Min-Max MPC based on a network problem

Systems and Control Letters

Volumn 57, Issue 2, 2008, Pages 184-192

  Alamo, T ^a   Munoz de la Pena D ^a   Camacho, E F ^a  

^a UNIVERSIDAD DE SEVILLA   (Spain)

Author keywords

Networks; Predictive control; Quadratic programming; Robust control; Uncertain linear systems

Indexed keywords

COST FUNCTIONS; MODEL PREDICTIVE CONTROL; NETWORK MANAGEMENT; OPTIMIZATION; PROBLEM SOLVING; QUADRATIC PROGRAMMING; ROBUST CONTROL; UNCERTAIN SYSTEMS;

COMPUTATIONAL BURDEN; QUADRATIC COST FUNCTIONS; QUADRATIC PROGRAMMING PROBLEM;

PREDICTIVE CONTROL SYSTEMS;

EID: 37049025548     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2007.08.013     Document Type: Article

References (32)

1. Alamo T., Muñoz de la Peña D., and Camacho E.F. Min max MPC based on a graph problem. Proceedings of the 42st IEEE Conference on Decision and Control (December 2003), Maui, Hawaii USA 917-922
2. Alamo T., Muñoz de la Peña D., Limon D., and Camacho E.F. Constrained minmax predictive control: Modifications of the objective function leading to polynomial complexity. IEEE Transactions on Automatic Control 50 5 (2005) 710-714
3. Allwright J.C., and Papavasiliou G.C. On linear programming and robust model-predictive control using impulse-response. System Control Lett. 18 (1992) 159-164
4. Bazaraa M.S., and Shetty C.M. Nonlinear Programming. Theory and Algorithms (1979), Wiley, New York
5. Bemporad A. Reducing conservativeness in predictive control of constrained systems with disturbances. Proceedings of the American Control Conference (1998), Tampa, FL, USA 1384-1389
6. Bemporad A., Borrelli F., and Morari M. Min-max control of constrained uncertain discrete-time linear systems. IEEE Trans. Automatic Control 48 9 (2003) 1600-1606
7. Boyd S., and Vandenberghe L. Convex Optimization (2004), Cambridge University Press, Cambridge
8. Camacho E.F., and Bordóns C. Model Predictive Control. second ed. (2004), Springer, Berlin
9. P.J. Campo, M. Morari, Robust model predictive control, in: Proceedings of the American Control Conference, 1987, pp. 1021-1026.
10. Evans J.R., and Minieka E. Optimization Algorithms for Networks and Graphs (1992), Marcel Dekker Inc., New York
11. Ford L.R., and Fulkerson D.R. Maximal flow through a network. Canad. J. Math. 8 (1956) 399-404
12. Geary A., and Bertsekas D.P. Incremental subgradient methods for nondifferentiable optimization. Proceedings of the American Control Conference (1999), Phoenix, AZ 907-912
13. ILOG, Inc. CPLEX 9.0 User Manual, Gentilly Cedex, France, 2004.
14. Kerrigan E.C., and Maciejowski J.M. Feedback min-max model predictive control using a single linear program: Robust stability and the explicit solution. Int. J. Robust Nonlinear Control 14 (2004) 395-413
15. Kiwiel K.C. Proximity control in bundle methods for convex nondifferentiable optimization. Math. Programming 46 (1990) 105-122
16. Kothare M.V., Balakrishnan V., and Morari M. Robust constrained model predictive control using linear matrix inequalities. Automatica 32 (1996) 1361-1379
17. Langson W., Chryssochoos I., Rakovic S.V., and Mayne D.Q. Robust model predictive control using tubes. Automatica 40 1 (2004) 125-133
18. Lee J.H., and Yu Z. Worst case formulations of model predictive control for systems with bounded parameters. Automatica 3 5 (1997) 763-781
19. Lodi A., Allemand K., and Leibling T.M. An evolutionary heuristic for quadratic 0-1 programming. European J. Oper. Res. 119 (1999) 662-670
20. J. Löfberg, Minimax approaches to robust model predictive control, Ph.D. Thesis, April 2003.
21. A. Makhorin, GNU Linear Programming Kit, 〈http://www.gnu.org/software/glpk〉, 2005.
22. Mayne D.Q., Rawlings J.B., Rao C.V., and Scokaert P.O.M. Constrained model predictive control: Stability and optimality. Automatica 36 (2000) 789-814
23. Mayne D.Q., Seron M.M., and Rakovic S.V. Robust model predictive control of constrained linear systems with bounded disturbances. Automatica 41 2 (2005) 219-224
24. Megias D., Serrano J., and de Prada C. Min-max constrained quasi-infinite horizon model predictive control using linear programming. J. Process Control 12 4 (2002) 495-505
25. Muñoz de la Peña D., Alamo T., Bemporad A., and Camacho E.F. A decomposition algorithm for feedback min-max model predictive control. IEEE Trans. on Automatic Control 51 10 (2006) 1688-1692
26. Muñoz de la Peña D., Ramirez D.R., Alamo T., and Camacho E.F. Application of an explicit min-max mpc to a scaled laboratory process. Control Eng. Practice 13 12 (2005) 1463-1471
27. Muñoz de la Peña D., Ramirez D.R., Alamo T., and Camacho E.F. Explicit solution of min-max mpc with additive uncertainties and quadratic criterion. System Control Lett. 55 4 (2006) 266-274
28. Picard J.C., and Ratliff H.D. Minimum cuts and related problems. Networks 5 (1974) 357-370
29. Ramirez D.R., Alamo T., Camacho E.F., and Muñoz de la Peña D. Min-max mpc based on a computationally efficient upper bound of the worst case cost. J. Process Control 16 5 (2006) 511-519
30. Scokaert P.O.M., and Mayne D.Q. Min-max feedback model predictive control for constrained linear systems. IEEE Trans. Automatic Control 43 8 (1998) 1136-1142
31. Wang Y.J., and Rawlings J.B. A new robust model predictive control method I: theory and computation. J. Process Control 13 (2003)
32. Witsenhausen H.S. A minimax control problem for sampled linear systems. IEEE Trans. Automatic Control 13 1 (1968) 5-21