Estimation in Systems with Sigmoidal Activation Functions
The use of neural networks in identification and control of
engineering systems has been intensely debated over the past decade.
Despite the fact that several stability results have been derived in
the literature concerning neural networks in identification and
control, most of them are local in nature and/or include fairly
restrictive conditions under which the stability is valid. In
contrast to these analytical results, the actual demonstration in
applications and numerical simulations reports just the contrary:
Neural networks indeed serve as powerful numerical computational units
that are capable of very good approximations of nonlinear maps and
provide complex functionalities of estimation, control, and
optimization over a large region of operation. Our goal is to fill
this glaring gap and develop global stability tools that are capable
of explaining the true scope of operation of a neural network when
used for nonlinear control. The main idea behind our approach is to
directly address and exploit the distinguishing feature of nonlinear
regression in neural networks and derive the underlying convergence
and stability properties. Our preliminary results
show that it is possible to derive conditions under which global
convergence takes place in identification problems using neural
networks. On-going work concerns training algorithms as well as conditions
under which global system identification using neural networks as well
as global stability using neural controllers can be derived.On-going work concerns training algorithms as well as conditions under which global system identification
using neural networks as well as global stability using neural controllers can be determined.
Estimation in Systems with Sigmoidal Activation Functions 
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