Enlarging the domain of attraction of MPC controllers. (English) Zbl 1061.93045

Summary: This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost.
In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC.


93B51 Design techniques (robust design, computer-aided design, etc.)
93D20 Asymptotic stability in control theory
Full Text: DOI


[1] Bertsekas, D.P., On the minimax reachability of target sets and target tubes, Automatica, 7, 233-247, (1971) · Zbl 0215.21801
[2] Blanchini, F., Set invariance in control, Automatica, 35, 1747-1767, (1999) · Zbl 0935.93005
[3] Bravo, J. M., Limon, D., Alamo, T., & Camacho, E. (2003). On the computation of invariant sets for constrained nonlinear systems: an interval arithmetic approach. In Proceedings of the ECC. · Zbl 1086.93035
[4] Camacho, E. F., & Bordons, C. (2004). Model predictive control. (2nd ed.), Berlin: Springer. · Zbl 1080.93001
[5] Cannon, M.; Deshmukh, V.; Kouvaritakis, B., Nonlinear model predictive control with polytopic invariant sets, Automatica, 39, 1487-1494, (2003) · Zbl 1033.93022
[6] Chen, H.; Allgöwer, F., A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability, Automatica, 34, 10, 1205-1218, (1998) · Zbl 0947.93013
[7] Chen, W., Ballance, D., & O’Reilly, J. (2001). Optimisation of attraction domains of nonlinear MPC via LMI methods. In Proceedings of the ACC.
[8] De Doná, J.A.; Seron, M.M.; Mayne, D.Q.; Goodwin, G.C., Enlarged terminal sets guaranteeing stability of receding horizon control, Systems & control letters, 47, 57-63, (2002) · Zbl 1094.93544
[9] Limon, D., Alamo, T., & Camacho, E. F. (2002). Stability analysis of systems with bounded additive uncertainties based on invariant sets: Stability and feasibility of MPC. In Proceedings of the ACC.
[10] Limon, D., Alamo, T., & Camacho, E. F. (2003). Stable constrained MPC without terminal constraint. In Proceedings of the ACC. · Zbl 1366.93483
[11] Limon, D., Gomes da Silva, J., Alamo, T., & Camacho, E. F. (2003). Improved MPC design based on saturating control laws. In Proceedings of the ECC. · Zbl 1293.93296
[12] Magni, L.; De Nicolao, G.; Magnani, L.; Scattolini, R., A stabilizing model-based predictive control algorithm for nonlinear systems, Automatica, 37, 1351-1362, (2001) · Zbl 0995.93033
[13] Mayne, D.Q.; Rawlings, J.B.; Rao, C.V.; Scokaert, P.O.M., Constrained model predictive controlstability and optimality, Automatica, 36, 789-814, (2000) · Zbl 0949.93003
[14] Michalska, H.; Mayne, D.Q., Robust receding horizon control of constrained nonlinear systems, IEEE transactions on automatic control, 38, 11, 1623-1633, (1993) · Zbl 0790.93038
[15] Scokaert, P.O.M.; Mayne, D.Q.; Rawlings, J.B., Suboptimal model predictive control (feasibility implies stability), IEEE transactions on automatic control, 44, 3, 648-654, (1999) · Zbl 1056.93619
[16] Scokaert, P.O.M.; Rawlings, J.B.; Meadows, E.S., Discrete-time stability with perturbationsapplication to model predictive control, Automatica, 33, 3, 463-470, (1997) · Zbl 0876.93064
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.