Optimization over state feedback policies for robust control with constraints

Automatica

Volumn 42, Issue 4, 2006, Pages 523-533

  Goulart, Paul J ^a   Kerrigan, Eric C ^b,c   MacIejowski, Jan M ^a,d,e,f,g,h  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

^c ROYAL ACADEMY OF ENGINEERING   (United Kingdom)

^d Royal Academy of Engineering ^*  (United Kingdom)

^e PEMBROKE COLLEGE   (United Kingdom)

^f IEE   (United Kingdom)

^g InstMC   (United Kingdom)

^h IEEE   (United Kingdom)

Author keywords

Constraint satisfaction; Optimal control; Predictive control; Robust control; Robust optimization

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; CONSTRAINT THEORY; DISCRETE TIME CONTROL SYSTEMS; FEEDBACK CONTROL; OPTIMAL CONTROL SYSTEMS;

CONSTRAINT SATISFACTION; DISTURBANCE SET; ROBUST OPTIMIZATION; SECOND-ORDER CONE PROGRAM (SOCP);

ROBUSTNESS (CONTROL SYSTEMS);

EID: 33144457616     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2005.08.023     Document Type: Article

References (28)

1. Bemporad, A. (1998). Reducing conservativeness in predictive control of constrained systems with disturbances. In Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, USA, December, pp. 1384-1391.
2. A. Bemporad, M. Morari, V. Dua, and E.N. Pistikopoulos The explicit linear quadratic regulator for constrained systems Automatica 38 1 2002 3 20
3. A. Ben-Tal, A. Goryashko, E. Guslitzer, and A. Nemirovski Adjustable robust solutions of uncertain linear programs Mathematical Programming 99 2 2004 351 376
4. D.P. Bertsekas, A. Nedic, and A.E. Ozdaglar Convex analysis and optimization 2003 Athena Scientific
5. D.P. Bertsekas, and I.B. Rhodes Sufficiently informative functions and the minimax feedback control of uncertain dynamic systems IEEE Transactions on Automatic Control AC-18 2 1973 117 124
6. F. Blanchini Set invariance in control Automatica 35 1 1999 1747 1767
7. L. Chisci, J.A. Rossiter, and G. Zappa Systems with persistent state disturbances: Predictive control with restricted constraints Automatica 37 7 2001 1019 1028
8. M.A. Dahleh, and I.J. Diaz-Bobillo Control of uncertain systems 1995 Prentice Hall Englewood Cliffs
9. S.J. Gartska, and R.J.-B. Wets On decision rules in stochastic programming Mathematical Programming 7 1974 117 143
10. Goulart, P.J., & Kerrigan, E.C. (2005). An efficient decomposition-based formulation for robust control with constraints. In Proceedings of the 16th IFAC World Congress on Automatic Control, Prague, Czech Republic.
11. Guslitser, E. (2002). Uncertainty-immunized solutions in linear programming. Master's Thesis, Technion, Israeli Institute of Technology.
12. Jia, D., Krogh, B.H., & Stursberg, O. (2005). An LMI approach to robust model predictive control. Journal of Optimization Theory and Applications, 127(2), 347-365.
13. Z. Jiang, and Y. Wang Input-to-state stability for discrete-time non-linear systems Automatica 37 6 2001 857 869
14. Kerrigan, E.C., & Alamo, T. (2004). A convex parameterization for solving constrained min-max problems with a quadratic cost. In Proceedings of the 2004 American Control Conference, Boston, MA, USA.
15. H.K. Khalil Nonlinear systems 2002 Prentice Hall USA
16. Kim, J., Yoon, T., Jadbabaie, A., & De Persis, C. (2004). Input-to-state stabilizing MPC for naturally stable linear systems subject to input constraints. In Proceedings of the 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, December 2004, pp. 5041-5046.
17. I. Kolmanovsky, and E.G. Gilbert Theory and computations of disturbance invariant sets for discrete-time linear systems Mathematical Problems in Engineering 4 4 1998 317 363
18. M.V. Kothare, V. Balakrishnan, and M. Morari Robust constrained model predictive control using linear matrix inequalities Automatica 32 10 1996 1361 1379
19. Y.I. Lee, and B. Kouvaritakis Constrained receding horizon predictive control for systems with disturbances International Journal of Control 72 11 1999 1027 1032
20. Limón Marruedo, D., Álamo, T., & Camacho, E.F. (2002). Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive disturbances. In Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA, pp. 4619-4624.
21. M.S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret Applications of second-order cone programming Linear Algebra and its Applications 284 1-3 1998 193 228
22. Löfberg, J. (2003). Approximations of closed-loop MPC. In Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, USA, pp. 1438-1442.
23. J.M. Maciejowski Predictive control with constraints 2002 Prentice Hall UK
24. D.Q. Mayne, J.B. Rawlings, C.V. Rao, and P.O.M. Scokaert Constrained model predictive Control: Stability and optimality Automatica 36 6 2000 789 814 Survey paper
25. D.Q. Mayne, M.M. Seron, and S.V. Raković Robust model predictive control of constrained linear systems with bounded disturbances Automatica 41 2 2005 219 224
26. P.O.M. Scokaert, and D.Q. Mayne Min-max feedback model predictive control for constrained linear systems IEEE Transactions on Automatic Control 43 8 1998 1136 1142
27. Smith, R.S. (2004). Robust model predictive control of constrained linear systems. In Proceedings of the 2004 American Control Conference, Boston, MA, USA.
28. van Hessem, D.H., & Bosgra, O.H. (2002). A conic reformulation of model predictive control including bounded and stochastic disturbances under state and input constraints. In Proceedings of the 41st IEEE Conference on Decision and Control, pp. 4643-4648.