Standard representation and unified stability analysis for dynamic artificial neural network models

An overview is provided of dynamic artificial neural network models (DANNs) for nonlinear dynamical system identification and control problems, and convex stability conditions are proposed that are less conservative than past results. The three most popular classes of dynamic artificial neural netwo...

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Bibliographic Details
Published in:Neural networks 2018-02, Vol.98, p.251-262
Main Authors: Kim, Kwang-Ki K., Patrón, Ernesto Ríos, Braatz, Richard D.
Format: Article
Language:English
Subjects:
Absolute stability
Dynamic artificial neural networks
Linear matrix inequalities
Nonlinear stability analysis
Semidefinite programming
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Summary:An overview is provided of dynamic artificial neural network models (DANNs) for nonlinear dynamical system identification and control problems, and convex stability conditions are proposed that are less conservative than past results. The three most popular classes of dynamic artificial neural network models are described, with their mathematical representations and architectures followed by transformations based on their block diagrams that are convenient for stability and performance analyses. Classes of nonlinear dynamical systems that are universally approximated by such models are characterized, which include rigorous upper bounds on the approximation errors. A unified framework and linear matrix inequality-based stability conditions are described for different classes of dynamic artificial neural network models that take additional information into account such as local slope restrictions and whether the nonlinearities within the DANNs are odd. A theoretical example shows reduced conservatism obtained by the conditions.
ISSN:0893-6080
1879-2782
DOI:10.1016/j.neunet.2017.11.014