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Adaptive NN control of uncertain nonlinear pure-feedback systems. (English) Zbl 0998.93025
This paper deals with the control of nonlinear pure-feedback systems with unknown nonlinear function. Adaptive neural network control schemes are proposed for such systems. Under mild assumptions on the partial derivatives of the unknown functions, the developed control scheme achieves semi-global uniform ultimate boundedness of all signals in the closed loop.

93C40Adaptive control systems
92B20General theory of neural networks (mathematical biology)
93C10Nonlinear control systems
Full Text: DOI
[1] Apostol, T. M.: Mathematical analysis. (1963)
[2] Chen, F. C.; Khalil, H. K.: Adaptive control of a class of nonlinear discrete-time systems using neural networks. IEEE transactions on automatic control 40, No. 5, 791-801 (1995) · Zbl 0925.93461
[3] Dong, X.; Chen, G.; Chen, L.: Adaptive control of the uncertain Duffing oscillator. International journal of bifurcation and chaos 7, No. 7, 1651-1658 (1997) · Zbl 0967.93512
[4] Ferrara, A.; Giacomini, L.: Control of a class of mechanical systems with uncertainties via a constructive adaptive/second order VSC approach. Transactions of ASME, journal of dynamic systems, measurement and control 122, No. 1, 33-39 (2000)
[5] Freeman, R. A.; Kokotovic\grave{}, P.: Robust nonlinear control design. (1996)
[6] Ge, S. S.; Hang, C. C.; Zhang, T.: Adaptive neural network control of nonlinear systems by state and output feedback. IEEE transactions on systems, man and cybernetics--part B cybernetics 29, No. 6, 818-828 (1999)
[7] Ge, S. S., Hang, C. C., Lee, T. H., & Zhang, T. (2001). Stable adaptive neural network control. Kluwer Academic (in Press). · Zbl 1001.93002
[8] Haykin, S.: Neural networks: A comprehensive foundation. (1999) · Zbl 0934.68076
[9] Hunt, L. R.; Meyer, G.: Stable inversion for nonlinear systems. Automatica 33, No. 8, 1549-1554 (1997) · Zbl 0890.93046
[10] Jiang, Z. P.; Praly, L.: Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties. Automatica 34, No. 7, 825-840 (1998) · Zbl 0951.93042
[11] Kanellakopoulos, I.; Kokotovic, P. V.; Morse, A. S.: Systematic design of adaptive controller for feedback linearizable systems. IEEE transactions on automatic control 36, No. 11, 1241-1253 (1991) · Zbl 0768.93044
[12] Krstic\grave{}, M.; Kanellakopoulos, I.; Kokotovic\grave{}, P. V.: Adaptive nonlinear control without overparameterization. Systems and control letters 19, 177-185 (1992)
[13] Krstic\grave{}, M.; Kanellakopoulos, I.; Kokotovic\grave{}, P.: Nonlinear and adaptive control design. (1995)
[14] Lewis, F. L.; Jagannathan, S.; Yeildirek, A.: Neural network control of robot manipulators and nonlinear systems. (1999)
[15] Nam, K.; Arapostations, A.: A model-reference adaptive control scheme for pure-feedback nonlinear systems. IEEE transactions on automatic control 33, 803-811 (1988) · Zbl 0649.93040
[16] Narendra, K. S.; Parthasarathy, K.: Identification and control of dynamic systems using neural networks. IEEE transactions on neural networks 1, No. 1, 4-27 (1990)
[17] Pan, Z.; Basar, T.: Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems. IEEE transactions on automatic control 43, No. 8, 1066-1083 (1998) · Zbl 0957.93046
[18] Polycarpou, M. M., & Ioannou, P. A. (1992). Modeling, identification and stable adaptive control of continuous-time nonlinear dynamical systems using neural networks. Proceedings of American Control Conference (pp. 36-40). Boston, MA.
[19] Polycarpou, M. M.; Mears, M. J.: Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators. International journal of control 70, No. 3, 363-384 (1998) · Zbl 0945.93563
[20] Rovithakis, G. A.; Christodoulou, M. A.: Adaptive control of unknown plants using dynamical neural networks. IEEE transactions on systems, man, cybernetics 24, 400-412 (1994) · Zbl 0824.93037
[21] Sanner, R. M.; Slotine, J. E.: Gaussian networks for direct adaptive control. IEEE transactions on neural networks 3, No. 6, 837-863 (1992)
[22] Seto, D.; Annaswamy, A. M.; Baillieul, J.: Adaptive control of nonlinear systems with a triangular structure. IEEE transactions on automatic control 39, 1411-1428 (1994) · Zbl 0806.93034
[23] Spooner, J. T.; Passino, K. M.: Stable adaptive control using fuzzy systems and neural networks. IEEE transactions on fuzzy systems 4, No. 3, 339-359 (1996)
[24] Yao, B.; Tomizuka, M.: Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form. Automatica 33, 893-900 (1997) · Zbl 0876.93083
[25] Yesidirek, A.; Lewis, F. L.: Feedback linearization using neural networks. Automatica 31, No. 11, 1659-1664 (1995) · Zbl 0847.93032