Adaptive model predictive control for a class of constrained linear systems based on the comparison model. (English) Zbl 1111.93036

Summary: This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.


93C40 Adaptive control/observation systems
93B51 Design techniques (robust design, computer-aided design, etc.)
93D25 Input-output approaches in control theory
93C05 Linear systems in control theory
93A30 Mathematical modelling of systems (MSC2010)
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI


[1] Badgwell, T. A., Robust model predictive control of stable linear systems, International Journal of Control, 68, 4, 797-818 (1997) · Zbl 0889.93025
[2] Blanchini, F., Set invariance in control, Automatica, 35, 11, 1747-1767 (1999) · Zbl 0935.93005
[3] Fukushima, H.; Bitmead, R. R., Robust constrained predictive control using comparison model, Automatica, 41, 1, 97-106 (2005) · Zbl 1067.93029
[5] Ioannou, P. A.; Sun, J., Robust adaptive control (1996), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0839.93002
[6] Kothare, M. V.; Balakrishnan, V.; Morari, M., Robust constrained model predictive control using linear matrix inequalities, Automatica, 32, 10, 1361-1379 (1996) · Zbl 0897.93023
[7] Krstić, M.; Kanellakopoulos, I.; Kokotović, P., Nonlinear and adaptive control design (1995), Wiley-Interscience: Wiley-Interscience New York · Zbl 0763.93043
[8] Lee, Y. I.; Kouvaritakis, B., Constrained receding horizon predictive control for systems with disturbances, International Journal of Control, 72, 11, 1027-1032 (1999) · Zbl 0962.93034
[9] Lee, Y. I.; Kouvaritakis, B., Robust receding horizon predictive control for systems with uncertain dynamics and input saturation, Automatica, 36, 10, 1497-1504 (2000) · Zbl 0966.93046
[10] Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O.M., Constrained model predictive control: Stability and optimality, Automatica, 36, 6, 789-814 (2000) · Zbl 0949.93003
[11] Michalska, H.; Mayne, D. Q., Robust receding horizon control of constrained nonlinear systems, IEEE Transactions on Automatic Control, 38, 11, 1623-1632 (1993) · Zbl 0790.93038
[12] Miller, R. K.; Michel, A. N., Ordinary differential equations (1982), Academic Press: Academic Press New York · Zbl 0499.34024
[13] Morari, M.; Lee, J. H., Model predictive control: past, present and future, Computers and Chemical Engineering, 23, 667-682 (1999)
[14] Rawlings, J. B., Tutorial overview of model predictive control, IEEE Control System Magazine, 20, 3, 38-52 (2000)
[15] Scokaert, P. O.M.; Mayne, D. Q., Min-max feedback model predictive control for constrained linear systems, IEEE Transactions on Automatic Control, 43, 8, 1136-1142 (1998) · Zbl 0957.93034
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