Approximation of state-space trajectories by locally recurrent globally feed-forward neural networks

Neural Networks

Volumn 21, Issue 1, 2008, Pages 59-64

  Patan, Krzysztof ^a  

^a UNIVERSITY OF ZIELONA GÓRA   (Poland)

Author keywords

Approximation ability; Cascade network; Lipschitz mapping; Recurrent networks; State space representation; Universal approximation theorem

Indexed keywords

APPROXIMATION ALGORITHMS; DYNAMIC MODELS; PROBLEM SOLVING; RECURRENT NEURAL NETWORKS; STATE SPACE METHODS;

APPROXIMATION ABILITY; CASCADE NETWORKS; LIPSCHITZ MAPPING; RECURRENT NETWORKS; STATE SPACE REPRESENTATION; UNIVERSAL APPROXIMATION THEOREM;

FEEDFORWARD NEURAL NETWORKS;

ACCURACY; ARTICLE; ARTIFICIAL NEURAL NETWORK; FILTER; NETWORK LEARNING; PERCEPTRON; POSITIVE FEEDBACK; PRIORITY JOURNAL;

COMPUTER SIMULATION; FEEDBACK; HUMANS; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; SIGNAL PROCESSING, COMPUTER-ASSISTED; TIME FACTORS;

EID: 39649122393     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2007.10.004     Document Type: Article

References (22)

1. Ayoubi, M. (1994). Fault diagnosis with dynamic neural structure and application to a turbo-charger. In Proc. int. symp. fault detection supervision and safety for technical processes. (pp. 618-623). Vol. 2
2. Campolucci P., and Piazza F. Intrinsic stability-control method for recursive filters and neural networks. IEEE Transactions on Circuit and Systems - II: Analog and Digital Signal Processing 47 8 (2000) 797-802
3. Campolucci P., Uncini A., Piazza F., and Rao B.D. On-line learning algorithms for locally recurrent neural networks. IEEE Transactions on Neural Networks 10 (1999) 253-271
4. Cannas B., Cincotti S., Marchesi M., and Pilo F. Learning of Chua's circuit attractors by locally recurrent neural networks. Chaos, Solitons and Fractals 12 (2001) 2109-2115
5. Cybenko G. Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals, and Systems 2 (1989) 303-314
6. Garzon M., and Botelho F. Dynamical approximation by recurrent neural networks. Neurocomputing 29 (1999) 25-46
7. Gupta M.M., Jin L., and Homma N. Static and dynamic neural networks. From fundamentals to advanced theory (2003), John Wiley & Sons, New Jersey
8. Gupta M.M., and Rao D.H. Dynamic neural units with application to the control of unknown nonlinear systems. Journal of Intelligent and Fuzzy Systems 1 (1993) 73-92
9. Haykin S. Neural networks. A comprehensive foundation. 2nd ed. (1999), Prentice-Hall, New Jersey
10. Hirsch M., and Smale S. Differential equations, dynamical systems and linear algebra (1974), Academic Press, New York
11. Hornik K., Stinchcombe M., and White H. Multilayer feedforward networks are universal approximators. Neural Networks 2 (1989) 359-366
12. Jin L., Nikiforuk P.N., and Gupta M.M. Approximation of discrete-time state-space trajectories using dynamic recurrent neural networks. IEEE Transactions on Automatic Control 40 (1995) 1266-1270
13. Leshno M., Lin V., Pinkus A., and Schoken S. Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Networks 6 (1993) 861-867
14. Marcu T., Mirea L., and Frank P.M. Development of dynamical neural networks with application to observer based fault detection and isolation. International Journal of Applied Mathematics and Computer Science 9 3 (1999) 547-570
15. Nelles O. Nonlinear system identification. From classical approaches to neural networks and fuzzy models (2001), Springer-Verlag, Berlin
16. Patan, K. (2004). Training of the dynamic neural networks via constrained optimization. In Proc. IEEE int. joint conference on neural networks. Published on CD-ROM
17. Patan K., Korbicz J., and Prȩtki P. Global stability conditions of locally recurrent neural networks. Lecture notes on computer science Vol. 3697 (2005) 191-196
18. Patan K., and Parisini T. Identification of neural dynamic models for fault detection and isolation: The case of a real sugar evaporation process. Journal of Process Control 15 (2005) 67-79
19. Scarselli F., and Tsoi A.C. Universal approximation using feedforward neural networks: A survey of some existing methods, and some new results. Neural Networks 11 (1998) 15-37
20. Tsoi A.C., and Back A.D. Locally recurrent globally feedforward networks: A critical review of architectures. IEEE Transactions on Neural Networks 5 (1994) 229-239
21. Zamarreno J.M., and Vega P. State space neural network. Properties and application. Neural Networks 11 (1998) 1099-1112
22. Zhang J., Morris A.J., and Martin E.B. Long term prediction models based on mixed order locally recurrent neural networks. Computers & Chemical Engineering 22 (1998) 1051-1063