Continuity and exponential stability of mixed constrained model predictive control

SIAM Journal on Control and Optimization

Volumn 42, Issue 3, 2003, Pages 839-870

  Choi, Jinhoon ^a   Kwon, Wook Hyun ^b  

^a Sogang University   (South Korea)

^b Seoul National University   (South Korea)

Author keywords

Continuity; Exponential stability; Model predictive control

Indexed keywords

CONTINUITY; EXPONENTIAL STABILITY; MODEL PREDICTIVE CONTROL;

ALGORITHMS; FINITE ELEMENT METHOD; FUNCTIONS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; RANDOM PROCESSES;

CONTROL SYSTEMS;

EID: 1442296572     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012901385204     Document Type: Article

References (38)

1. A. BEMPORAD, M. MORARI, V. DUA, AND E. N. PISTIKOPOULOS, The explicit linear quadratic regulator for constrained systems, Automatica J. IFAC, 38 (2002), pp. 3-20.
2. R. R. BITMEAD, M. GEVERS, AND V. WERTZ, Adaptive Optimal Control, Prentice-Hall, Englewood Cliffs, NJ, 1990.
3. F. M. CALLIER AND C. A. DESOER, Linear System Theory, Springer-Verlag, New York, 1991.
4. D. CHMIELEWSKI AND V. MANOUSIOUTHAKIS, On constrained infinite-time linear quadratic optimal control, Systems Control Lett., 29 (1996), pp. 121-129.
5. J. CHOI, On the stabilization of linear discrete systems subject to input saturation, Systems Control Lett., 36 (1999), pp. 241-244.
6. J. CHOI, Constrained exponential stabilizability of marginal and/or unstable linear systems, Internat. J. Control, 73 (2000), pp. 652-654.
7. J. CHOI, On the constrained asymptotic stabilizability of unstable linear discrete time systems via linear feedback, in Proceedings of the 2001 American Control Conference, Vol. 6, IEEE Press, Piscataway, NJ, 2001, pp. 4926-4929.
8. J. CHOI, H. S. KO, AND K. S. LEE, Constrained linear quadratic optimal control of chemical processes, Computers and Chemical Engineering, 24 (2000), pp. 823-827.
9. J. CHOI AND K. S. LEE, Mixed constrained infinite horizon linear quadratic optimal control, Asian J. Control, submitted.
10. C. R. CUTLER AND B. L. RAMAKER, Dynamic matrix control - a computer control algorithm, in Proceedings of the Joint Automated Control Conference, American Automatic Control Council, 1980.
11. A. L. DONTCHEV AND W. W. HAGER, Lipschitzian stability in nonlinear control and optimization, SIAM J. Control Optim., 31 (1992), pp. 569-603.
12. S. E. DREYFUS, Dynamic Programming and the Calculus of Variations, Academic Press, New York, 1965.
13. E. G. GILBERT AND K. T. TAN, Linear systems with state and control constraints: The theory and application of maximal output admissible sets, IEEE Trans. Automat. Control, 36 (1991), pp. 1008-1020.
14. P. GUTMAN AND M. CWIKEL, An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states, IEEE Trans. Automat. Control, 32 (1987), pp. 251-254.
15. W. W. HAGER, Lipschitz continuity for constrained processes, SIAM J. Control Optim., 17 (1979), pp. 321-338.
16. A. HALANAY, Quelques questions de la théorie de la stabilité pour les systèmes aux différences finie, Arch. Ration. Mech. Anal., 12 (1963), pp. 150-154.
17. W. W. HOGAN, Point-to-set maps in mathematical programming, SIAM Rev., 15 (1973), pp. 591-603.
18. S. KEERTHI AND E. GILBERT, Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving horizon approximations, J. Optim. Theory Appl., 57 (1988), pp. 265-293.
19. W. H. KWON AND A. E. PEARSON, A modified quadratic cost problem and feedback stabilization of a linear system, IEEE Trans. Automat. Control, 22 (1977), pp. 838-842.
20. W. H. KWON, A. M. BRUCKSTEIN, AND T. KAILATH, Stabilizing feedback design via the moving horizon method, Internat J. Control, 37 (1983), pp. 631-643.
21. Z. LIN, Global and Semi-global Control Problems for Linear Systems Subject to Input Saturation and Minimum-Phase Input-Output Linearizable Systems, Ph.D. dissertation, Washington State University, Pullman, WA, 1994.
22. Z. LIN AND A. SABERI, Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks, Systems Control Lett., 24 (1995), pp. 125-132.
23. E. S. MEADOWS AND J. RAWLINGS, Topics in model predictive control, in Methods of Model Based Process Control, R. Berber, ed., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995, pp. 331-347.
24. K. R. MUSKE AND J. RAWLINGS, Linear model predictive control of unstable processes, J. Process Control, 3 (1993), pp. 85-96.
25. J. B. RAWLINGS AND K. R. MUSKE, The stability of constrained receding horizon control, IEEE Trans. Automat. Control, 38 (1993), pp. 1512-1516.
26. J. RICHALET, A. RAULT, J. L. TESTUD, AND J. PAPON, Model predictive heuristic control: Application to industrial processes, Automatica J. IFAC, 14 (1978), pp. 413-428.
27. P. O. M. SCOKAERT, J. B. RAWLINGS, AND E. S. MEADOWS, Discrete-time stability with perturbations: Application to model predictive control, Automatica J. IFAC, 33 (1997), pp. 463-470.
28. P. O. M. SCOKAERT AND J. B. RAWLINGS, Constrained linear quadratic regulation, IEEE Trans. Automat. Control, 43 (1998), pp. 1163-1169.
29. M. M. SERON, G. C. GOODWIN, AND J. A. DE DON'A, Geometry of Model Predictive Control for Constrained Linear Systems, Technical report EE0031, The University of Newcastle, NSW, Australia, 2000.
30. E. D. SONTAG, An algebraic approach to bounded controllability of linear systems, Internat. J. Control, 39 (1984), pp. 181-188.
31. M. SZNAIER AND M. J. DAMBORG, Suboptimal control of linear systems with state and control inequality constraints, in Proceedings of the 26th IEEE Conference on Decision and Control, IEEE Press, Pisctataway, NJ, 1987, pp. 761-762.
32. E. Y. TSE AND M. ATHANS, Adaptive stochastic control for a class of systems, IEEE Trans. Automat. Control, 17 (1972), pp. 38-52.
33. A. TSIRUKIS AND M. MORARI, Controller design with actuator constraints, in Proceedings of the 31st IEEE Conference on Decision and Control, Vol. 3, IEEE Press, Piscataway, NJ, 1992, pp. 2623-2628.
34. M. VIDYASAGAR, Nonlinear Systems Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1993.
35. Y. YANG, Global Stabilization of Linear Systems with Bounded Feedback, Ph.D. dissertation, Rutgers, the State University of New Jersey, New Brunswick, 1993.
36. Y. YANG, unpublished work, 1993.
37. E. ZAFIRIOU AND H.-W. CHIOU, Output constraint softening for SISO model predictive control, in Proceedings of the American Control Conference, Vol. 1, IEEE Press, Piscataway, NJ, 1993, pp. 372-376.
38. A. ZHENG AND M. MORARI, Stability of model predictive control with mixed constraints, IEEE Trans. Automat. Control, 40 (1995), pp. 1818-1823.