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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.

MSC:
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
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