Gong, J. Q.; Yao, Bin Neural network adaptive robust control of nonlinear systems in semi-strict feedback form. (English) Zbl 0996.93055 Automatica 37, No. 8, 1149-1160 (2001). Neural networks (NN) and an adaptive robust control design philosophy have been integrated to design performance oriented control laws for a class of nonlinear systems in the semi-strict feedback form. In a sense this is the generalization of recently proposed NN adaptive robust control. Both, repeatable unknown nonlinearities and nonrepeatable unknown nonlinearities, such as external disturbances, are considered. All unknown but repeatable nonlinear functions are approximated by outputs of multi-layer NNs. All NN weights are tuned on-line with no prior training needed. Certain robust control terms can then be constructed to achieve a guaranteed output tracking transient performance. The proposed strategy is then applied to the precision motion control of linear motor drive systems with nonnegligible electrical dynamics. The analysis of experimental results shows a good performance of the method. But additional spikes in the position error of the motor are observed caused by Coulomb friction. It is not surprising to see these spikes since NNs can only approximate continuous functions and are not able to handle discontinuities, like Coulomb friction, well. But this problem should require another analysis that is not performed here. Reviewer: Ladislav Andrey (Praha) Cited in 20 Documents MSC: 93C40 Adaptive control/observation systems 92B20 Neural networks for/in biological studies, artificial life and related topics 93C95 Application models in control theory 93C10 Nonlinear systems in control theory Keywords:neural networks; adaptive control; robust control; nonlinear systems; semi-strict feedback form; output tracking; transient performance; linear motor drive; spikes; Coulomb friction PDFBibTeX XMLCite \textit{J. Q. Gong} and \textit{B. Yao}, Automatica 37, No. 8, 1149--1160 (2001; Zbl 0996.93055) Full Text: DOI References: [1] Canudas de Wit, C.; Olsson, H.; Astrom, K. J.; Lischinsky, P., A new model for control of systems with friction, IEEE Transactions on Automatic Control, 40, 3, 419-425 (1995) · Zbl 0821.93007 [2] Commuri, S.; Lewis, F. L., Cmac neural networks for control of nonlinear dynamical systems: structure, stability and passivity, Automatica, 33, 4, 635-641 (1997) · Zbl 0883.93045 [3] Cybenko, G., Approximation by superpositions of sigmoidal function, Mathematics of Control, Signals and Systems, 2, 303-314 (1989) · Zbl 0679.94019 [4] Fu, L.-C.; Chang, W.-D.; Yang, J.-H.; Kuo, T.-S., Adaptive robust bank-to-turn missile autopilot design using neural networks, Journal of Guidance, Control, and Dynamics, 20, 2, 346-354 (1997) · Zbl 0900.93152 [5] Funahashi, K.-I., On the approximate realization of continuous mappings by neural networks, Neural Networks, 2, 183-192 (1989) [6] Gong, J. Q., & Yao, B. (1999). Adaptive robust control without knowing bounds of parameter variations. Proceedings of the 38th IEEE conference on decision and control; Gong, J. Q., & Yao, B. (1999). Adaptive robust control without knowing bounds of parameter variations. Proceedings of the 38th IEEE conference on decision and control [7] Gong, J. Q., & Yao, B. (2001). Neural network adaptive robust control with application to precision motion control of linear motors. International Journal of Adaptive Control and Signal Processing; Gong, J. Q., & Yao, B. (2001). Neural network adaptive robust control with application to precision motion control of linear motors. International Journal of Adaptive Control and Signal Processing · Zbl 0991.93549 [8] Gong, J. Q., & Yao, B. (2000b). Neural network-based adaptive robust control of a class of nonlinear systems in normal form. Proceedings of the American control conferenceAsian Journal of Control; Gong, J. Q., & Yao, B. (2000b). Neural network-based adaptive robust control of a class of nonlinear systems in normal form. Proceedings of the American control conferenceAsian Journal of Control [9] Goodwin, G. C.; Mayne, D. Q., A parameter estimation perspective of continuous time model reference adaptive control, Automatica, 23, 1, 57-70 (1989) · Zbl 0617.93033 [10] Hirsch, M. W., Convergent activation dynamics in continuous time networks, Neural Networks, 2, 331-349 (1989) [11] Hornik, K., Approximation capabilities of multilayer feedforward networks, Neural Networks, 4, 251-257 (1991) [12] Hunt, K. J.; Sbarbaro, D.; Zbikowski, R.; Gawthrop, P. J., Neural networks for control systems-a survey, Automatica, 28, 6, 1083-1112 (1992) · Zbl 0763.93004 [13] Kelly, D. G., Stability in contractive nonlinear neural networks, IEEE Transactions on Biomedical Engineering, 37, 3, 231-242 (1990) [14] Khalil, H. K., Nonlinear systems (1996), Prentice Hall: Prentice Hall Englewood Cliffs, NJ · Zbl 0626.34052 [15] Krstic, M.; Kanellakopoulos, I.; Kokotovic, P. V., Nonlinear and adaptive control design (1995), Wiley: Wiley New York · Zbl 0763.93043 [16] Lewis, F. L.; Yesidirek, A.; Liu, K., Neural net robot controller with guaranteed tracking performance, IEEE Transcations on Neural Networks, 6, 703-715 (1995) [17] Liang, X. B.; Yamaguchi, T., On the analysis of global and absolute stability of nonlinear continuous neural networks, IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, E80-A, 1, 223-229 (1997) [18] Park, J.; Sandberg, I. W., Universal approximation using radial-basis-function networks, Neural Computation, 3, 246-257 (1991) [19] Polycarpou, M. M., Stable adaptive neural control scheme for nonlinear systems, IEEE Transcations on Automatic Control, 41, 447-451 (1996) · Zbl 0846.93060 [20] Polycarpou, M. M., & Ioannou, P. A. (1993). A robust adaptive nonlinear control design. Proceedings of the American control conference; Polycarpou, M. M., & Ioannou, P. A. (1993). A robust adaptive nonlinear control design. Proceedings of the American control conference [21] Sanner, R. M.; Slotine, E. J.-J., Gaussian networks for direct adaptive control, IEEE Transactions on Neural Networks, 3, 6, 837-863 (1992) [22] Sastry, S.; Bodson, M., Adaptive control: Stability, convergence and robustness (1989), Prentice Hall: Prentice Hall Englewood Cliffs, NJ · Zbl 0721.93046 [23] Sussmann, H. J., Uniqueness of the weights for minimal feedforward nets with a given input-output map, Neural Networks, 5, 589-593 (1992) [24] Tzirkel-Hancock, E.; Fallside, F., Stable control of nonlinear systems using neural networks, International Journal of Robust and Nonlinear Control, 2, 63-86 (1992) · Zbl 0756.93046 [25] Yao, B. (1997). High performance adaptive robust control of nonlinear systems: a general framework and new schemes. Proceedings of the IEEE conference on decision and control; Yao, B. (1997). High performance adaptive robust control of nonlinear systems: a general framework and new schemes. Proceedings of the IEEE conference on decision and control [26] Yao, B., & Tomizuka, M. (1994). Smooth robust adaptive sliding mode control of robot manipulators with guaranteed transient performance. Proceedings of the American control conferenceASME Journal of Dynamic SystemsMeasurement and Control118; Yao, B., & Tomizuka, M. (1994). Smooth robust adaptive sliding mode control of robot manipulators with guaranteed transient performance. Proceedings of the American control conferenceASME Journal of Dynamic SystemsMeasurement and Control118 [27] Yao, B., & Tomizuka, M. (1997). Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form AutomaticaProceedings of the 1995 American control conference; Yao, B., & Tomizuka, M. (1997). Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form AutomaticaProceedings of the 1995 American control conference · Zbl 0876.93083 [28] Yao, B., & Tomizuka, M. (2001). Adaptive robust control of MIMO nonlinear systems in semi-strict feedback forms. AutomaticaIEEE conference on decision and controlIFAC world congress; Yao, B., & Tomizuka, M. (2001). Adaptive robust control of MIMO nonlinear systems in semi-strict feedback forms. AutomaticaIEEE conference on decision and controlIFAC world congress [29] Yao, B., & Xu, L. (1999). Adaptive robust control of linear motors for precision manufacturing. Proceedings of the 14th IFAC world congressBeijingInternational Journal of Mechatronics; Yao, B., & Xu, L. (1999). Adaptive robust control of linear motors for precision manufacturing. Proceedings of the 14th IFAC world congressBeijingInternational Journal of Mechatronics [30] Zhang, Y.; Ioannou, P. A.; Chien, C. C., Parameter convergence of a new class of adaptive controllers, IEEE Transactions on Automatic Control, 41, 10, 1489-1493 (1996) · Zbl 0863.93045 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.