Adaptive control of nonlinear systems using neural networks. (English) Zbl 0759.93046

Considered is an adaptive regulation problem for a discrete time single input, single output relative degree one system represented by \[ y_{k+1}=f(y_ k,\dots,y_{k-n+1},u_{k-1},\dots,u_{k-m})+g(y_ k,\dots,y_{k-n+1},u_ {k-1},\dots,u_{k-n})u_ k. \] It is assumed the system is minimum phase, linearizable and the function \(f(\cdot)\), \(g(\cdot)\) are smooth and can be exactly represented by a multilayer neutral network. Using a linear learning rule it is shown how it is possible to regulate the plant output to zero asymptotically.


93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
92B20 Neural networks for/in biological studies, artificial life and related topics
93C55 Discrete-time control/observation systems
93D21 Adaptive or robust stabilization
Full Text: DOI


[1] CHEN F.-C., IEEE Control System Magazine, Special Issue on Neural Networks for Control Systems 10 (3) pp 44–
[2] CHEN F. C., Proceedings of the 1991 American Control Conference pp 667– (1991)
[3] CYBENKO , G. , 1988 , Approximation by superpositions of a sigmoidal function . Technical Report No, 856, Department of Electrical and Computer Engineering , University of Illinois at Urbana-Champaign . · Zbl 0679.94019
[4] FUNAHASHI K., Neural Networks 2 pp p183– (1989)
[5] HECHT-NIELSEN R., Proceedings of the International Joint Conference on Neural Networks 1 pp 593– (1989)
[6] HORNIK K., Neural Networks 2 pp 359– (1989) · Zbl 1383.92015
[7] ISIDORI A., Nonlinear Control Systems (1989) · Zbl 0693.93046
[8] KUMAR R. P., Stochastic Systems Estimation, Identification and Adaptive Control (1986) · Zbl 0706.93057
[9] LI W., Proceedings of the 1989 American Control Conference pp 1136– (1989)
[10] MONACO S., Proceedings of the 1987 IEEE-Conference on Decision and Control pp 979– (1987)
[11] NARENDRA K. S., IEEE Transactions on Neural Networks 1 pp 4– (1990)
[12] PSALTIS D., IEEE Control Systems Magazine 8 (2) pp 17– (1988)
[13] RUDIN W., Principles of Mathematical Analysis (1976) · Zbl 0346.26002
[14] RUMELHART D., Parallel Distributed Processing 1 (1986)
[15] SASTRY S. S., IEEE Transactions on Automatic Control 34 pp 1123– (1989) · Zbl 0693.93046
[16] TAYLOR D. G., IEEE Transactions on Automatic Control 34 pp 405– (1989) · Zbl 0671.93033
[17] ZEMAN V., Proceedings of the 1989 IEEE Conference on Decision and Control pp 1759– (1989)
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.