Abstract
In this chapter, the problem of regulating a constrained uncertain and/or time-varying linear discrete-time system to the origin subject to bounded disturbances is addressed. The robust counterpart of the interpolation technique generalizes the results presented in the previous chapter, recursive feasibility and robustly asymptotic stability being preserved. In the implicit case, depending on the shape of invariant sets, i.e. polyhedral or ellipsoidal, and depending on the objective functions, i.e. linear or quadratic, at most two LPs or one QP or one LMI problems are solved on-line at each time instant. In the explicit case, the control law is shown to be a piecewise affine function of state.
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References
Blanchini, F., Miani, S.: Constrained stabilization via smooth Lyapunov functions. Syst. Control Lett. 35(3), 155–163 (1998)
Jiang, Z.P., Wang, Y.: Input-to-state stability for discrete-time nonlinear systems. Automatica 37(6), 857–869 (2001)
Kothare, M.V., Balakrishnan, V., Morari, M.: Robust constrained model predictive control using linear matrix inequalities. Automatica 32(10), 1361–1379 (1996)
Langson, W., Chryssochoos, I., Raković, S., Mayne, D.: Robust model predictive control using tubes. Automatica 40(1), 125–133 (2004)
Lazar, M., de la Pena, D.M., Heemels, W., Alamo, T.: On input-to-state stability of min-max nonlinear model predictive control. Syst. Control Lett. 57(1), 39–48 (2008)
Marruedo, D.L., Alamo, T., Camacho, E.: Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties. In: Proceedings of the 41st IEEE Conference on Decision and Control, vol. 4, pp. 4619–4624. IEEE Press, New York (2002)
Olaru, S., De Doná, J.A., Seron, M., Stoican, F.: Positive invariant sets for fault tolerant multisensor control schemes. Int. J. Control 83(12), 2622–2640 (2010)
Pluymers, B., Rossiter, J., Suykens, J., De Moor, B.: Interpolation based MPC for LPV systems using polyhedral invariant sets. In: Proceedings of the 2005 American Control Conference, pp. 810–815. IEEE Press, New York (2005)
Rakovic, S.V., Kerrigan, E.C., Kouramas, K.I., Mayne, D.Q.: Invariant approximations of the minimal robust positively invariant set. IEEE Trans. Autom. Control 50(3), 406–410 (2005)
Sontag, E.D., Wang, Y.: On characterizations of the input-to-state stability property. Syst. Control Lett. 24(5), 351–359 (1995)
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Nguyen, HN. (2014). Interpolating Control—Robust State Feedback Case. In: Constrained Control of Uncertain, Time-Varying, Discrete-Time Systems. Lecture Notes in Control and Information Sciences, vol 451. Springer, Cham. https://doi.org/10.1007/978-3-319-02827-9_5
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DOI: https://doi.org/10.1007/978-3-319-02827-9_5
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