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IEEE TRANSACTIONS ON FUZZY SYSTEMS,VOL.8,NO.4,AUGUST2000349 Identification and Control of Dynamic Systems Using Recurrent Fuzzy Neural Networks

Ching-Hung Lee and Ching-Cheng Teng

Abstract—This paper proposes a recurrent fuzzy neural net-work(RFNN)structure for identifying and controlling nonlinear dynamic systems.The RFNN is inherently a recurrent multilayered connectionist network for realizing fuzzy inference using dynamic fuzzy rules.Temporal relations are embedded in the network by adding feedback connections in the second layer of the fuzzy neural network(FNN).The RFNN expands the basic ability of the FNN to cope with temporal problems.In addition,results for the FNN-fuzzy inference engine,universal approximation,and convergence analysis are extended to the RFNN.For the control problem,we present the direct and indirect adaptive control approaches using the RFNN.Based on the Lyapunov stability approach,rigorous proofs are presented to guarantee the convergence of the RFNN by choosing appropriate learning rates.Finally,the RFNN is ap-plied in several simulations(time series prediction,identification, and control of nonlinear systems).The results confirm the effec-tiveness of the RFNN.

Index Terms—Control,fuzzy logic,fuzzy neural network(FNN), identification,neural network.

I.I NTRODUCTION

R ECENTLY,feedforward neural networks have been shown to obtain successful results in system identi-fication and control[10].Such neural networks are static input/output mapping schemes that can approximate a con-tinuous function to an arbitrary degree of accuracy.Results have also been extended to recurrent neural networks[6]–[8]. For example,Jin et al.[7]studied the approximation of continuous-time dynamic systems using the dynamic recurrent neural network(DRNN)and a Hopfield-type DRNN was presented by Funahashi and Nakamura[6].Recurrent neural network systems learn and memorize information implicitly with weights embedded in them.

As is widely known,both fuzzy logic systems and neural net-work systems are aimed at exploiting human-like knowledge processing capability.Moreover,combinations of the two have found extensive applications.This approach involves merging or fusing fuzzy systems and neural networks into an integrated system to reap the benefits of both.For instance,Lin and Lee [9]proposed a general neural network model for a fuzzy logic control and decision system,which is trained to control an un-manned vehicle.In previous literature,we presented a fuzzy

Manuscript received December2,1999;revised March16,2000.This work was supported by the National Science Council,Taiwan,R.O.C.,under contract NSC89-2213-E009-126.

C.-H.Lee is with the Department of Electronic Engineering,Lunghwa Insti-tute of Technology,Taoyuan333,Taiwan,R.O.C.

C.-C.Teng is with the Department of Electrical and Control Engineering, National Chiao Tung University,Hsinchu300,Taiwan,R.O.C.

Publisher Item Identifier S1063-6706(00)06585-1.neural network(FNN)to establish a model reference control structure and verified that our FNN is a universal approximator [4],[5].The design process for the FNN in[4]and[5]combined tapped delays with the backpropagation(BP)algorithm to solve the dynamic mapping problems.However,a major drawback of the FNN is that its application domain is limited to static prob-lems due to its feedforward network structure.Processing tem-poral problems using the FNN is inefficient.Hence,we propose a recurrent fuzzy neural network(RFNN)based on supervised learning,which is a dynamic mapping network and is more suit-able for describing dynamic systems than the FNN.Of partic-ular interest is that it can deal with time-varying input or output through its own natural temporal operation[16].For this ability to temporarily store information,the structure of the network is simplified.That is,fewer nodes are required for system identi-fication.

In this paper,the proposed RFNN,which is a modified version of the FNN,is used to identify and control a nonlinear dynamic system.The RFNN is a recurrent multilayered connectionist network for realizing fuzzy inference and can be constructed from a set of fuzzy rules.The temporal relations embedded in the RFNN are developed by adding feedback connections in the second layer of the FNN.This modification provides the memory elements of the RFNN and expands the basic ability of the FNN to include temporal problems.Since a recurrent neuron has an internal feedback loop,it captures the dynamic response of a system,thus the network model can be simplified.We show that all the characteristics of the FNN—fuzzy inference,universal approximation,and convergence properties—are extended to the RFNN.We also study the proposed RFNNs approximation and dynamics mapping abilities.For the control problem,we present the direct and indirect adaptive control approaches using the RFNN.In addition,to guarantee the convergence of the RFNN,the Lyapunov stability approach is applied to select appropriate learning rates.Finally,the proposed RFNN is applied to some numerical examples:time sequence prediction,identification of nonlinear systems without tapped delays,identification of a chaotic system,and adaptive control of a nonlinear system.

The paper is organized as follows.In Section II,an RFNN structure is developed and the universal approximation of the RFNN is studied.The comparison between the FNN and the RFNN is also described.The training architectures for identi-fication and control and the learning algorithm are presented in Section III.Section IV presents the stability analysis of the RFNN,which is based on the Lyapunov approach to show the convergence of the RFNN.Simulation results are discussed in Section V.Section VI gives the conclusion of this paper.Note

1063–6706/00$10.00©2000IEEE

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