Abstract
With Kleinman’s controller, its extended form and Riccati iteration as analyzing tools, the stability of GPC under various parameter cases is discussed. The overall closed-loop stability conclusions of GPC in equivalence with Kleinman’s controller are obtained, which cover some existing results and provide the theoretical foundation for stable design of predictive control.
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References
Wang, W., Generalized Predictive Control: Theory and Application (in Chinese), Beijing: Science Press, 1998.
Clarke, D. W., Scattolini, R., Constrained receding-horizon predictive control, Proc. IEE, Pt D, 1991, 138(4): 347–354.
Scokaert, P. O. M., Infinite horizon generalized predictive control, Int. J. Contr., 1997, 66(1): 161–175.
Xi, Y. G., Geng, X. J., Chen, H., Recent advances in research on predictive control performance, Control Theory and Application (in Chinese), 2000, 17(4): 469–475.
Yamuna, R. K., Unbehauen, H., Study of predictive controller tuning methods, Automatica, 1997, 33(12): 2243–2248.
Clarke, D. W., Mohtadi, C., Tuffs, P. S., Generalized predictive control, Part I: Basic algorithm and Part II: Extensions and interpretations, Automatica, 1987, 23(2): 137–160.
Clarke, D. W., Mohtadi, C., Properties of generalized predictive control, Automatica, 1989, 25(6): 859–875.
Kleinman, D. L., Stabilizing a discrete, constant, linear system with application to iterative methods for solving the Riccati equation, IEEE Trans. Automat. Contr., 1974, 19(3): 252–254.
Kwon, W. H., Pearson, A. E., On the stabilization of a discrete constant linear system, IEEE Trans. Automat. Contr., 1975, 20(6): 800–801.
Yaz, E., Selbuz, H., A note on the receding horizon control method, Int. J. Contr., 1984, 39(4): 853–855.
Xi, Y. G., Zhang, J., Study on the closed-loop properties of GPC, Science in China (Series E), 1997, 40(1): 54–63.
Scattolini, R., Bittanti, S., On the choice of the horizon in long-range predictive control-some simple criteria, Automatica, 1990, 26(5): 915–917.
Elshafei, A. L., Dumont, G., Elnaggar, A., Stability and convergence analyses of an adaptive GPC based on state-space modeling, Int. J. Contr., 1995, 61(1): 193–210.
Peng, L., Fisher, D. G., Shah, S. L., On-line tuning of GPC using a pole placement criterion, Proceedings of American Control Conference, CA, U.S.A., 1993, FM11: 2637–2641.
Kowalczuk, Z., Suchomski, P., Marcinczyk, A., Discrete-time and continuous-time generalized predictive control with anticipated filtration: tuning rules, Int. J. Applied Mathematics and Computer Science, 1996, 6(4): 707–732.
McIntosh, A. R., Shah, S. L., Fisher, D. G., Analysis and tuning of adaptive generalized predictive control, Canadian J. Chem. Eng., 1991, 69(2): 97–110.
Peng, Y., Hanus, R., A tuning strategy for generalized predictive control, Control Theory and Advanced Technology, 1991, 7(1): 153–166.
Soeterboek, R., Predictive Control, a Unified Approach, New York, London: Prentice-Hall, 1992.
Camacho, E. F., Bordons, C., Model Predictive Control, Berlin, Heidelberg, New York: Springer, 1998.
Landau, I. D., Lozano, R., M’Saad, M., Adaptive Control, Berlin: Springer, 1998.
Kwon, W. H., Choi, H., Byun, D. G. et al., Recursive solution of generalized predictive control and its equivalence to receding horizon tracking control, Automatica, 1992, 28(6): 1235–1238.
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Ding, B., Xi, Y. Stability analysis of generalized predictive control based on Kleinman’s controllers. Sci China Ser F 47, 458–474 (2004). https://doi.org/10.1007/BF02901658
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DOI: https://doi.org/10.1007/BF02901658