A novel robust model predictive control approach with pseudo terminal designs. (English) Zbl 1451.93109
Summary: Robust model predictive control (RMPC) has gained much attention in the past two decades. For classic finite-horizon RMPC, a terminal constraint set together with a terminal cost function are usually employed for the purpose of closed-loop stability. However, computational burden and feasibility region may need to be carefully addressed when the prediction horizon length becomes large, especially for the cases with additive disturbances. In this paper, a novel RMPC approach with pseudo terminal designs is proposed. Specifically, a bank of pseudo terminal sets (PTSs) are designed given a predefined terminal constraint set. Besides, a pseudo terminal cost (PTC) term is considered for each PTS. With the proposed approach, a long-horizon RMPC problem can be divided into several short-horizon ones. It is shown that both the PTSs and the corresponding PTCs can be computed off-line recursively. In the online implementation, selecting a PTS is realized in a self-triggered way. Meanwhile, a time-varying cost function, which is always an upper bound of the infinite-horizon cost function, is optimized online.
MSC:
| 93B45 | Model predictive control |
| 93B35 | Sensitivity (robustness) |
| 93C05 | Linear systems in control theory |
Keywords:
robust model predictive control; off-line computation; affine causal controller; self-triggered cost functionReferences:
| [1] | Angeli, D.; Casavola, A.; Franzè, G.; Mosca, E., An ellipsoidal off-line MPC scheme for uncertain polytopic discrete-time systems, Automatica, 44, 3113-3119 (2008) · Zbl 1153.93363 |
| [2] | Bacic, M.; Cannon, M.; Lee, Y. I.; Kouvaritakis, B., General interpolation in MPC and its advantages, IEEE Trans. Autom. Control, 48, 1092-1096 (2003) · Zbl 1364.93232 |
| [3] | Borrelli, F.; Bemporad, A.; Morari, M., Predictive Control for Linear and Hybrid Systems (2017), Cambridge University Press · Zbl 1365.93003 |
| [4] | Bumroongsri, P.; Kheawhom, S., An ellipsoidal off-line model predictive control strategy for linear parameter varying systems with applications in chemical processes, Syst. Control Lett., 61, 435-442 (2012) · Zbl 1250.93053 |
| [5] | Cao, Y.; Frank, P. M., Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach, IEEE Trans. Fuzzy Syst., 8, 200-211 (2000) |
| [6] | Chisci, L.; Rossiter, J. A.; Zappa, G., Systems with persistent disturbances: predictive control with restricted constraints, Automatica, 37, 1019-1028 (2001) · Zbl 0984.93037 |
| [7] | Ding, B.; Xi, Y.; Cychowski, M. T.; OMahony, T., Improving off-line approach to robust MPC based-on nominal performance cost, Automatica, 43, 158-163 (2007) · Zbl 1140.93366 |
| [8] | Goulart, P. J.; Kerrigan, E. C.; Maciejowski, J. M., Optimization over state feedback policies for robust control with constraints, Automatica, 42, 523-533 (2006) · Zbl 1102.93017 |
| [9] | Henrion, D.; Lofberg, J.; Kocvara, M.; Stingl, M., Solving polynomial static output feedback problems with PENBMI, Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 7581-7586 (2005) |
| [10] | Kim, S. H., Model predictive control algorithm based on off-line region dependency, Math. Prob. Eng., 2016 (2016) · Zbl 1400.93173 |
| [11] | Kothare, M. V.; Balakrishnan, V.; Morari, M., Robust constrained model predictive control using linear matrix inequalities, Automatica, 32, 1361-1379 (1996) · Zbl 0897.93023 |
| [12] | Kouvaritakis, B.; Cannon, M., Model Predictive Control (2016), Springer · Zbl 0909.93024 |
| [13] | Lazar, M.; Heemels, W. P.M. H.; De La Peña, D. M.; Alamo, T., Further results on robust MPC using linear matrix inequalities, Nonlinear Model Predictive Control, 89-98 (2009), Springer · Zbl 1195.93033 |
| [14] | Lee, J. H., Model predictive control: review of the three decades of development, Int. J. Control Autom. Syst., 9, 415-424 (2011) |
| [15] | Limon, D.; Alamo, T.; Camacho, E. F., Enlarging the domain of attraction of MPC controllers, Automatica, 41, 629-635 (2005) · Zbl 1061.93045 |
| [16] | Liu, C.; Li, H.; Gao, J.; Xu, D., Robust self-triggered min – max model predictive control for discrete-time nonlinear systems, Automatica, 89, 333-339 (2018) · Zbl 1388.93038 |
| [17] | Löfberg, J., Yalmip: a toolbox for modeling and optimization in MatLab, Proceedings of the IEEE International Symposium on Computer Aided Control Systems Design, New Orleans, LA, 284-289 (2004) |
| [18] | Lu, Y.; Arkun, Y., Quasi-min-max MPC algorithms for LPV systems, Automatica, 36, 527-540 (2000) · Zbl 0981.93027 |
| [19] | Magni, L.; Raimondo, D. M.; Scattolini, R., Regional input-to-state stability for nonlinear model predictive control, IEEE Trans. Autom. Control, 51, 1548-1553 (2006) · Zbl 1366.93608 |
| [20] | Mayne, D.; Langson, W., Robustifying model predictive control of constrained linear systems, Electron. Lett., 37, 1422-1423 (2001) |
| [21] | Mayne, D. Q., Model predictive control: recent developments and future promise, Automatica, 50, 2967-2986 (2014) · Zbl 1309.93060 |
| [22] | Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O., Constrained model predictive control: stability and optimality, Automatica, 36, 789-814 (2000) · Zbl 0949.93003 |
| [23] | Pluymers, B.; Roobrouck, L.; Buijs, J.; Suykens, J. A.; De Moor, B., Constrained linear MPC with time-varying terminal cost using convex combinations, Automatica, 41, 831-837 (2005) · Zbl 1093.93012 |
| [24] | Pluymers, B.; Suykens, J. A.; De Moor, B., Min – max feedback MPC using a time-varying terminal constraint set and comments on efficient robust constrained model predictive control with a time-varying terminal constraint set, Syst. Control Lett., 54, 1143-1148 (2005) · Zbl 1129.93486 |
| [25] | Skaf, J.; Boyd, S., Design of affine controllers via convex optimization, IEEE Trans. Autom. Control, 55, 2476-2487 (2010) · Zbl 1368.93667 |
| [26] | Sugeno, M.; Kang, G., Structure identification of fuzzy model, Fuzzy Sets Syst., 28, 15-33 (1988) · Zbl 0652.93010 |
| [27] | Tahir, F.; Jaimoukha, I. M., Causal state-feedback parameterizations in robust model predictive control, Automatica, 49, 2675-2682 (2013) · Zbl 1364.93195 |
| [28] | Wan, Z.; Kothare, M. V., Robust output feedback model predictive control using off-line linear matrix inequalities, J. Process Control, 12, 763-774 (2002) |
| [29] | Wan, Z.; Kothare, M. V., Efficient robust constrained model predictive control with a time varying terminal constraint set, Syst. Control Lett., 48, 375-383 (2003) · Zbl 1157.93395 |
| [30] | W. Yang, G. Feng, T. Zhang, Robust model predictive control of uncertain linear systems with persistent disturbances and input constraints, in: Proceedings of the European Control Conference, Zurich, Switzerland, 2013, pp. 542-547.; W. Yang, G. Feng, T. Zhang, Robust model predictive control of uncertain linear systems with persistent disturbances and input constraints, in: Proceedings of the European Control Conference, Zurich, Switzerland, 2013, pp. 542-547. |
| [31] | Yang, W.; Feng, G.; Zhang, T., Robust model predictive control for discrete-time Takagi-Sugeno fuzzy systems with structured uncertainties and persistent disturbances, IEEE Trans. Fuzzy Syst., 22, 1213-1228 (2014) |
| [32] | Yang, W.; Feng, G.; Zhang, T., Decreasing-horizon robust model predictive control with specified settling time to a terminal constraint set, Asian J. Control, 18, 664-673 (2016) · Zbl 1346.93169 |
| [33] | Zhu, K.; Song, Y.; Ding, D.; Wei, G.; Liu, H., Robust MPC under event-triggered mechanism and round-robin protocol: an average dwell-time approach, Inf. Sci. (Ny), 457, 126-140 (2018) · Zbl 1448.93082 |
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