Beyond volterra and wiener: Some new results and open problems in nonlinear circuits and systems

Midwest Symposium on Circuits and Systems

Volumn , Issue , 1998, Pages 124-127

  De Figueiredo, Rui J P ^a  

^a University of California at Irvine   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; DYNAMICAL SYSTEMS; NONLINEAR DYNAMICAL SYSTEMS; TIMING CIRCUITS;

BEST APPROXIMATIONS; FOCK SPACES; LAGUERRE; NEW RESULTS; NEW TECHNOLOGIES; NONLINEAR CIRCUITS AND SYSTEMS; SERIES REPRESENTATIONS; VOLTERRA;

NEURAL NETWORKS;

EID: 0009548806     PISSN: 15483746     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/MWSCAS.1998.759452     Document Type: Conference Paper

References (15)

1. Volterra, V., Theory of functionals and of integral and integro-differential equations, Dover Publications, New York, 1959.
2. Wiener, N. Nonlinear Problems in Random Theory, M.I.T. Press, Cambridge, MA, 1958.
3. de Figueiredo, R. J. P., and T. A. W. Dwyer, III, "A best approximation framework and implementation for simulation of large-scale nonlinear systems", IEEE Transactions on Circuits and Systems, Vol. CAS-27, No. 11, November 1980, pp. 1005-1014.
4. de Figueiredo, R. J. P., "A Generalized Fock Space Framework for Nonlinear System and Signal Analysis", IEEE Trans. on Circuits and Systems, vol. CAS- 30, no. 9, pp. 637-647, September 1983 (Special invited issue on "Nonlinear Circuits and Systems").
5. Zyla, L.V. and R. J. P. de Figueiredo, "Nonlinear SystemIdentification based on a Fock Space Framework", SIAM Jour. of Control and Optimization, November 1993 (Memorial issue in honor of J.P. LaSalle, pp. 931-939.
6. de Figueiredo, R. J. P., and G. Chen, Nonlinear Feedback Control Systems: An Operator Theory Approach, Academic Press, 1993.
7. de Figueiredo, R. J. P., "A new nonlinear functional analytic framework for modeling artificial neural networks" (invited paper), Proc. of the IEEE Intnl. Symposium on Circuits and Systems, New Orleans, LA, May 1-3, 1990, pp. 723-726.
8. de Figueiredo, R. J. P., "Mathematical foundations of optimal interpolative neural networks", in Artificial Intelligence, Expert Systems, and Symbolic Computing, E. Houstis and J. R. Rice, Editors, Elsevier, Amsterdam, 1992, pp. 303-319.
9. de Figueiredo, R. J. P., "An optimal multilayer neural interpolating (OMNI) net in a Generalized Fock Space setting", Proc. IJCNN-92, Baltimore, MD. Vol. 1, 1992, pp. 111-118.
10. de Figueiredo, R. J. P., "Neural Modeling and Identification of Nonlinear Systems in an Abstract Space Setting", in Mechanics and Control, V, R. S. Gutalu, Ed., Plenum Press, 1993, pp. 309-317.
11. de Figueiredo, R. J. P., "The OI, OS, OMNI and OSMAN Networks as Best Approximations of Nonlinear Systems Under Training Data Constraints (invited paper)", 1996 IEEE Intnl. Symposium on Circuits and Systems, Seattle, Washington.
12. Sin, S. K., and R. J. P. de Figueiredo, "An Evolution Oriented Learning Algorithm for the Optimal Interpolative Net", IEEE Trans. on Neural Networks, vol. 3, no. 2, March 1992, pp. 315-323.
13. de Figueiredo, R. J. P., "Optimal Interpolative and smoothing functional artificial neural networks (FANNs) based on a Generalized Fock Space Framework, " Circuits, Systems, and Signal Processing, vol. 17, no. 2, 1998, pp. 271-287.
14. de Figueiredo, R. J. P., Hu, Y., "On Nonlinear Filtering of Non-Gaussian Processes through Volterra Series, " Volterra Centennial Memorial Volume, Kluwer, 1998.
15. de Figueiredo, R. J. P., Hu, Y., "Nonlinear Filters for Non-Gaussian Signal Processing - Part A: The Wiener-Hopf Equation in a Generalized Fock Space", to be published.