A randomized approach to Stochastic Model Predictive Control

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2012, Pages 7315-7320

  Prandini, Maria ^a   Garatti, Simone ^a   Lygeros, John ^b  

^a POLITECNICO DI MILANO   (Italy)

^b ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINED OPTIMIZATION; LINEAR SYSTEMS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

CHANCE CONSTRAINED OPTIMIZATION PROBLEMS; CHANCE-CONSTRAINED; CONTROL POLICY; FINITE HORIZONS; HARD CONSTRAINTS; PARAMETERIZED; PROBABILISTIC CONSTRAINTS; RANDOMIZED APPROACH;

MODEL PREDICTIVE CONTROL;

EID: 84874266484     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2012.6426462     Document Type: Conference Paper

References (30)

1. T. Alamo, R. Tempo, and A. Luque. On the sample complexity of randomized approaches to the analysis and design under uncertainty. In American Control Conference (ACC), Baltimore, Maryland, 2010.
2. I. Batina. Model predictive control for stochastic systems by randomized algorithms. PhD thesis, Technische Universiteit Eindhoven, 2004.
3. A. Bemporad, F. Borrelli, and M. Morari. Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control, 48(9):1600-1606, 2003.
4. A. Bemporad and M. Morari. Robust model predictive control: a survey. In Robustness in Identification and Control, volume 245 of Lecture Notes in Control and Information Sciences, pages 207-226. Springer, 1999.
5. A. Ben-Tal, A. Goryashko, E. Guslitzer, and A. Nemirovski. Adjustable robust solution of uncertain linear programs. Mathematical Programming, 99(2):351-376, 2004.
6. G. Calafiore and M.C. Campi. Uncertain convex programs: randomized solutions and confidence levels. Mathematical Programming, 102(1):25-46, 2005.
7. G. Calafiore and M.C. Campi. The scenario approach to robust control design. IEEE Transactions on Automatic Control, 51(5):742-753, 2006.
8. G.C. Calafiore and L. Fagiano. Robust model predictive control via random convex programming. In Proc. 50th IEEE Conf. on Decision and Control and European Control Conference (CDC-ECC), pages 1910-1915, Dec. 2011.
9. M.C. Campi and S. Garatti. The exact feasibility of randomized solutions of uncertain convex programs. SIAM Journal on Optimization, 19(3):1211-1230, 2008.
10. M.C. Campi and S. Garatti. A sampling-and-discarding approach to chance-constrained optimization: Feasibility and optimality. Journal of Optimization Theory and Applications, 148(2):257-280, 2011.
11. M.C. Campi, S. Garatti, and M. Prandini. The scenario approach for systems and control design. Annual Reviews in Control, 33(2):149-157, 2009.
12. M. Cannon, B. Kouvaritakis, and X. Wu. Model predicitve control for systems with stochastic multiplicative uncertainty and probabilistic constraints. Automatica, 45:167-172, 2009.
13. M. Cannon, B. Kouvaritakis, and X. Wu. Probabilistic constrained MPC for multiplicative and additive stochastic uncertainty. IEEE Transactions on Automatic Control, 54(7):1626-1632, 2009.
14. D. Chatterjee, J. Lygeros, and P. Hokayem. Stochastic Receding Horizon Control With Bounded Control Inputs: A Vector Space Approach. IEEE Transactions on Automatic Control, 56:2704-2710, November 2011.
15. D. Chatterjee, F. Ramponi, P. Hokayem, and J. Lygeros. On mean square boundedness of stochastic linear systems with bounded controls. Systems and Control Letters, 61:375-380, 2012.
16. E. Cinquemani, M. Agarwal, D. Chatterjee, and J. Lygeros. Convexity and convex approximations of discrete-time stochastic control problems with constraints. Automatica, 47(9):2082-2087, 2011.
17. D. Muñoz de la Peña, T. Alamo, A. Bemporad, and F. Camacho. A decomposition algorithm for feedback min-max model predictive control. IEEE Transactions on Automatic Control, 51(10):1688-1692, 2006.
18. P.J. Goulart, E.C. Kerrigan, and J.M. Maciejowski. Optimization over state feedback policies for robust control with constraints. Automatica, 42(4):523-533, April 2006.
19. M. Grant and S. Boyd. CVX: Matlab software for disciplined convex programming, version 1.21. http://cvxr.com/cvx, Feb 2011.
20. P. Hokayem, D. Chatterjee, and J. Lygeros. On Stochastic Receding Horizon Control with Bounded Control Inputs. In IEEE Conference on Decision and Control, pages 6359-6364, December 2009.
21. P. Hokayem, E. Cinquemani, D. Chatterjee, F. Ramponi, and J. Lygeros. Stochastic receding horizon control with output feedback and bounded controls. Automatica, 48(1):77-88, January 2012.
22. M. Kothare, V. Balakrishnan, and M. Morari. Robust constrained model predictive control using linear matrix inequalities. Automatica, 32(10):1361-1379, 1996.
23. J. Löfberg. Minimax approaches to robust model predictive control. PhD thesis, Linköping studies in Science and Technology, 2003.
24. J. Löfberg. Yalmip: a toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
25. A. Prèkopa. Stochastic programming. Kluwer, Boston, MT, USA, 1995.
26. A. Prèkopa. Probabilistic programming. In A. Ruszczyǹski and A. Shapiro, editors, Stochastic Programming, volume 10 of handbooks in operations research and management science, London, UK, 2003. Elsevier.
27. J.A. Primbs and C.H. Sung. Stochastic receding horizon control of constrained linear systems with state and control multiplicative noise. IEEE Transactions on Automatic Control, 54(2):221-230, 2009.
28. D.M. Raimondo, D.Limon, M. Lazar, L. Magni, and E.F. Camacho. Min-max model predictive control of nonlinear systems: A unifying overview on stability. European Journal of Control, 15:521, 2009.
29. P.O.M. Scokaert and D.Q. Mayne. Min-max feedback model predicitve control for constrained linear systems. IEEE Transactions on Automatic Control, 43:1136-1142, 1998.
30. D.H. van Hessem and O.H. Bosgra. Stochastic closed-loop model predictive control of continuous nonlinear chemical processes. J. Proc. Control, 16(3):225-241, 2006.