, pp. 2172–2178, 2007Google Scholar
  12. 12.
    P. A. Trodden and A. G. Richards, Multi-vehicle cooperative search using distributed model predictive control, In AIAA Guidance, Navigation, and Control Conference, 2008Google Scholar
  13. 13.
    P.A. Trodden, A.G. Richards, Adaptive cooperation in robust distributed model predictive control, In Proceedings of the IEEE Multi-conference on Systems and Control, 2009Google Scholar
  14. 14.
    P.A. Trodden, A.G. Richards, Distributed model predictive control of linear systems with persistent disturbances. International Journal of Control 83(8), 1653–1663 (2010)Google Scholar
  15. 15.
    A.N. Venkat, I.A. Hiskens, J.B. Rawlings, S.J. Wright, Distributed MPC strategies with application to power system automatic generation control. IEEE Transaction on Control System Technology 16(6), 1192–1206 (2008)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Automatic Control and Systems EngineeringUniversity of SheffieldSheffieldUK
  2. 2.Department of Aerospace EngineeringUniversity of BristolBristolUK

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