On optimality of nonlinear model predictive control. (English) Zbl 1120.93318
Summary: In this note the optimality property of nonlinear model predictive control (MPC) is analyzed. It is well known that the MPC approximates arbitrarily well the infinite horizon (IH) controller as the optimization horizon increases. Hence, it makes sense to suppose that the performance of the MPC is a not decreasing function of the optimization horizon. This work, by means of a counterexample, shows that the previous conjecture is fallacious, even for simple linear systems.
MSC:
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
| 93B35 | Sensitivity (robustness) |
| 90B30 | Production models |
| 93C55 | Discrete-time control/observation systems |
| 93C10 | Nonlinear systems in control theory |
References:
| [1] | Chen, C. C.; Shaw, L., On receding horizon feedback control, Automatica, 18, 3, 349-352 (1982) · Zbl 0479.93031 |
| [2] | Chen, H.; Allgöwer, F., A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability, Automatica, 34, 1205-1217 (1998) · Zbl 0947.93013 |
| [3] | De Nicolao, G.; Bitmead, R. R., Fake Riccati equations for stable receding-horizon control, (European Control Conference ’97. European Control Conference ’97, Bruxelles, 1-4 July (1997)) · Zbl 0854.93060 |
| [4] | De Nicolao, G.; Magni, L.; Scattolini, R., Stabilizing receding-horizon control of nonlinear time-varying systems, IEEE Trans. Autom. Control, AC-43, 1030-1036 (1998) · Zbl 0951.93063 |
| [5] | Hu, B.; Linnemann, A., Toward infinite-horizon optimality in nonlinear model predictive control, IEEE Trans. Autom. Control, 47, 679-682 (2002) · Zbl 1364.93339 |
| [6] | Magni, L.; De Nicolao, G.; Magnani, L.; Scattolini, R., A stabilizing model-based predictive control for nonlinear systems, Automatica, 37, 1351-1362 (2001) · Zbl 0995.93033 |
| [7] | Magni, L.; Sepulchre, R., Stability margins of nonlinear receding horizon control via inverse optimality, Systems Control Lett., 32, 241-245 (1997) · Zbl 0902.93061 |
| [8] | Mayne, D. Q.; Michalska, H., Receding horizon control of nonlinear systems, IEEE Trans. Autom. Control, 35, 814-824 (1990) · Zbl 0715.49036 |
| [9] | Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O.M., Constrained model predictive control: stability and optimality, Automatica, 36, 789-814 (2000) · Zbl 0949.93003 |
| [10] | Rawlings, J. B.; Muske, K. R., The stability of constrained receding horizon control, IEEE Trans. Autom. Control, 38, 1512-1516 (1993) · Zbl 0790.93019 |
| [11] | Vincent, T. L.; Grantham, W. J., Nonlinear and Optimal Control Systems (1997), Wiley: Wiley New York |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
