Stochastic tubes in model predictive control with probabilistic constraints

Proceedings of the 2010 American Control Conference, ACC 2010

Volumn , Issue , 2010, Pages 6274-6279

  Cannon, Mark ^a   Kouvaritakis, Basil ^a   Raković, Saša V ^a,b   Cheng, Qifeng ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Constrained control; Probabilistic constraints; Stochastic systems

Indexed keywords

MODEL PREDICTIVE CONTROL; PREDICTIVE CONTROL SYSTEMS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS;

CLOSED LOOP STABILITY; CONSTRAINED CONTROLS; HARD CONSTRAINTS; OFFLINE; ON-LINE COMPUTATIONAL LOADS; PREDICTION HORIZON; PROBABILISTIC CONSTRAINTS; SCALINGS;

STOCHASTIC SYSTEMS;

EID: 77957780942     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2010.5531518     Document Type: Conference Paper

References (21)

1. P.O.M. Scokaert and D.Q. Mayne. Min-max feedback model predictive control for constrained linear systems. IEEE Trans. Autom. Control, 43(8):1136-1142, 1998.
2. D.H. van Hessem and O.H. Bosgra. A conic reformulation of model predictive control including bounded and stochastic disturbances under state and input constraints. In Proc. 41st IEEE Conf. Decision Control, pages 4643-4648, 2002.
3. P. Li, M. Wendt, and G. Wozny. A probabilistically constrained model predictive controller. Automatica, 38(7):1171-1176, 2002.
4. J. Yan and R. Bitmead. Incorporating state estimation into model predictive control and its application to network traffic control. Automatica, 41(4):595-604, 2005.
5. Z.K. Nagy. Model based robust control approach for batch crystallization product design. Comput. Chem. Eng., 33(10):1685-1691, 2009.
6. Z.K. Nagy and R.D. Braatz. Worst-case and distributional robustness analysis of finite-time control trajectories for nonlinear distributed parameter systems. IEEE Trans. Control Syst. Tech., 11(5), 2003.
7. M. Cannon, B. Kouvaritakis, and X. Wu. Probabilistic constrained MPC for multiplicative and additive stochastic uncertainty. IEEE Trans. Autom. Control, 54(7):1626-1632, 2009.
8. M. Cannon, B. Kouvaritakis, and D. Ng. Probabilistic tubes in linear stochastic model predictive control. Systems & Control Letters, 58(10):747-753, 2009.
9. J.R. Gossner, B. Kouvaritakis, and J.A. Rossiter. Robust receding horizon control for systems with uncertain dynamics and input saturation. Automatica, 36(10):1497-1504, 2000.
10. Y.I. Lee and B. Kouvaritakis. Robust receding horizon predictive control for systems with uncertain dynamics and input saturation. Automatica, 36(10):1497-1504, 2000.
11. D.Q. Mayne, M.M. Seron, and S.V. Rakovíc. Robust model predictive control of constrained linear systems with bounded disturbances. Automatica, 41(2):219-224, 2005.
12. S.V. Rakovíc and M. Fiacchini. Approximate reachability analysis for linear discrete time systems using homothety and invariance. In Proc. 17th IFAC World Congress, Seoul, 2008.
13. Y.I. Lee, B. Kouvaritakis, and M. Cannon. Constrained receding horizon predictive control for nonlinear systems. Automatica, 38(12):2093-2102, 2002.
14. S.V. Rakovíc, A.R. Teel, D.Q. Mayne, and A. Astolfi. Simple robust control invariant tubes for some classes of nonlinear discrete time systems. In Proc. 45th IEEE Conf. Decision and Control, pages 6397- 6402, 2006.
15. S.V. Rakovíc. Set theoretic methods in model predictive control. In Nonlinear Model Predictive Control: Towards New Challenging Applications, volume 384 of LNCIS, pages 41-54. Springer, 2009.
16. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM, 1994.
17. W. Feller. An introduction to probability theory and its applications, volume 2. John Wiley, 1971.
18. A. Papoulis. Probability, Random Variables and Stochastic Processes. McGraw-Hill, 1965.
19. J.R. Norris. Markov chains. Cambridge University Press, 1997.
20. D.Q. Mayne, J.B. Rawlings, C.V. Rao, and P.O.M. Scokaert. Constrained model predictive control: Stability and optimality. Automatica, 36(6):789-814, 2000.
21. E.G. Gilbert and K.T. Tan. Linear systems with state and control constraints: The theory and practice of maximal admissible sets. IEEE Trans. Autom. Control, 36(9):1008-1020, 1991.