Learning Control of Nonliner Systems by Using a Neural Network
Member Yoshihiro Ohnishi (Kure National College of Technology,onishi@kurenct.ac.jp)
Member Toru Yamamoto (Hiroshima University,yama@hiroshimau.ac.jp)
Member Sigeru Omatsu (Osaka Prefecture University,omatu@cs.osakafuu.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 neuralnet 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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