Upper Bounds for Approximation of Continuous-Time Dynamics Using Delayed Outputs and Feedforward Neural Networks

IEEE Transactions on Automatic Control

Volumn 48, Issue 9, 2003, Pages 1606-1610

  Lavretsky, Eugene ^a   Hovakimyan, Naira ^b   Calise, Anthony J ^c  

^a BOEING COMPANY   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^c Georgia Institute of Technology   (United States)

Author keywords

Adaptive estimation; Adaptive output feedback; Approximation; Continuous time dynamics; Feedforward neural networks

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; NONLINEAR SYSTEMS; SAMPLING; STATE ESTIMATION;

UPPER BOUNDS;

FEEDFORWARD NEURAL NETWORKS;

EID: 0141638578     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.816987     Document Type: Article

References (22)

1. A. Levin and K. Narendra, "Control of nonlinear dynamical systems using neural networks-Part II: Observability, identification and control," IEEE Trans. Neural Networks, vol. 7, pp. 30-42, Jan. 1996.
2. S. Seshagiri and H. K. Khalil, "Output feedback control of nonlinear systems using RBF neural networks," IEEE Trans. Neural Networks, vol. 11, pp. 69-79, Jan. 2000.
3. G. Cybenko, "Approximation by superpositions of sigmoidal functions," Math. Control Signals, Syst., vol. 2, no. 4, pp. 303-314, 1989.
4. A. Barron, "Universal approximation bounds for superposition of a sigmoidal function," IEEE Trans. Inform. Theory, vol. 39, pp. 930-945, Mar. 1993.
5. _, "Approximation and estimation bounds for artificial neural networks," Mach. Learn., vol. 14, no. 2, pp. 115-133, 1994.
6. A. Pinkus, "Approximation theory of the MLP model in neural networks," Acta Numerica, vol. 44, no. 9, pp. 143-195, 1999.
7. A. J. Calise, N. Hovakimyan, and M. Idan, "Adaptive output feedback control of nonlinear systems using neural networks," Auiomatica. vol. 37, no. 8, pp. 1201-1211, 2001.
8. N. Hovakimyan, F. Nardi, A. Calise, and N. Kim, "Adaptive output feedback control of uncertain systems using single hidden layer neural networks," IEEE Trans. Neural Networks, vol. 13, pp. 1420-1431, Nov. 2002.
9. N. Hovakimyan, A. J. Calise, and V. Madyastha, "An adaptive observer design methodology for bounded nonlinear processes," presented at the Conf. Decision Control, 2002.
10. A. Isidori, Nonlinear Control Systems. Berlin, Germany: Springer-Verlag, 1995.
11. A. Tomambe, "Output feedback stabilization of a class of nonminimum phase nonlinear systems," Syst. Control Lett., vol. 19, pp. 193-204. 1992.
12. A. Teel and L. Praly, "Global stabilizability and observability imply semi-global slabilizability by output feedback," Syst. Control Lett., vol. 22, pp. 313-325, 1994.
13. M. Maggiore and K. Passino, "Output feedback control for stabilizable and incompletely observable nonlinear systems: Theory," presented at the Amer. Control Conf., 2000.
14. T. Parthasarthy, On Global Univalence Theorems, ser. Lecture Notes in Mathematics. New York: Springer-Verlag, 1983, vol. 977.
15. R. G. Bartle. The Elements of Real Analysis. New York: Wiley, 1964.
16. R. Courant and F. John, Introduction to Calculus and Analysis. New York: Springer-Verlag, 1989, vol. 2.
17. J. Park and I. Sandberg, "Universal approximation using radial basis function networks," Neural Comput., vol. 3, pp. 246-257, 1991.
18. _, "Approximation and radial-basis-function networks," Neural Comput., vol. 5, pp. 305-316, 1993.
19. S. Haykin, Neural Networks: A Comprehensive Foundation. Upper Saddle River, NJ: Prentice-Hall, 1999.
20. H. K. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice-Hall, 2002.
21. Z. P. Jiang and D. Hill, "A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics," IEEE Trans. Automat. Contr., vol. 44, pp. 1705-1711, Sept. 1999.
22. N. Hovakimyan, H. Lee, and A. Calise, "On approximate NN realization of an unknown dynamic function from its input-output history," presented at the Amer. Control Conf., 2000.