Feedback stabilization using two-hidden-layer nets
Sontag, E.D.
Dept. of Math., Rutgers Univ., New Brunswick, NJ ;
This paper appears in: Neural Networks, IEEE Transactions on
Publication Date: Nov 1992
Volume: 3,
Issue: 6
On page(s): 981-990
ISSN: 1045-9227
References Cited: 14
CODEN: ITNNEP
INSPEC Accession Number: 4322840
Digital Object Identifier: 10.1109/72.165599
Current Version Published: 2002-08-06
Abstract
The representational capabilities of one-hidden-layer and
two-hidden-layer nets consisting of feedforward interconnections of
linear threshold units are compared. It is remarked that for certain
problems two hidden layers are required, contrary to what might be in
principle expected from the known approximation theorems. The
differences are not based on numerical accuracy or number of units
needed, nor on capabilities for feature extraction, but rather on a much
more basic classification into direct and inverse problems. The former
correspond to the approximation of continuous functions, while the
latter are concerned with approximating one-sided inverses of continuous
functions, and are often encountered in the context of inverse
kinematics determination or in control questions. A general result is
given showing that nonlinear control systems can be stabilized using two
hidden layers, but not, in general, using just one
Index
Terms
Available to subscribers and IEEE members.
References
Available to subscribers and IEEE members.
Citing Documents
Available to subscribers and IEEE members.
Cart
