Contractive model predictive control for constrained nonlinear systems

IEEE Transactions on Automatic Control

Volumn 45, Issue 6, 2000, Pages 1053-1071

  Kothare, Simone Loureiro De Oliveira ^a   Morari, Manfred ^b  

^a AIR PRODUCTS AND CHEMICALS INC   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

Constrained control; Model predictive control; Nonlinear control

Indexed keywords

ALGORITHMS; CLOSED LOOP CONTROL SYSTEMS; COMPUTER SIMULATION; CONSTRAINT THEORY; FUNCTIONS; LYAPUNOV METHODS; NONLINEAR SYSTEMS; SYSTEM STABILITY; THEOREM PROVING;

CONSTRAINED CONTROL; CONTRACTIVE CONSTRAINT; LYAPUNOV FUNCTION; MODEL PREDICTIVE CONTROL; SOFTWARE PACKAGE MATLAB;

PREDICTIVE CONTROL SYSTEMS;

EID: 0034196113     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.863592     Document Type: Article

References (72)

1. M. Alamir and G. Bornard, "New sufficient conditions for global stability of receding horizon control for discrete-time nonlinear systems," in Advances in Model-Based Predictive Control, D. Clarke, Ed. Oxford, U.K.: Oxford Univ.Press, 1994, pp. 173-181.
2. _, "On the stability of receding horizon control of nonlinear discrete-time systems," Syst. Control Lett., vol. 23, pp. 291-296, 1994.
3. _, "Stability of a truncated infinite constrained receding horizon scheme: The general discrete nonlinear case," Automatica, vol. 31, no. 9, pp. 1353-1356, September 1995.
4. F. Allgöwer, "Definition and computation of a nonlinearity measure and application to approximate I/O-linearization," Insitut fiir System-dynamik und Regelungstechnik, Universitiit Stuttgart, Tech. Rep. 95-1, 1994.
5. _, "Analysis and controller synthesis for nonlinear processes using nonlinearity measures," in AIChE Annu. Meeting, Miami, FL, 1995.
6. A. Astolfi, "Asymptotic stabilization of nonholonomic systems with discontinuous control," Ph.D. dissertation, Swiss Federal Institute of Technology (ETH), 1995.
7. _, "Discontinuous control of nonholonomic systems," Syst. Control Lett., vol. 27, pp. 37-45, 1995.
8. V. Balakrishnan, Z. Zheng, and M. Morari, "Constrained stabilization of discrete-time systems," in Advancesin Model-Based Predictive Control, D. Clarke, Ed. Oxford, U.K.: Oxford Univ. Press, 1994, pp. 205-216.
9. J. S. Baras, A. Bensoussan, and M. R. James, "Dynamic observers as asymptotic limits of recursive filters: Special cases," SIAM J. Appl. Math., vol. 48, no. 5, pp. 1147-1158, October 1988.
10. G. Becker, A. Packard, D. Philbrick, and G. Balas, "Control of parametrically-dependent linear systems: A single quadratic Lyapunov approach," in Proc. American Control Conf., vol. 3, San Francisco, CA, June 1993, pp. 2795-2799.
11. B. W. Bequette, "Nonlinear control of chemical processes: A review," Ind. Eng. Chem. Res., vol. 30, pp. 1391-1413, 1991.
12. L. Biegler and J. Rawlings, "Optimization approaches to nonlinear model predictive control," in Conf. Chemical Process Control (CPC-IV), South Padre Isand, TX, 1991, CACHF-AIChE, pp. 543-571.
13. R. R. Bitmead, M. Gevers, and V. Wertz, Adaptive Optimal Control. The Thinking Man's GPC, ser. International Series in Systems and Control Engineering. Englewood Cliffs, NJ: Prentice-Hall, 1990.
14. F. Blanchini, "Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions," IEEE Trans. Automat. Contr., vol. 39, no. 2, pp. 428-433, 1994.
15. M. Bouslimani, M. M'Saad, and L. Dugard, "Stabilizing receding horizon control: A unified continuous/discrete time formulation," in Proc. Conf. Decision and Control, San Antonio, TX, Dec. 1993, p. 1298.
16. R. Brockett, "Asymptotic stability and feedback stabilization," in Differential Geometric Control Theory, R. Brockett, R. Millman, and H. Sussman, Eds: Birkhäuser, 1983, pp. 181-193.
17. P. J. Campo and M. Morari, "Robust model predictive control," in Proc. Amer. Control Conf., 1987, pp. 1021-1026.
18. C. Chen and L. Shaw, "On receding horizon feedback control," Automatica, pp. 349-352, 1982.
19. D. W. Clarke, "Advances in model-based predictive control," in Advances in Model-Based Predictive Control, D. W. Clarke, Ed. Oxford, U.K.: Oxford Univ. Press, 1994, pp. 3-21.
20. C. R. Cutler and B. L. Ramaker, "Dynamic matrix control - A computer control algorithm," in Proc. Joint Automatic Control Conf., San Francisco, CA, 1980, WP5-B.
21. L. M. De Nicolao and R. Scattolini, "Robust predictive control of systems with uncertain impulse response," Automatica, vol. 32, no. 10, pp. 1475-1479, 1996.
22. S. L. De Oliveira, "Model predictive control (MPC) for constrained nonlinear systems," Ph.D. diss., California Institute of Technology, Pasadena, CA, Mar. 1996.
23. S. L. De Oliveira, D. M. Merquior, and E. L. Lima, "Feedback linearization + contractive MPC: Stability analysis/application to a polymerization process," in NATO Advanced Study Institute on Nonlinear Model-Based Process Control, E. R. Berber, Ed. Antalya, Turkey: Kluwer Academic, 1997, to be published.
24. J. J. Deyst and C. F. Price, "Conditions for asymptotic stability of the discrete minimum-variance linear estimator," IEEE Trans. Automat. Contr., vol. AC-13, no. 6, pp. 702-705, 1979.
25. F. Doyle III, F. Allgöwer, S. L. De Oliveira, E. Gilles, and M. Morari, "On nonlinear systems with poorly behaved zero dynamics," in Proc. Amer. Control Conf., Chicago, IL, June 1992, pp. 2571-2575.
26. W. Eaton and J. Rawlings, "Feedback control of nonlinear processes using on-line optimization techniques," Comp. Chem. Eng., vol. 14, pp. 459-479, 1990.
27. C. Economou, M. Morari, and O. Palsson, "Internal model control. 5. Extension to nonlinear systems," Ind. Eng. Chem. Process Des. Dev., vol. 25, no. 1, pp. 403-411, 1986.
28. C E. Garciá, "Quadratic dynamic matrix control of nonlinear processes. An application to a batch reactor process," in Proc. AIChE Annu. Meeting, San Francisco, CA, 1984.
29. C. E. Garciá and A. M. Morshedi, "Quadratic programming solution of dynamic matrix control (QDMC)," Chem. Eng. Commun., vol. 46, pp. 73-87, 1986.
30. H. Genceli and M. Nikolaou, "Robust stability analysis of constrained Li-norm model predictive control," AICHE J., vol. 39, no. 12, pp. 1954-1965, 1993.
31. P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright, "User's guide for NPSOL 5.0: A FORTRAN package for nonlinear programming," Stanford Univ., Tech. Rep., Nov. 1994.
32. A. H. Jazwinski, Stochastic Processes and Filtering Theory. New York: Academic, 1970.
33. 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. Optimizat. Theory Applicat., vol. 57, no. 2, pp. 265-293, May 1988.
34. L. Kershenbaum, D. Q. Mayne, R. Pytlak, and R. B. Vinter, "Receding horizon control," in Advances in Model-Based Predictive Control, D.W. Clarke, Ed. Oxford, U.K.: Oxford Univ. Press, 1994, pp. 233-246.
35. M. V. Kothare, V. Balakrishnan, and M. Morari, "Robust constrained model predictive control using linear matrix inequalities," Automatica, vol. 32, no. 10, pp. 1361-1379, Oct. 1996.
36. W. Kwon and A. Pearson, "A modified quadratic cost problem and feedback stabilization of a linear system," IEEE Trans. Automat. Contr., vol. AC-22, no. 5, pp. 838-842, 1977.
37. W. H. Kwon, "Advances in predictive control: Theory and application," in Proc. 1st Asian Control Conf., Tokyo, Japan, July 1994, updated in October, 1995.
38. F. L. Lewis, Optimal Estimation. New York: Wiley, 1986.
39. L. Ljung, "Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems," IEEE Trans. Automat. Contr., vol. 24, no. 1, pp. 36-50, Feb. 1979.
40. A. I. Lur'e, Some Nonlinear Problems in the Theory of Automatic Control (in Russian). London, U.K.: Her Majesty's Stationery Office, 1951.
41. A. I. Lur'e and V. N. Postnikov, "On the theory of stability of control systems," Appl. Math. Mech., vol. 8, no. 3, 1944.
42. A. Malmgren and K. Nordström, "A contraction property for state feedback design of linear discrete-time systems," Automatica, vol. 30, no. 9, pp. 1485-1489, 1994.
43. _, "Optimal state feedback control with a prescribed contraction property," Automatica, vol. 30, no. 11, pp. 1751-1756, 1994.
44. D. Mayne and H. Michalska, "An implementable receding horizon controller for the stabilization of nonlinear systems," in Proc. Conf. Decision and Control, Honolulu, HI, 1990, pp. 3396-3397.
45. _, "Receding horizon control of nonlinear systems," IEEE Trans. Automat. Contr., vol. 35, pp. 814-824, 1990.
46. _, "Approximate global linearization of nonlinear systems via on-line optimization," in Proc. Eur. Control Conf., Grenoble, France, 1991, pp. 182-187.
47. _, "Model predictive control of nonlinear systems," in Proc. Amer. Control Conf., Boston, MA, 1991, pp. 2343-2348.
48. _, "Receding horizon control of nonlinear systems without differentiability of the optimal value function," Syst. Control Lett., vol. 16, pp. 123-130, 1991.
49. R. M'Closkey and R. Murray, "Experiments in exponential stabilization of a mobile robot towing a trailer," in Proc. Amer. Control Conf., vol. 1, Baltimore, MD, June 1994, pp. 988-993.
50. E. Meadows, M. Henson, J. Eaton, and J. Rawlings, "Receding horizon control and discontinuous state feedback stabilization," Int. J. Control, vol. 62, no. 5, pp. 1217-1229, 1995.
51. E. Meadows and J. Rawlings, "Receding horizon control with an infinite horizon," in Proc. Amer. Control Conf., San Francisco, CA, 1993, pp. 2926-2930.
52. H. Michalska and D. Mayne, "Robust receding horizon control of constrained nonlinear systems," IEEE Trans. Automat. Contr., vol. 38, no. 11, pp. 1623-1633, Nov. 1993.
53. _, "Moving horizon observers," in Proc. FAC Nonlinear Control Systems Design Symp. (NOLCOS'92), M. Fliess, Ed., Bordeaux, France, 1992, pp. 576-581.
54. _, "Moving horizon observers and observer-based control," IEEE Trans. Automat. Contr., vol. 40, no. 6, pp. 995-1006, June 1995.
55. R. R. Muske and J. B. Rawlings, "Nonlinear moving horizon state estimation," in NATO Advanced Study Insitute on Methods of Model Based Control Proceedings, E. R. Berber, Ed.. Antalya, Turkey, 1994.
56. V. Nevistić and M. Morari, "Constrained control of feedback-linearizable systems," in Proc. Eur. Control Conf., Rome, Italy, 1995, pp. 1726-1731.
57. G. D. Nicolao and R. Scattolini, "Stability and output terminal constraints in predictive control," in Advances in Model-Based Predictive Control. Oxford, U.K.: Oxford Univ. Press, 1994, pp. 105-121.
58. T. Parisini and R. Zoppoli, "A receding-horizon regulator for nonlinear systems and a neural approximation," Automatica, vol. 31, no. 10, pp. 1443-1451, 1995.
59. L. R. Petzold, "A description of DASSL: A differential/algebraic system solver," Sandia National Laboratories, Livermore, CA, Tech. Rep. 82-8637, 1982.
60. J. Pomet, "Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift," Syst. Control Lett., vol. 18, pp. 147-158, 1992.
61. V. M. Popov, Hyperstability of Control Systems. Berlin, Germany: Springer-Verlag, 1973.
62. S. J. Qin and T. Badgwell, "An overview of industrial predictive control technology," in Proc. Conf. Chemical Process Control (CPC-V), Assessment and New Directions for Research, Tahoe City, CA, Jan. 1996.
63. J. B. Rawlings and K. R. Muske, "The stability of constrained receding horizon control," IEEE Trans. Automat. Contr., vol. 38, pp. 1512-1516, Oct. 1993.
64. D. G. Robertson, J. H. Lee, and J. B. Rawlings, "A moving horizon-based approach to least squares estimation," AICHE J., 1996, to be published.
65. P. O. M. Scokaert and J. B. Rawlings, "Stability of model predictive control under perturbations," in Proc. IFAC Nonlinear Control Systems Design Symp. (NOLCOS'95), vol. 1, Tahoe City, CA, June 1995, pp. 21-26.
66. Y. Song, "Estimation and control in discrete-time nonlinear systems," Ph.D. diss., Dept. of Aerospace Engineering, Univ. of Michigan, 1992.
67. Y. Song and J. W. Grizzle, "The extended Kalman filter as a local asymptotic observer for nonliner discrete-time systems," J. Math. Syst., Estim. Control, vol. 5, no. 1, pp. 59-78, 1995.
68. A. Teel, R. Murray, and G. Walsh, "Nonholonomic control systems From steering to stabilization," in Proc. Conf. Decision and Control, Tucson, AZ, Dec. 1992, pp. 1603-1609.
69. T. H. Yang and E. Polak," Moving horizon control of linear systems with input saturation and plant uncertainty," Int. J. Control, vol. 58, no. 3, pp. 613-638, Sept. 1993.
70. _, "Moving horizon control of linear systems with input saturation, disturbances and plant uncertainty," Int. J. Control, vol. 58, no. 3, pp. 639-663, Sept. 1993.
71. _, "Moving horizon control of nonlinear systems with input saturation, disturbances and plant uncertainty," Int. J. Control, vol. 58, no. 4, pp. 875-903, Sept. 1993.
72. Z. Q. Zheng, "Robust control of systems subject to constraints," Ph.D. dissertation, California Institute of Technology, Pasadena, CA, 1995.