Universal stabilization using control Lyapunov functions, adaptive derivative feedback, and neural network approximators

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 28, Issue 3, 1998, Pages 472-477

  Kosmatopoulos, Elias B ^a  

^a University of Southern California ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; APPROXIMATION THEORY; CLOSED LOOP CONTROL SYSTEMS; CONTROL NONLINEARITIES; CONTROL SYSTEM ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; FEEDBACK CONTROL; FUNCTIONS; LYAPUNOV METHODS; NEURAL NETWORKS; NONLINEAR CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS);

ADAPTIVE DERIVATIVE FEEDBACK; CONTROL LYAPUNOV FUNCTIONS (CLF);

SYSTEM STABILITY;

EID: 0032095696     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/3477.678656     Document Type: Article

References (26)

1. A. Arstein, "Stabilization with relaxed controls," Nonlinear Anal., vol. 7, pp. 1163-1173, 1983.
2. A. R. Barron, "Universal approximation bounds for superpositions of a sigmoidal function," IEEE Trans. Inform. Theory, vol. 39, no. 3, pp. 930-945, 1993.
3. N. E. Cotter, "The Stone-Weierstrass theorem and its application to neural networks," IEEE Trans. Neural Networks, vol. 1, no. 4, pp. 290-295, 1990.
4. G. Cybenko, "Approximations by superpositions of a sigmoidal function," Math. Contr., Signals, Syst., vol. 2, pp. 303-314, 1989.
5. P. A. Ioannou and J. Sun, Stable and Robust Adaptive Control. Englewood Cliffs, NJ: Prentice Hall, 1995.
6. A. Isidori, Nonlinear Control Systems, 2nd ed. New York: Springer-Verlag, 1989.
7. I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, "Systematic design of adaptive controllers for feedback linearizable systems," IEEE Trans. Automat. Contr., vol. 36, pp. 1241-1253, Nov. 1991.
8. H. K. Khalil and F. Esfandiari, "Semiglobal stabilization of a class of nonlinear systems using output feedback," IEEE Trans. Automat. Contr., vol. 38, pp. 1412-1415, Sept. 1993.
9. E. B. Kosmatopoulos and M. A. Christodoulou, "Filtering, prediction, and learning properties of ECE neural networks," IEEE Trans. Syst., Man, Cybern., vol. 24, pp. 971-981, July 1994.
10. E. B. Kosmatopoulos, M. M. Polycarpou, M. A. Christodoulou, and P. A. Ioannou, "High-order neural network structures for identification of dynamical systems," IEEE Trans. Neural Networks, vol. 6, no. 2, pp. 422-431, Mar. 1995.
11. E. B. Kosmatopoulos and M. A. Christodoulou, "Structural properties of gradient recurrent high-order neural networks," IEEE Trans. Circuits Syst. II, vol. 42, Sept. 1995.
12. E. B. Kosmatopoulos, "A switching adaptive controller for feedback linearizable systems," IEEE Trans. Automat. Contr., to be published.
13. _, "Neural stabilizers for unknown systems," unpublished.
14. F. L. Lewis, K. Liu, and A. Yesildirek, "Neural net robot controller with guaranteed tracking performance," IEEE Trans. Neural Networks, vol. 6, pp. 703-715, May 1995.
15. H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems. Berlin, Germany: Springer-Verlag, 1990.
16. M. M. Polycarpou and P. A. Ioannou, "Identification and control of nonlinear systems using neural network models: Design and stability analysis," Tech. Rep. 91-09-01, Univ. Southern Calif., Los Angeles, Sept. 1991.
17. J.-B. Pomet, "Remarks on sufficient information for adaptive nonlinear regulation," in Proc. 31st IEEE Conf. Decision Control, Tuscon, AZ, Dec. 1992, vol. 2, pp. 1737-1741.
18. J.-B. Pomet and L. Praly, "Adaptive nonlinear stabilization: Estimation from the Lyapunov equation," IEEE Trans. Automat. Contr., vol. 37, pp. 729-740, 1992.
19. G. A. Rovithakis and M. A. Christodoulou, "Adaptive control of unknown plants using dynamical neural networks," IEEE Trans. Syst., Man, Cybern., vol. 24, pp. 400-412, Mar. 1994.
20. D. Seto, A. M. Annaswamy, and J. Baillieul, "Adaptive control of nonlinear systems with a triangular structure," IEEE Trans. Automat. Contr., vol. 39, pp. 1411-1428, July 1994.
21. R. M. Sanner and J.-J. E. Slotine, "Gaussian networks for direct adaptive control," in Proc. Amer. Contr. Conf., ACC'91, 1991, pp. 2153-2159;
22. also in IEEE Trans. Neural Networks, vol. 3, pp. 837-863, Nov. 1992.
23. E. D. Sontag, "A "universal" construction of Arstein's theorem on nonlinear stabilization," Syst. Contr. Lett., vol. 13, no. 2, pp. 117-123, 1989.
24. J. Tsinias, "Stabilization of affine in control nonlinear systems," Nonlinear Anal., vol. 12, no. 11, pp. 1283-1296, 1988.
25. J. Tsinias, "Sufficient Lyapunov-like conditions for stabilization," Math. Contr., Signals, Syst., vol. 2, no. 4, pp. 343-357, 1989.
26. _, "Existence of control Lyapunov functions and applications to state feedback stabilizability of nonlinear systems," SIAM J. Contr. Optim., vol. 29, pp. 457-473, Mar. 1991.