Uniform approximation and gamma networks

Neural Networks

Volumn 10, Issue 5, 1997, Pages 781-784

  Sandberg, Irwin W ^a,b   Xu, Lilian ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b The University of Texas at Austin   (United States)

Author keywords

Approximation; Dynamic systems; Focused gamma networks; Gamma networks; Myopic maps; Networks; Uniform approximation; Uniform fading memory

Indexed keywords

APPROXIMATION THEORY; IDENTIFICATION (CONTROL SYSTEMS); REAL TIME SYSTEMS;

GAMMA NETWORKS; MYOPIC MAPS; UNIFORM FADING MEMORY;

NEURAL NETWORKS;

ARTIFICIAL NEURAL NETWORK; PRIORITY JOURNAL; SHORT SURVEY;

EID: 0031194380     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(97)00001-4     Document Type: Article

References (19)

1. Boyd, S., & Chua, L. O. (1985). Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Transactions on Circuits and Systems, 32, 1150-1161.
2. Chen, T., & Chen, H. (1993). Approximations of continuous functionals by neural networks with application to dynamical systems. IEEE Transactions on Neural Networks, 4, 910-918.
3. Chen, T., & Chen, H. (1995). Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its applications to dynamic systems. IEEE Transactions on Neural Networks, 6, 911-917.
4. Cybenko, G. (1989). Approximation by superposition of a single function. Mathematics of Control, Signals and Systems, 2, 303-314.
5. de Vries, B., & Principe, J.C. (1991). Adaline with adaptive recursive memory. Proceedings of IEEE-SP Workshop on Neural Networks for Signal Processing, pp. 101-110.
6. de Vries, B., & Principe, J.C. (1992). The gamma model - a new neural model for temporal processing. Neural Networks. 5, 565-576.
7. de Vries, B., Principe, J.C., Kuo, J., & de Oliveira, P.G. (1992). Modeling applications with the focused gamma net. Advances of Neural information Processing Systems, 4, 101-110.
8. Funahashi, K. (1989). On the approximate realization of continuous mappings by neural networks. IEEE Transactions on Neural Networks, 2, 183-192.
9. Kosmatopoulos, E., Polycarpou, M., Christodoulou, M., & Ioannou, P. (1995). High-order neural network structures for identification of dynamical systems. IEEE Transactions on Neural Networks, 6, 422-430.
10. Mhaskar, H. N., & Micchelli, C. A. (1992). Approximation by superposition of sigmoidal and radial basis functions. Advances in Applied Mathematics, 2, 350-373.
11. Park, J., & Sandberg, I. W. (1993). Approximation and radial-basis function networks. Neural Computation, 5, 305-316.
12. Sandberg, I. W. (1991a). Structure theorems for nonlinear systems. Multidimensional Systems and Signal Processing, 2, 267-286. (See also the Errata in (1992) 3, 101.
13. A conference version of the paper appears in Haji-Sheikh, A.H. (Ed.) (1991). Integral Methods in Science and Engineering - 90. New York: Hemisphere Publishing, pp. 92-110 (
14. Proceedings of the International Conference on Integral Methods in Science and Engineering, Arlington, Texas, May 1990).).
15. Sandberg, I.W. (1991b). Approximation theorems for discrete-time systems. IEEE Transactions on Circuits and Systems, 38, 564-566.
16. Sandberg, I.W., & Xu, L. (1996). Network approximation of input-output maps and functionals. Journal of Circuits, Systems, and Signal Processing, to appear.
17. Sandberg, I.W., & Xu, L. (1997a). Uniform approximation of multidimensional myopic maps. IEEE Transactions on Circuits and Systems, to appear.
18. Sandberg, I.W., & Xu, L. (1997b). Uniform approximation of discrete-space multidimensional myopic maps. Journal of Circuits, Systems, and Signal Processing, to appear.
19. Schetzen, M. (1980). The Volterra and Wiener Theories of Nonlinear Systems. New York: John Wiley.