Learning Control of Nonliner Systems by Using a Neural Network

Member Yoshihiro Ohnishi (Kure National College of Technology,onishi@kure-nct.ac.jp)

Member Toru Yamamoto (Hiroshima University,yama@hiroshima-u.ac.jp)

Member Sigeru Omatsu (Osaka Prefecture University,omatu@cs.osakafu-u.ac.jp)

Key words:learning control,neural network,system identiﬁcation,generalized minimum variance control

The eﬀectiveness of neural networks is discussed for

nonlinear systems.Especially,some control schemes

by using the neural network have been proposed.The

conventional neural-net based control schemes can be

classiﬁed into the two groups.The one is that control

input is directly calculated by the neural network.As

the control input is given by the output of the neural

network,it is easy to implement for the controlled ob-

ject.However,it is diﬃcult to describe the structure

of the controller as the transfer function.The other

is that control parameters are calculated by the neural

network,and this control input can be calculated by

these control parameters.Although this scheme makes

easy to grasp the physical meanings of control param-

eters,the properties of controlled object can not be

directly understood.

In this paper,a generalized minimum variance con-

trol (GMVC) scheme by using a neural network is pro-

posed.According to the proposed control scheme,sys-

tem parameters are ﬁrstly estimated by the neural net-

work.The neural network is constructed for the pur-

pose of the parameter estimation.Note that every unit

included in the output layer of this neural network is

given by system parameters.The weighting factors of

the neural network are updated based on the error back-

propagation method.Next,the control law is derived

by minimizing the GMVC cost function.Then the con-

trol input is calculated by using the estimated values

which are calculated by the neural network.By this

procedure,the explicit STC based on GMVC can be

designed.

This paper is organized as follows:The system de-

scription is ﬁrstly discussed,and the estimator using

the neural network is proposed.Next,the GMVC law

is derived by minimizing the cost function.Further-

more,some simulation examples have been illustrated

to show the eﬀectiveness of the newly proposed control

scheme.

Figure 1 shows the estimation result by employing

the proposed estimator for the nonlinear system after

10,000 iterations.In Fig 1,the symbol ’ˆy’ means the

estimated output,and the symbol ’e’ means the esti-

mated error.

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Fig.1 The estimation result by the proposed estimator.

Figure 2 shows the control result by using the pro-

posed control method.This control input is calculated

based on the estimated parameters which are calculated

by using the neural network.

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