Feedback stabilization using two-hidden-layer nets
- 1 January 1992
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Neural Networks
- Vol. 3 (6) , 981-990
- https://doi.org/10.1109/72.165599
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.Keywords
This publication has 11 references indexed in Scilit:
- Feedforward nets for interpolation and classificationJournal of Computer and System Sciences, 1992
- Approximation theory and feedforward networksNeural Networks, 1991
- Identification and control of dynamical systems using neural networksIEEE Transactions on Neural Networks, 1990
- Feedback Stabilization of Nonlinear SystemsPublished by Springer Nature ,1990
- Approximation by superpositions of a sigmoidal functionMathematics of Control, Signals, and Systems, 1989
- On the approximate realization of continuous mappings by neural networksNeural Networks, 1989
- Multilayer feedforward networks are universal approximatorsNeural Networks, 1989
- Real addition and the polynomial hierarchyInformation Processing Letters, 1985
- Remarks on piecewise-linear algebraPacific Journal of Mathematics, 1982
- Differential TopologyPublished by Springer Nature ,1976