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NL_q theory: checking and imposing stability of recurrent neural networks for nonlinear modelling (1997)
| Venue: | SPS Best Paper Award |
| Citations: | 9 - 1 self |
BibTeX
@ARTICLE{Suykens97nl_qtheory:,
author = {J.A.K. Suykens and J. Vandewalle and B. De Moor},
title = {NL_q theory: checking and imposing stability of recurrent neural networks for nonlinear modelling},
journal = {SPS Best Paper Award},
year = {1997},
volume = {45},
pages = {2682--2691}
}
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Abstract
It is known that many discrete time recurrent neural networks, such as e.g. neural state space models, multilayer Hopfield networks and locally recurrent globally feedforward neural networks, can be represented as NL q systems. Sufficient conditions for global asymptotic stability and input/output stability of NL q systems are available, including three types of criteria: diagonal scaling and criteria depending on diagonal dominance and condition number factors of certain matrices. In this paper, it is discussed how Narendra's dynamic backpropagation procedure, used for identifying recurrent neural network from I/O measurements, can be modified with an NL q stability constraint in order to ensure globally asymptotically stable identified models. An example illustrates how system identification of an internally stable model, corrupted by process noise, may lead to unwanted limit cycle behaviour and how this problem can be avoided by adding the stability constraint.
Keyphrases
recurrent neural network nonlinear modelling nl_q theory stable identified model system identification diagonal dominance global asymptotic stability sufficient condition unwanted limit cycle behaviour nl stability constraint diagonal scaling condition number factor nl system multilayer hopfield network input output stability feedforward neural network stable model dynamic backpropagation procedure certain matrix process noise stability constraint neural state space model
