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Research Papers

Developments in Robust and Stochastic Predictive Control in the Presence of Uncertainty

[+] Author and Article Information
B. Kouvaritakis

Department of Engineering Science, Oxford University, Oxford OX1 3PJ, UKe-mail: basil.kouvaritakis@eng.ox.ac.uk

M. Cannon

Department of Engineering Science, Oxford University, Oxford OX1 3PJ, UKe-mail: mark.cannon@eng.ox.ac.uk

Manuscript received July 30, 2014; final manuscript received October 29, 2014; published online April 20, 2015. Assoc. Editor: Athanasios Pantelous.

ASME J. Risk Uncertainty Part B 1(2), 021003 (Apr 20, 2015) (9 pages) Paper No: RISK-14-1034; doi: 10.1115/1.4029744 History: Received July 30, 2014; Accepted February 05, 2015; Online April 20, 2015

Model-based predictive control (MPC), arguably the most effective control methodology for constrained systems, has seen rapid growth over the last few decades. The theory of classical MPC is well established by now, and robust MPC (RMPC) that deals with uncertainty (either in the form of additive disturbance or imprecise and/or time-varying knowledge of the system parameters) is itself reaching a state of maturity. There have been a number of new developments reported in the area of stochastic MPC (SMPC), which deals with the case where uncertainty is random and some or all of the constraints are probabilistic. The present paper surveys these developments, setting the scene by first discussing the key ingredients of classical MPC, then highlighting some major contributions in RMPC, and finally, describing recent results in SMPC. The discussion of the latter is restricted to uncertainty with bounded support, which is consistent with practice and provides the basis for the establishment of control theoretic properties, such as recurrent feasibility, stability, and convergence.

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References

Kailath, T., 1980, Linear Systems, Prentice-Hall, New York.
Mayne, D. Q., Rawlings, J. B., Rao, C. V., and Scokaert, P. O. M., 2000, “Constrained Model Predictive Control: Stability and Optimality,” Automatica, 36(6), pp. 789–814. 10.1016/S0005-1098(99)00214-9
Gilbert, E. G., and Tan, K. T., 1991, “Linear Systems With State and Control Constraints: The Theory and Application of Maximal Output Admissible Sets,” IEEE Trans. Autom. Control, 36(9), pp. 1008–1020. 10.1109/9.83532
Kouvaritakis, B., Rossiter, J. A., and Chang, A. O. T., 1992, “Stable Generalised Predictive Control: An Algorithm With Guaranteed Stability,” Proc. IEE Pt-D, 139(4), pp. 349–362. [CrossRef]
Bertsekas, D. P., and Rhodes, I. B., 1973, “Sufficiently Informative Functions and the Minimax Feedback Control of Uncertain Dynamic Systems,” IEEE Trans. Autom. Control, 18(2), pp. 117–124. 10.1109/TAC.1973.1100241
Scokaert, P. O. M., and Mayne, D. Q., 1998, “Min-Max Feedback Model Predictive Control for Constrained Linear Systems,” IEEE Trans. Autom. Control, 43(8), pp. 1136–1142. 10.1109/9.704989
van Hessem, D. H., and Bosgra, O. H., 2002, “A Conic Reformulation of Model Predictive Control Including Bounded and Stochastic Disturbances Under State and Input Constraints,” Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, IEEE, pp. 4643–4648.
Löfberg, J., 2003, “Approximations of Closed-Loop MPC,” Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, IEEE, pp. 1438–1442.
Goulart, P. J., Kerrigan, E. C., and Maciejowski, J. M., 2006, “Optimization Over State Feedback Policies for Robust Control with Constraints,” Automatica, 42(4), pp. 523–533. 10.1016/j.automatica.2005.08.023
Rakovic, S. V., Kouvaritakis, B., Cannon, M., Panos, C., and Findeisen, R., 2012, “Parameterized Tube Model Predictive Control,” IEEE Trans. Autom. Control, 57(11), pp. 2746–2761. 10.1109/TAC.2012.2191174
Rakovic, S. V., Kouvaritakis, B., Cannon, M., and Panos, C., 2012, “Fully Parameterized Tube Model Predictive Control,” Int. J. Robust Nonlinear Control, 22(12), pp. 1330–1361. 10.1002/rnc.2825
Munoz-Carpintero, D., Kouvaritakis, B., and Cannon, M., 2014, “Striped Parameterized Tube Model Predictive Control,” Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, International Federation of Automatic Control, pp. 11998–12003.
Lee, Y. I., and Kouvaritakis, B., 1999, “Constrained Receding Horizon Predictive Control for Systems With Disturbances,” Int. J. Control, 72(11), pp. 1027–1032. [CrossRef]
Lee, Y. I., and Kouvaritakis, B., 2000, “Linear Matrix Inequalities and Polyhedral Invariant Sets in Constrained Robust Predictive Control,” Int. J. Robust Nonlinear Control, 10(13), pp. 1079–1090. 10.1002/(ISSN)1099-1239
Lee, Y. I., Kouvaritakis, B., and Cannon, M., 2002, “Constrained Receding Horizon Predictive Control for Nonlinear Systems,” Automatica, 38(12), pp. 2093–2102. 10.1016/S0005-1098(02)00133-4
Evans, M. A., Cannon, M., and Kouvaritakis, B., 2012, “Robust MPC for Linear Systems With Bounded Multiplicative Uncertainty,” Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii, IEEE, pp. 248–253.
Fleming, J., Kouvaritakis, B., and Cannon, M., 2014, “Robust Tube MPC for Linear Systems With Multiplicative Uncertainty,” IEEE Trans. Autom. Control (in press), 10.1109/TAC.2014.2336358.
Kouvaritakis, B., Cannon, M., and Tsachouridis, V., 2004, “Recent Developments in Stochastic MPC and Sustainable Development,” Ann. Rev. Control, 28(1), pp. 23–35. [CrossRef]
Kouvaritakis, B., Cannon, M., and Couchman, P., 2006, “MPC as a Tool for Sustainable Development Integrated Policy Assessment,” IEEE Trans. Autom. Control, 51(1), pp. 145–149. 10.1109/TAC.2005.861702
Evans, M. A., Cannon, M., and Kouvaritakis, B., 2014, “Robust MPC Tower Damping for Variable Speed Wind Turbines,” IEEE Trans. Control Sys. Techno., 23(1), pp. 290–296. [CrossRef]
Kouvaritakis, B., Cannon, M., Rakovic, S. V., and Cheng, Q., 2010, “Explicit Use of Probabilistic Distributions in Linear Predictive Control,” Automatica, 46(10), pp. 1719–1724. 10.1016/j.automatica.2010.06.034
Cannon, M., Kouvaritakis, B., Rakovic, S. V., and Cheng, Q., 2011, “Stochastic Tubes in Model Predictive Control With Probabilistic Constraints,” IEEE Trans. Autom. Control, 56(1), pp. 194–200. 10.1109/TAC.2010.2086553
Fleming, J., Cannon, M., and Kouvaritakis, B., 2014, “Stochastic Tube MPC for LPV Systems With Probabilistic Set Inclusion Conditions,” Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles, IEEE, pp. 4783–4788.
Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory (Studies in Applied Mathematics, Vol. 15), SIAM, Philadelphia.
Rossiter, J. A., Rice, M. J., and Kouvaritakis, B., 1998, “A Numerically Robust State-Space Approach to Stable Predictive Control Strategies,” Automatica, 34(1), pp. 65–73. 10.1016/S0005-1098(97)00171-4
Kouvaritakis, B., Rossiter, J. A., and Schuurmans, J., 2000, “Efficient Robust Predictive Control,” IEEE Trans. Autom. Control, 45(8), pp. 1545–1549. 10.1109/9.871769
Cannon, M., and Kouvaritakis, B., 2005, “Optimizing Prediction Dynamics for Robust MPC,” IEEE Trans. Autom. Control, 50(11), pp. 1892–1897. 10.1109/TAC.2005.858679
Lee, Y. I., and Kouvaritakis, B., 2000, “Receding Horizon H-Infinity Predictive Control for Systems With Input Saturation,” Proc. IEE Pt-D, 147(2), pp. 153–158.
Kouvaritakis, B., Cannon, M., and Rossiter, J. A., 2002, “Who Needs QP for Linear System MPC Anyway?” Automatica, 38(5), pp. 879–884. 10.1016/S0005-1098(01)00263-1
Rakovic, S. V., Kerrigan, E., Kouramas, K., and Mayne, D., 2005, “Invariant Approximations of the Minimal Robustly Positively Invariant Set,” IEEE Trans. Autom. Control, 50(3), pp. 406–410. 10.1109/TAC.2005.843854
Mayne, D. Q., Seron, M. M., and Rakovic, S. V., 2005, “Robust Model Predictive Control of Constrained Linear Systems With Bounded Disturbances,” Automatica, 41(2), pp. 219–224. 10.1016/j.automatica.2004.08.019
Rakovic, S. V., Kouvaritakis, B., Findeisen, R., and Cannon, M., 2012, “Homothetic Tube Model Predictive Control,” Automatica, 48(8), pp. 1631–1638. 10.1016/j.automatica.2012.05.003
Kothare, M. V., Balakrishnan, V., and Morari, M., 1996, “Robust Constrained Model Predictive Control Using Linear Matrix Inequalities,” Automatica, 32(10), pp. 1361–1379. 10.1016/0005-1098(96)00063-5
Schuurmanns, J., and Rossiter, J. A., 2000, “Robust Piecewise Linear Control for Polytopic Systems With Input Constraints,” IEE Proc. CTA, 147(1), pp. 13–18. [CrossRef]
Casavola, A., Gianneli, M., and Mosca, E., 2000, “Min-Max Predictive Control Strategies for Input-Saturated Polytopic Systems,” Automatica, 36(1), pp. 125–133. 10.1016/S0005-1098(99)00112-0
Blanchini, F., and Miani, S., 2007, Set-Theoretic Methods in Control, Springer, New York.
Gautam, A., Chu, Y.-C., and Soh, Y. C., 2012, “Optimized Dynamic Policy for Receding Horizon Control of Linear Time-Varying Systems With Bounded Disturbances,” IEEE Trans. Autom. Control, 57(4), pp. 973–988. 10.1109/TAC.2011.2170109
Munoz-Carpintero, D., Cannon, M., and Kouvaritakis, B., 2013, “Recursively Feasible Robust MPC for Linear Systems With Additive and Multiplicative Uncertainty Using Optimized Polytopic Dynamics,” Proceedings of the 52nd IEEE Conference on Decision and Control, Florence, Italy, IEEE, pp. 1101–1106.
Astrom, K. J., and Wittenmark, B., 1973, “On Self Tuning Regulators,” Automatica, 9(2), pp. 185–199. 10.1016/0005-1098(73)90073-3
Clarke, D. W., and Gawthrop, P. J., 1975, “Self-Tuning Controller,” Proc. Inst. Electr. Eng., 122(9), pp. 929–934. 10.1049/piee.1975.0252
Schwarm, A. T., and Nikolaou, M., 1999, “Chance-Constrained Model Predictive Control,” AIChE J., 45(8), pp. 1743–1752. 10.1002/(ISSN)1547-5905
Stoorvogel, A. A., Weiland, S., and Batina, I., 2007, Model Predictive Control by Randomized Algorithms for Systems With Constrained Inputs and Stochastic Disturbances, wwwhome.math.utwente.nl/∼stoorvogelaa/subm01.pdf.
Calafiore, G. C., and Fagiano, L., 2013, “Stochastic Model Predictive Control of LPV Systems Via Scenario Optimization,” Automatica, 49(6), pp. 1861–1866. 10.1016/j.automatica.2013.02.060
Cannon, M., 2008, “Stochastic Model Predictive Control: State Space Methods,” Tutorial Workshop on Stochastic MPC, IFAC World Congress, Seoul, Korea, http://users.ox.ac.uk/~engs0169/pdf/cannon_ifac08c.pdf.
Kouvaritakis, B., Cannon, M., and Munoz-Carpintero, D., 2013, “Efficient Prediction Strategies for Disturbance Compensation in Stochastic MPC,” Int. J. Sys. Sci., 44(7), pp. 1344–1353. [CrossRef]
Campi, M. C., and Garatti, S., 2011, “A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality,” J. Optim. Theory Appl., 148(2), pp. 257–280. 10.1007/s10957-010-9754-6
Cannon, M., Kouvaritakis, B., and Wu, X., 2009, “Model Predictive Control for Systems With Stochastic Multiplicative Uncertainty and Probabilistic Constraints,” Automatica, 45(1), pp. 167–172. 10.1016/j.automatica.2008.06.017
Cannon, M., Kouvaritakis, B., and Wu, X., 2009, “Probabilistic Constrained MPC for Multiplicative and Additive Stochastic Uncertainty,” IEEE Trans. Autom. Control, 54(7), pp. 1626–1632. 10.1109/TAC.2009.2017970
Cannon, M., Kouvaritakis, B., and Ng, D., 2009, “Probabilistic Tubes in Linear Stochastic Model Predictive Control,” Sys. Control Lett., 58(10), pp. 747–753. [CrossRef]
Korda, M., Gondhalekar, R., Oldewurtel, F., and Jones, C. N., 2014, “Stochastic MPC Framework for Controlling the Average Constraint Violation,” IEEE Trans. Autom. Control, 59(7), pp. 1706–1721. 10.1109/TAC.2014.2310066
Cheng, Q., Cannon, M., Kouvaritakis, B., and Evans, M., 2014, “Stochastic MPC for Systems with Both Multiplicative and Additive Disturbances,” 19th IFAC World Congress, Cape Town, South Africa, International Federation of Automatic Control, pp. 2291–2296.

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