Set membership prediction of nonlinear time series

IEEE Transactions on Automatic Control

Volumn 50, Issue 11, 2005, Pages 1655-1669

  Milanese, Mario ^a   Novara, Carlo ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Nonlinear systems; Nonparametric methods; Prediction; Robust estimation; Set membership; Time series

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONTROL SYSTEM ANALYSIS; GRADIENT METHODS; MEMBERSHIP FUNCTIONS; OPTIMAL CONTROL SYSTEMS; REGRESSION ANALYSIS; ROBUSTNESS (CONTROL SYSTEMS); TIME SERIES ANALYSIS;

LINEAR AUTOREGRESSIVE MODEL; NONLINEAR TIME SERIES; NONPARAMETRIC METHODS; ROBUST ESTIMATION; SET MEMBERSHIP PREDICTION;

NONLINEAR CONTROL SYSTEMS;

EID: 28744439310     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.858693     Document Type: Article

References (44)

1. B. Widrow and S. D. Stearns, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1985.
2. L. Wu, M. Niranjan, and F. Fallside, "Fully vector-quantized neural network-based code-excited nonlinear predictive speech coding," IEEE Trans. Speech Audio Process., vol. 2, no. 4, pp. 482-489, Oct. 1994.
3. B. Y. Ryabko, "Prediction of random sequences and universal coding," Prob. Inform. Trans., vol. 24, pp. 87-96, 1988.
4. J. M. Hutchinson, A. W. Lo, and T. Poggio, "A nonparametric approach to pricing and hedging derivative securities via learning networks," J. Finance, vol. XLIX, no. 3, pp. 677-687, 1994.
5. A. S. Weigend and N. A. Gershenfeld, Time Series Prediction: Forecasting the Future and Understanding the Past. Reading, MA: Addison-Wesley, 1994.
6. A. Porporato and L. Ridolfi, "Nonlinear analysis of river flow time sequences," Water Resour. Res., vol. 33, no. 6, pp. 1353-1367, 1997.
7. A. W. Jayawardena and A. B. Gurung, "Noise reduction and prediction of hidrometereological time series," J. Hydrol., vol. 227, pp. 242-264, 2000.
8. B. Sivakumar, "Chaos theory in hydrology: Important issues and interpretations," J. Hydrol., vol. 227, no. 1-4, pp. 1-20, 2000.
9. J. Houghton, "The bakerian lecture, 1991: The predictability of weather and climate," Phil. Trans. Roy. Soc. London A, vol. 337, pp. 521-572, 1991.
10. G. Box and G. Jenkins, Time Series Analysis: Forecasting and Control. San Francisco, CA: Holden Day, 1976.
11. G. M. Jenkins, Practical Experiences With Modeling and Forecasting Time Series. London, U.K.: Time Series Library, 1979.
12. D. Q. Mayne, I. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: Stability and optimality," Automatica, vol. 36, no. 6, pp. 789-814, 2000.
13. L. Ljung, System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall, 1999.
14. D. S. Modha and E. Masry, "Memory-universal prediction of stationary random processes," IEEE Trans. Inform. Theory, vol. 44, no. 1, pp. 117-133, Jan. 1998.
15. K. R. Muller, A. Smola, G. Rätsch, B. Schölkopf, J. Kohlmorgen, and V. Vapnik, "Predicting time series with support vector machines," in Advances in Kernel Methods - Support Vector Learning. Cambridge, MA: MIT Press, 1999, pp. 243-254.
16. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. Washington, DC: Winston, 1977.
17. J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: A unified overview," Automatica, vol. 31, pp. 1691-1723, 1995.
18. A. Juditsky, H. Hjalmarsson, A. Benveniste, B. Delyon, L. Ljung, J. Sjöberg, and Q. Zhang, "Nonlinear black-box modeling in system identification: Mathematical foundations," Automatica, vol. 31, pp. 1725-1750, 1995.
19. R. Haber and H. Unbehauen, "Structure identification of nonlinear dynamic systems-A survey on input/output approaches," Automatica, vol. 26, pp. 651-677, 1990.
20. M. Milanese and R. Tempo, "Optimal algorithms theory for robust estimation and prediction," IEEE Trans. Autom. Control, vol. AC-30, no. 8, pp. 730-738, Aug. 1985.
21. M. Milanese and A. Vicino, "Optimal algorithms estimation theory for dynamic systems with set membership uncertainty: An overview," Automatica, vol. 27, pp. 997-1009, 1991.
22. M. Milanese, J. Norton, H. P. Lahanier, and E. Walter, Bounding Approaches to System Identification. New York: Plenum, 1996.
23. ∞ Approach. New York: Wiley, 2000.
24. J. R. Partington, Interpolation, Identification and Sampling. New York: Clarendon, 1997, vol. 17.
25. J. F. Traub, G. W. Wasilkowski, and H. Woźniakowski, Information-Based Complexity. New York: Academic, 1988.
26. A. Pinkus, n-Widths in Approximation Theory. Berlin, Germany: Springer-Verlag, 1985.
27. d," J. Complexity, no. 17, pp. 722-740, 2001.
28. M. Milanese and C. Novara, "Set membership identification of nonlinear systems," Automatica, vol. 40/6, pp. 957-975, 2004.
29. H. Edelsbrunner, Algorithms in Combinatorial Geometry. Berlin, Germany: Springer-Verlag, 1987.
30. K. S. Narendra and S. Mukhopadhyay, "Neural networks for system identification," in Sysid 97, vol. 2, 1997, pp. 763-770.
31. A. Stenman, F. Gustafsson, and Ljung, "Just in time models for dynamical systems," in Proc. 35th IEEE Conf. Decision and Control, Kobe, Japan, 1996, pp. 1115-1120.
32. Q. Zheng and H. Kimura, "Just in time modeling for function prediction and its applications," Asian J. Control, vol. 3, no. 1, pp. 35-44, 2001.
33. E. D. Sontag, "Nonlinear regulation. The piecewise linear approach," IEEE Trans. Autom. Control, vol. AC-26, no. 2, pp. 346-357, Apr. 1981.
34. G. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari, "A clustering technique for the identification of piecewise affine systems," in Hybrid Systems: Computation and Control, A. Sangiovanni-Vincentelli and M. D. Di Benedetto, Eds. New York: Springer-Verlag, 2001, Lecture Notes in Computer Science.
35. C. W. J. Granger and A. P. Andersen, Introduction to Bilinear Time Series Models. Gottingen, Germany: Vandenhoek and Ruprecht, 1978.
36. J. Hertz, A. Krogh, and G. Palmer, Introduction to the Theory of Neural Computation. Reading, MA: Addison - Wesley, 1991.
37. V. Vapnik, The Nature of Statistical Learning Theory. New York: Springer-Verlag, 1995.
38. H. Tong and K. S. Lim, "Threshold autoregression, limit cycles and cyclical data," J. Royal Statist. Soc., ser. B, vol. 42, pp. 245-292, 1980.
39. A. Vicino, R. Tempo, R. Genesio, and M. Milanese, "Optimal error and GMDH predictors," Int. J. Forecasting, no. 3, pp. 313-328, 1987.
40. A. G. Ivakhnenko, "Heuristic self-organization in problems of engineering cybernetics," Automatica, vol. 6, pp. 207-219, 1970.
41. M. Milanese, C. Novara, F. Mastronardi, and D. Amoroso, "Experimental modeling of vertical dynamics of vehicles with controlled suspensions," in Proc. SAE World Congr., Detroit, MI, 2004.
42. M. Milanese, C. Novara, P. Gabrielli, and L. Tenneriello, "Experimental modeling of controlled suspension vehicles from onboard sensors," in Proc. 1st IFAC Symp. Advances in Automotive Control, Salerno, Italy, 2004.
43. M. Milanese and C. Novara, "Set membership prediction of river flow," Syst. Control Lett., vol. 53/1, pp. 31-39, 2004.
44. G. Finzi, M. Milanese, C. Novara, and M. Volta, "Nonlinear set membership forecast of urban ozone peaks," in Proc. IFAC 2005, Prague, Czech Republic, 2005.