Nonlinear stable adaptive control based upon Elman networks

Abstract

Elman networks' dynamical modeling capability is discussed in this paper firstly. According to Elman networks' unique structure ,a weight training algorithm is designed and a nonlinear adaptive controller is constructed. Without the PE presumption, neural networks controller's closed-loop properties are studied and the whole Elman networks' passivity is demonstrated. § 1 IntroductionAfter nearly twenty yearys' evolution,rich achievements on neural networks control (NNC) have been gained in nonlinear control fields [1]. Based on the multi-layered feed-forward neural networks (MFNN) and the full-connected recurrent neural networks (FRNN),researchers have developed many kinds of new algorithms and viewpoints as well. Because MFNN is essentially a kind of static mapping neural networks ,it can't realize a perfect description to a nonlinear system's dynamics whereas FRNN can. So in NNC, FRNN has its unique advantage over MFNN. However,the training of FRNN weight values is much more complicated[2] than that of MFNN,therefore this restriction can't bring FRNN's whole advantage into play in modeling system dynamics and real-time control. In recent years,finding a kind of simple recurrent networks model to fit the nonlinear control has become a new research hotspot[3'4].Elman networks[5] unique charmhas attacted lots of researchers' attentions, and wide slope researches have been developed in aspects such as nonlinear modeling,temporal signal process and automata theory [6][7][8]. In [6] the dynamic backpropagation algorithm (DBP) was applied to trainElman networks' weight values for modeling nonlinear dynamic systems. In [7] it was shown that Elman networks can simulate any frontier-to-root

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