Nonlinear Model-Predictive Control: Closed-loop Stability Analysis

AIChE Journal

Volumn 42, Issue 12, 1996, Pages 3388-3402

  Sistu, Phani B ^a   Bequette, B Wayne ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; DIFFERENCE EQUATIONS; LYAPUNOV METHODS; NONLINEAR SYSTEMS; PREDICTIVE CONTROL SYSTEMS; SIMULATION; STABILITY; STABILITY CRITERIA;

DISCRETIZATION; NONLINEAR MODEL PREDICTIVE CONTROL;

NONLINEAR CONTROL SYSTEMS;

EID: 0030413802     PISSN: 00011541     EISSN: None     Source Type: Journal    
DOI: 10.1002/aic.690421210     Document Type: Article

References (42)

1. Bequette, B. W., "Nonlinear Control of Chemical Processes: A Review," Ind. Eng. Chem. Res., 30, 1391 (1991).
2. Biegler, L. T., and J. B. Rawlings, "Optimization Approaches to Nonlinear Model Predictive Control," CPC IV, Y. Arkun and H. Ray, eds., AIChE, p. 543 (1991).
3. Bitmead, R. R., M. Gevers, and V. Wertz, Adaptive Optimal Control, Prentice Hall, New York (1990).
4. Brengel, D. D., and W. D. Seider, "Multistep Nonlinear Predictive Controller," Ind. Eng. Chem. Res., 28, 1812 (1989).
5. Chen, C. C, and L. Shaw, "On Receding Horizon Control," Automatica, 15, 349 (1982).
6. Cutler, C. R., and B. L. Ramaker, "Dynamic Matrix Control - A Computer Control Algorithm," Proc. of the 1980 American Control Conf, San Francisco (1980).
7. de Oliveira, N. M. C., and L. T. Biegler, "An Extension of Newtontype Algorithms for Nonlinear Process Control," Automatica, 31(2), 281 (1995).
8. Eaton, J. W., and J. B. Rawlings, "Feedback Control of Nonlinear Processes Using On-Line Optimization Techniques," Comput. Chem. Eng., 14, 469 (1990).
9. Economou, C. G., An Operator Theory Approach to Nonlinear Controller Design, PhD Thesis, California Institute of Technology, Pasadena (1985).
10. Economou, C. G., M. Morari, and B. O. Palsson, "Internal Model Control: 5. Extension to Nonlinear Systems," Ind. Eng. Chem. Process Des. Dev., 25, 403 (1982).
11. Garcia, C. E., and M. Morari, "Internal Model Control: A Unifying Review and Some New Results," Ind. Eng. Chem. Process Des. Dev., 21, 308 (1982).
12. Garcia, C. E., "Quadratic Dynamic Matrix Control of Nonlinear Processes," AIChE Meeting, San Francisco (1984).
13. Garcia, C. E., D. M. Prett, and M. Morari, "Model Predictive Control: Theory and Practice-A Survey," Automatica, 25, 335 (1989).
14. Gill, P. E., W. Murray, M. A. Saunders, and M. H. Wright, "User's Guide for NPSOL (Version 4.0): A Fortran Program for Nonlinear Programming," Tech. Rep. SOL 86-2, Dept. of Operations Research, Stanford Univ., Stanford (1986).
15. Hahn, W., Stability of Motion, Springer-Verlag, New York (1967).
16. Henson, M. A., and D. E. Seborg, "Theoretical Analysis of Unconstrained Nonlinear Model Predictive Control," Int. J. Contr., 58, 1053 (1993).
17. Isidori, A., Nonlinear Control Systems: An Introduction, 2nd ed., Springer-Verlag, Berlin (1989).
18. Jang, S., B. Joseph, and H. Mukai, "Control of Constrained Multivariable Nonlinear Process Using a Two-Phase Approach," Ind. Eng. Chem. Res., 26, 809 (1987).
19. Kalman, R., and J. Bertram, "Control Systems Design and Analysis via the Second Method of Lyapunov," Trans. ASME Series D., J. Basic Eng., 82, 394 (1960).
20. Keerthi, S. S., and E. G. Gilbert, "Optimal Infinite Horizon Feedback Laws for a General Class of Constrained Discrete-Time Systems: Stability and Moving Horizon Approximations," J. Optimiz. Theory Appl., 57, 265 (1988).
21. Khalil, K. H., Nonlinear Systems, Macmillan, New York (1992).
22. Kravaris, C., and P. Daoutidis, "Nonlinear State Feedback Control of Second-order Nonminimum-phase Nonlinear Systems," Comput. Chem. Eng., 14, 439 (1990).
23. Kravaris, C., and J. C. Kantor, "Geometric Methods for Nonlinear Process Control: I. Background; II. Controller Synthesis," Ind. Eng. Chem. Res., 29, 2295 (1990).
24. Kwon, W. H., and A. E. Pearson, "On Feedback Stabilization of Time-Varying Discrete Linear Systems," IEEE Trans. Automat. Cont., AC-23, 479 (1978).
25. Li, W. C, and L. T. Biegler, "Multistep Newton-Type Control Strategies for Constrained, Nonlinear Process," Chem. Eng. Res. Res., 67, 562 (1989).
26. Mayne, D. Q., and H. Michalska, "Receding Horizon Control of Nonlinear Systems," IEEE Trans. Automat. Contr., AC-35, 814 (1990).
27. Mayne, D. Q., and H. Michalska, "Model Predictive Control of Nonlinear Systems," Proc. 1991 American Control Conf., p. 2343 (1991).
28. Meadows, E., M. A. Henson, J. W. Eaton, and J. B. Rawlings, "Receding Horizon Control and Discontinuous Feedback Stabilization," Int. J. Contr., 62(5), 1217 (1995).
29. Mehra, R. K., R. Rouhani, J. Etero, J. Richalet, and A. Roult, "Model Algorithmic Control: Review and Recent Developments," Proc. Engineering Foundation Conf. on Chemical Process Control II, D. E. Seborg and T. F. Edgar, eds., Sea Island, GA, p. 287 (1982).
30. Monaco, S., and D. Normand-Cyrot, "Zero Dynamics of Sampled Nonlinear Systems," Syst. and Contr. Lett., 11, 229 (1988).
31. Nijmeijer, H., and A. J. van der Schaft, Nonlinear Dynamical Control Systems, Springer-Verlag, New York (1990).
32. Ortega, J. M., "Stability of Difference Equations and Convergence of Iterative Processes," SIAM J. Numer. Anal., 10, 268 (1973).
33. O'Shea, R., "The Extension of Zubov's Method to Sampled-data Control Systems Described by Nonlinear Autonomous Difference Equations," IEEE Trans. Automat. Contr., AC-9, 62 (1964).
34. Rall, L. B., Computational Solutions of Nonlinear Operator Equations, Krieger, New York (1979).
35. Rawlings, J. B., and K. Muske, "The Stability of Constrained Receding Horizon Control," IEEE Trans. Automat. Cont., AC-38, 1512 (1993).
36. Sistu, P. B., and B. W. Bequette, "Nonlinear Predictive Control of Uncertain Chemical Processes: Application to a CSTR," AIChE J., 37, 1711 (1991).
37. Sistu, P. B., and B. W. Bequette, "A Comparison of Nonlinear Control Techniques for Continuous Stirred Tank Reactors," Chem. Eng. Sci., 47, 2553 (1992).
38. Sistu, P. B., and B. W. Bequette, "Model Predictive Control of Processes with Input Multiplicities," Chem. Eng. Sci., 50(6), 921 (1995).
39. Soroush, M., and C. Kravaris, "Discrete-Time Nonlinear Control Synthesis by Input/Output Linearization," AIChE J., 12, 1923 (1992).
40. Thomas, Y. A., "Linear Quadratic Optimal Estimation and Control with Receding Horizon," Electron. Lett., 11, 19 (1975).
41. Van de Vusse, J. G., "Plug-flow Type Reactor versus Tank Reactor," Chem. Eng. Sci., 19, 964 (1964).
42. Zames, G., "Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms and Approximate Inverses," IEEE Trans. Automat. Contr., AC-26, 301 (1981).