Beyond volterra and wiener: Optimal modeling of nonlinear dynamical systems in a neural space for applications in computational intelligence

Computational Intelligence: The Experts Speak

Volumn , Issue , 2003, Pages 65-98

  De Figueiredo, Rui J R ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Adaptation model; Computational intelligence; Computational modeling; Feedforward neural networks; Hilbert space; Kernel; Nonlinear dynamical systems

Indexed keywords

ARTIFICIAL INTELLIGENCE; DYNAMICAL SYSTEMS; HILBERT SPACES; NONLINEAR DYNAMICAL SYSTEMS;

ADAPTATION MODELS; COMPUTATIONAL MODEL; KERNEL; OPTIMAL MODEL; VOLTERRA;

FEEDFORWARD NEURAL NETWORKS;

EID: 84865258517     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1109/9780470544297.ch6     Document Type: Chapter

References (68)

1. R. J. R de Figueiredo. “A New Nonlinear Functional Analytic Framework for Modeling Artificial Neural Networks.” In Proceedings of the IEEE International Symposium on Circuits and Systems, New Orleans, LA, May 1990, pp. 723-726.
2. R. J. P. de Figueiredo. “An Optimal Matching-Score Net for Pattern Classification.” In Proceedings of 1990 International Joint Conference on Neural Networks, I J CNN-90, San Diego, CA, June 1990.
3. V. Volterra. Theory of Functionals and of Integral and Integro-Differential Equations. Dover, New York, 1959.
4. R. J. P. de Figueiredo and T. A. W. Dwyer III. “A Best Approximation Framework and Implementation for Simulation of Large-Scale Nonlinear Systems.” IEEE Trans. Circuits Syst., vol. CAS-27, no. 11, 1005-1014, 1980.
5. R. J. P. de Figueiredo. “A Generalized Fock Space Framework for Nonlinear System and Signal Analysis.” IEEE Trans. Circuits Syst., vol. CAS-30, no. 9, 637-647, 1983.
6. L. V. Zyla and R. J. P. de Figueiredo. “Nonlinear System Identification Based on a Fock Space Framework.” SIAM J. Control Optim., 931-939, Nov. 1983.
7. R. J. R de Figueiredo. “Mathematical Foundations of Optimal Interpolate Neural Networks.” InE. Houstis and J. R. Rice, (eds.), Artificial Intelligence, Expert Systems, and Symbolic Computing, pp. 303-319, Elsevier, Amsterdam, 1992.
8. R. J. P. de Figueiredo. “An Optimal Multilayer Neural Interpolating (OMNI) Net in a Generalized Fock Space Setting.” Proceedings of1992 International Joint Conference on Neural Networks, IJCNN-92, vol. 1, Baltimore, MD, 1992, pp. 111-118.
9. R. W. Newcomb and R. J. P. de Figueiredo. “A Multi-Input Multi-Output Functional Artificial Neural Network.” J. Intell. Fuzzy Syst., vol. 4, no. 3, 207-213, 1996.
10. R. J. P. de Figueiredo. “Optimal Interpolative and Smoothing Functional Artificial Neural Networks (FANNs) Based on a Generalized Fock Space Framework.” Circuits, Syst., Signal Process., vol. 17, no. 2, 271-287, 1998.
11. S. K. Sin and R. J. P. de Figueiredo. “An Incremental Fine Adjustment Algorithm for the Design of Optimal Interpolating Neural Networks.” Int. J. Pattern Recogn. Artif Intell., Nov. 1991.
12. S. K. Sin and R. J. P. de Figueiredo. “An Evolution Oriented Learning Algorithm for the Optimal Interpolative Net.” IEEE Trans. Neural Networks, vol. 3, no. 2, 315-323, 1992.
13. S. K. Sin and R. J. P. de Figueiredo. “Efficient Learning Procedures for Optimal Interpolating Networks.” Neural Networks, vol. 6, 99-113, 1993.
14. R. J. P. de Figueiredo and G. Chen. Nonlinear Feedback Control Systems: An Operator Theory Approach. Academic Press, New York, 1993.
15. A. Maccato and R. J. P. de Figueiredo. “Structured Neural Network Topologies with Application to Acoustic Transients.” Proceedings of the 1990 IEEE International Conference on Acoustics, Speech, and Signal Processing, Albuquerque, NM, April 1990, pp. 877-880.
16. A. Maccato and R. J. P. de Figueiredo. “A Neural Network Based Framework for Classification of Oceanic Acoustic Signals.” Proceedings of the 1989 OCEANS Conference, Seattle, WA, Sept. 18, 1989.
17. R. J. P. de Figueiredo and T. A. W. Dwyer III. “Approximation-Theoretic Methods for Nonlinear Deconvolution and Inversion.” Inf. Sei., vol. 31, 209-220, 1983.
18. R. J. P. de Figueiredo. “Implications and Applications of Kolmogorov’s superposition theorem.” IEEE Trans. Automatic Control, vol. AC-25, no. 5, 1227-1231, 1980.
19. R. J. P. de Figueiredo. “Generalized Nonlinear Functional and Operator Splines in Fock Spaces.” In Ward Cheney, (ed.), Approximation Theory, pp. 937-944, Academic Press, New York, 1980.
20. T. Eltoft and R. J. P. de Figueiredo. “A DCT-Based D-FANN for Nonlinear Adaptive Time Series Prediction.” IEEE Trans. Circuits Syst., Part II, 1131, 2000.
21. T. Eltoft and R. J. P. de Figueiredo. “A New Neural Network for Cluster-Detection and-Labelling.” IEEE Trans. Neural Networks, vol. 9, 1021-1035, 1998.
22. R. J. P. de Figueiredo and T. Eltoft. “Pattern Classification of Non-Sparse Data Using Optimal Interpolative Nets.” Neurocomputing, vol. 10, no. 4, 385-403, 1996.
23. R. J. P. de Figueiredo, W. R. Shankle, A. Maccato, M. B. Dick, P. Y. Mundkur, I. Mena, and C. W. Cotman. “Neural-Network-Based Classification of Cognitively Normal, Demented, Alzheimer’s Disease and Vascular Dementia from Brain SPECT Image Data.” In Proceedings of the National Academy of Sciences USA, vol. 92, June 1995, pp. 5530-5534.
24. A. Speis and R. J. P. de Figueiredo. “A Generalized Fock Space Framework for Nonlinear System Identification for Random Input-Output Data.” UCIInt. Rep., to be submitted for publication.
25. N. Wiener. Nonlinear Problems in Random Theory. MIT Press, Cambridge, MA, 1958.
26. A. G. Bose. “A Theory of Nonlinear Systems.” Tech. Rep. No. 309, Research Laboratory of Electronics, MIT, Cambridge, MA, 1956.
27. Y. W. Lee and M. Schetzen. “Measurement of the Wiener Kernels of a Nonlinear System by Cross-Correlation.” Int. J. Control, vol. 2, 237-254, 1965.
28. P. Z. Marmarelis and V. Z. Marmarelis. Analysis of Physiological Systems. Plenum Press, New York, 1978.
29. M. Schetzen. The Volterra and Wiener Theories on Non-Linear Systems. Wiley/Inter-science, New York, 1980.
30. W. J. Rugh. Nonlinear System Theory: The Volterra/Wiener Approach. Johns Hopkins University Press, Baltimore, MD, 1981.
31. L. Ljung and T. Söoderström. Theory and Practice of Recursive Identification. MIT Press, Cambridge, MA, 1983.
32. L. Ljung. System Identification: Theory for the User. Prentice Hall, Englewood Cliffs, NJ, 1987.
33. D. E. Rumelhart, J. L. McClelland, and the PDP Research Group. Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol. 1, Foundations. MIT Press, Cambridge, MA, 1986.
34. B. Widrow and S. D. Steams. Adaptive Signal Processing. Prentice Hall, Englewood Cliffs, NJ, 1985.
35. G. A. Carpenter and S. Grossberg. “Neural Dynamics of Category Learning and Recognition: Attention Memory Consolidation and Amnesia.” In J. Davis, R. Newburgh, and E. Wegman (eds.), Brain Structure, Learning and Memory, AAAS Symposium Series, Washington, DC, 1986.
36. S. I. Amari. “Mathematical Foundations of Neurocomputing.” Proc. IEEE, vol. 78, no. 9, 1443-1463, 1990.
37. J. M. Zurada. Introduction to Artificial Neural Systems. West, St. Paul, MN, 1992.
38. V. N. Vapnik. The Nature of Statistical Learning Theory. Springer-Verlag, New York, 1995.
39. V. N. Vapnik. Statistical Learning Theory. Wiley, New York, 1998.
40. A. Dingankar and I. W. Sandberg, “On Error Bounds for Neural Network Approximation.” In Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS-95, vol. 1, 1995, pp. 490-492.
41. L A. T. Dingankar and I. W. Sandberg. “Tensor Product Neural Networks and Approximation of Dynamical Systems.” In Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS-96, vol. 3, 1996, pp. 353-356.
42. J. C. Principe, N. R. Euliano, and W. C. Lefebre. Neural and Adaptive Systems. Wiley, New York, 2000.
43. S. Haykin. Adaptive Filter Theory, 3rd ed., Prentice Hall, Upper Saddle River, NJ, 1996.
44. W. G. Knecht. “Nonlinear Noise Filtering and Beam-Forming Using the Perception and Its Volterra Approximation.” IEEE Trans. Acoust., Speech, Signal Processing, vol. 2, no. 1, 55-62, 1994.
45. P. Werbos. “Generalization of Backpropagation with Application to a Recurrent Gas Market Model.” Neural Networks, vol. 1, 339-356, 1998.
46. A. Weigend, B. Huberman, and D. Rumelhart. “Predicting the Future: A Connectionist Approach.” Int. J. Neural Syst., vol. 7, no. 3-4, 403-30, 1990.
47. S. G. Tzafestas. Computational Intelligence in Systems and Control Design and Applications. Kluwer, Dordrecht, The Netherlands, 1999.
48. A. Gammerman. Computational Learning and Probabilistic Reasoning. Wiley, Chichester, UK, 1996.
49. G. Cybenko, “Approximation by Superpositions of a Sigmoidal Function.” Math. Control, Signals, Syst., vol. 2, no. 4, 303-314, 1989.
50. A. R. Barron. “Universal Approximation Bounds for Superpositions of a Sigmoidal Function.” IEEE Trans. Inform. Theory, vol. 39, issue 3, 930-945, 1993.
51. R A. Regalia. Adaptive IIR Filtering in Signal Processing and Control. Dekker, New York, 1995.
52. V. Fock. Konfigurationsraum und Zweite Quantelung. Z. Phys., vol. 75, 622-647, 1932.
53. F. Berezin. The Method of Second Quantization. Academic Press, New York, 1966.
54. 2 Euclidean (Quantum) Field Theory. Princeton University Press, Princeton, NJ, 1974.
55. V. Bargmann. “On a Hilbert Space of Analytic Functions and on Associated Integral Transform,” Part I. Commun. Pure Appl. Math., vol. 14, 187-214, 1961; also Part II. vol. 20, 1-101, 1967.
56. F. Beatrous and J. Burbea. Dissertations Mathematica. Warszawa, 1989.
57. n.” Bull. (New Ser.) Am. Math. Soc., vol. 8, no. 2, 1983.
58. T. W. A. Dwyer III. “Holomorphic Representation of Tempered Distributions and Weighted Fock Spaces.” In L. Nachbin, (ed.), Analyse Fonctionelle et Aplications, Hermann, Paris, 1975.
59. F. Treves. Topological Vector Spaces, Distributions and Kernels. Academic Press, New York, 1967.
60. E. Hille and R. S. Phillips. “Functional Analysis and Semigroups.” Am. Math. Soc. Colloq., Publ. 31, New York, 1957.
61. N. Aronsjahn. “Theory of Reproducing Kernels.” Am. Math. Soc. Trans., vol. 68,337-104, 1950.
62. F. B. Hildebrand. Introduction to Numerical Analysis. McGraw-Hill, New York, 1974.
63. J. Bolz, C. D. Gilbert, and T. N. Wisel. “Pharmacological Analysis of Cortical Circuitry.” Trends Neurosci., vol. 12, no. 8, 292-296, 1989.
64. J. C. Eccles and O. Creutzfeld (eds.). “The Principles of Design and Operation of the Brain.” In Proceedings of the Study Week Organized by the Pontifical Academy of Sciences, Cassia Pius IV, Vatican City, Springer-Verlag, New York, 1990.
65. R. J. P. de Figueiredo. “Beyond Volterra and Wiener: Some New Results And Open Problems in Nonlinear Circuits and Systems.” In Proceedings of the IEEE Midwest Symposium on Circuits and Systems, 1998, pp. 124-127.
66. L. A. Zadeh. “Outline of a New Approach to the Analysis of Complex Systems and Decision Processes.” IEEE Trans. Syst., Man Cybern., vol. 3, no. 1, 28-44, 1973.
67. L. A. Zadeh. In J. E. Hayes, D. Michie, and L. I. Mikulich, (eds.), A Theory of Approximate Reasoning, in Machine Intelligence, vol. 9, pp. 149-194. Elsevier, New York, 1979.
68. G. J. Klir, U. H. St. Clair, and B. Yuan. Fuzzy Set Theory: Foundations and Applications. Prentice Hall, Upper Saddle River, NJ, 1997.