Min-max control using parametric approximate dynamic programming

Control Engineering Practice

Volumn 18, Issue 2, 2010, Pages 190-197

  Nosair, Hussam ^a   Yang, Yu ^a   Lee, Jong Min ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Optimal control; Robust control; Uncertain linear systems; Worst case formulation

Indexed keywords

ADDITIVE DISTURBANCE; APPROXIMATE DYNAMIC PROGRAMMING; COMPUTATIONAL BURDEN; COMPUTATIONALLY EFFICIENT; MIN-MAX CONTROL; OPERATIONAL DATA; OPTIMAL CONTROL; OPTIMAL CONTROL POLICY; OPTIMAL CONTROLS; OPTIMAL COSTS; PERFORMANCE CRITERION; PIECE-WISE; QUADRATIC APPROXIMATION; UNCERTAIN LINEAR SYSTEM; UNCERTAIN PARAMETERS;

LINEAR SYSTEMS; OPTIMIZATION; ROBUST CONTROL; UNCERTAINTY ANALYSIS;

DYNAMIC PROGRAMMING;

EID: 76749115147     PISSN: 09670661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.conengprac.2009.09.001     Document Type: Article

References (26)

1. Badgwell T.A. Robust model predictive control of stable linear systems. International Journal of Control 68 (1997) 797-818
2. Bemporad A., Borrelli F., and Morari M. Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control 48 (2003) 1600-1606
3. Bertsekas D.P. Dynamic programming and optimal control. 3rd ed (2005), Athena Scientific, Belmont, MA
4. Börnberg J., and Diehl M. Approximate robust dynamic programming and robustly stable MPC. Automatica 42 (2006) 777-782
5. Borrelli F., Bemporad A., and Morari M. Geometric algorithm for multiparametric linear programming. Journal of Optimization Theory and Applications 118 (2003) 515-540
6. Campo, P. J., & Morari, M. (1987). Robust model predictive control. In: Proceedings of American control conference (Vol. 2, pp. 1021-1026).
7. Chang, C.-C., & Lin, C.-J. (2001). LIBSVM: a library for support vector machines. Software available at 〈http://www.csie.ntu.edu.tw/∼cjlin/libsvm〉.
8. de Farias D.P., and van Roy B. The linear programming approach to approximate dynamic programming. Operations Research 51 (2003) 850-865
9. Diehl M., and Börnberg J. Robust dynamic programming for min-max model predictive control of constrained uncertain systems. IEEE Transactions on Automatic Control 49 (2004) 2253-2257
10. Gruber, J. K., Ramirez, D. R., Alamo, T., Bordons, C., & Camacho, E. F. (2009). Control of a pilot plant using QP based min-max predictive control. Control Engineering Practice, in press, doi: 10.1016/j.conengprac.2009.06.011.
11. Hastie T., Tibshirani R., and Friedman J. The elements of statistical learning: data mining inference and prediction (2001), Springer, Berlin
12. Kothare M., Balakrishnan V., and Morari M. Robust constrained model predictive control using linear model inequalities. Automatica 14 (1996) 1361-1379
13. Lee J.H., and Lee J.M. Approximate dynamic programming based approaches to process control and scheduling. Computers and Chemical Engineering 30 (2006) 1603-1618
14. Lee J.H., and Yu Z. Worst-case formulations of model predictive control for systems with bounded parameters. Automatica 33 (1997) 763-781
15. Lee J.M., Kaisare N.S., and Lee J.H. Choice of approximator and design of penalty function for an approximate dynamic programming based control approach. Journal of Process Control 49 (2006) 2253-2257
16. Morari M., and Lee J.H. Model predictive control: Past, present and future. Computers and Chemical Engineering 23 (1999) 667-682
17. Nosair H., and Lee J.M. Parametric approximation of piecewise quadratic value functions for the control of complex systems. Proceedings of 17th IFAC World congress (2008) 3252-3257
18. Qin S.J., and Badgwell T.A. A survey of industrial model predictive control technology. Control Engineering Practice 11 (2003) 733-764
19. Ralhan S., and Badgwell T.A. Robust control of stable linear systems with continuous uncertainty. Computers and Chemical Engineering 24 (2000) 2533-2544
20. Scokaert P., and Mayne D.Q. Min-max feedback model predictive control for constrained linear systems. IEEE Transactions on Automatic Control 43 (1998) 1136-1142
21. Skogestad S., and Morari M. The dominant time constant for distillation columns. Computers and Chemical Engineering 11 (1987) 607-617
22. Sutton R.S., and Barto A.G. Reinforcement learning: An introduction. A Bradford Book (1998), The MIT Press, Cambridge
23. Szita, I., & Lorincz, A. (2003). Reinforcement learning with linear function approximation and LQ control converges. Technical report, arXiv:cs/0306120v2. URL: 〈http://www.citebase.org/abstract?id=oai:arXiv.org:cs/0306120〉.
24. Tødel P., Johansen T.A., and Bemporad A. An algorithm for multiparametric quadratic programming and explicit MPC solutions. Automatica 39 (2003) 489-497
25. Wan Z., and Kothare M. An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica 39 (2003) 837-846
26. Witsenhausen H.S. A min-max control problem for sampled linear systems. IEEE Transactions on Automatic Control AC-13 (1968) 5-21