Finite horizon model predictive control with ellipsoid mapping of uncertain linear systems

Finite horizon model predictive control with ellipsoid mapping of uncertain linear systems

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A model predictive control scheme was proposed for discrete-time uncertain linear systems subject to input constraints. The cost functional to be minimised is a finite horizon quadratic cost, which describes the performance of the corresponding nominal system. The control action is specified in terms of both feedback and open-loop components. The open-loop part of the control action steers the centre of associated ellipsoids into a set around the origin, while the feedback component forces the actual system states to remain in those ellipsoids. Both feedback and open-loop control are determined online by repeatedly solving a convex optimisation problem. The predictive control scheme guarantees recursive feasibility and robust stability if the convex optimisation problem is feasible at the initial time instant. A numerical example illustrates the effectiveness of the proposed approach.


    1. 1)
    2. 2)
    3. 3)
    4. 4)
    5. 5)
    6. 6)
      • Findeisen, R.: `Nonlinear model predictive control: a sampled-data feedback perspective', 2004, PhD, University of Stuttgart, Germany.
    7. 7)
    8. 8)
    9. 9)
    10. 10)
      • Chen, H., Scherer, C.W., Allgöwer, F.: `A game theoretic approach to nonlinear robust receding horizon control of constrained systems', Proc. American Control Conf, 1997, Albuquerque, New Mexico, p. 3073–3077.
    11. 11)
    12. 12)
    13. 13)
    14. 14)
    15. 15)
    16. 16)
    17. 17)
    18. 18)
    19. 19)
    20. 20)
      • Yu, S.-Y., Böhm, C., Chen, H., Allgöwer, F.: `Stabilizing model predictive control for LPV systems subject to constraints with parameter-dependent control law', Proc. American Control Conf, 2009, St. Louis, Missouri, p. 3118–3123.
    21. 21)
    22. 22)
      • B.G. Park , J.W. Lee , W.H. Kwon . Robust one-step receding horizon control for constrained systems. Int. J. Robust Nonlinear Control , 7 , 381 - 395
    23. 23)
      • Yu, S.-Y., Böhm, C., Chen, H., Allgöwer, F.: `MPC with one free control action for constrained LPV systems', Proc. IEEE Int. Conf. Control Applications, 2010, Yokohama, Japan, p. 1343–1348.
    24. 24)
    25. 25)
      • Smith, R.S.: `Robust model predictive control of constrained linear systems', Proc. American Control Conf., 2004, Boston, p. 245–250.
    26. 26)
      • Smith, R.S.: `Model predictive control of uncertain constrained linear systems: LMI based methods', Technical Report CUED/F-INFENG/TR.462, 2006.
    27. 27)
      • S. Boyd , L.E. Ghaoui , E. Feron , V. Balakrishnan . (1994) Linear matrix inequalities in system and control theory.
    28. 28)
    29. 29)
    30. 30)
      • Yu, S.-Y., Böhm, C., Chen, H., Allgöwer, F.: `Robust model predictive control with disturbance invariant sets', Proc. American Control Conf., 2010, Baltimore, MD, p. 6262–6267.
    31. 31)
      • S. Boyd , L. Vandenberghe . (2004) Convex optimization.
    32. 32)
      • Marruedo, D.L., Alamo, T., Camacho, E.F.: `Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties', Proc. 41th IEEE Conf. Decision Control, 2002, p. 4619–4624.

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