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1. G. L. Heileman,M. Georgiopoulos and C.T. Abdallah "A Dynamical Adaptive Resonance Architecture", IEEE Transactions on Neural Networks, vol. 5, No. 6, pp. 873-889, 1994. [pdf]
   
   Abstract: A set of nonlinear differential equations that describe the dynamics of the ART1 model are presented, along with the motivation for their use. These equations are extensions of those developed by Carpenter and Grossberg [1]. It is shown how these differential equations allow the ART1 model to be realized as a collective nonlinear dynamical system. Specifically, we present an ARTl-based neural network model whose description requires no external control features. That is, the dynamics of the model are completely determined by the set of coupled differential equations that comprise the model. It is shown analytically how the parameters of this model can be selected so as to guarantee a behavior equivalent to that of ART1 in both fast and slow learning scenarios. Simulations are performed in which the trajectories of node and weight activities are determined using numerical approximation techniques.






2. C.T. Abdallah, Heileman, G.L., M. Georgiopoulos, and D. Hush, "An Overview of Neural Networks Results for Systems and Control", IEEE Transactions on Neural Networks, vol. 5, No. 6, pp. 873-889, 1994. [dvi]
   
   Abstract: In this paper, we survey the applications of neural nets in the areas of systems and control. The paper provides a study of the limitations of neural nets, and stresses "hard" results as opposed to a listing of simulations and applications. Our general approach is to isolate the common properties used by neural networks in control, then to study the difficulties associated with achieving these properties. We avoid as much as possible a listing of neural networks simulations and try to stress their generic properties, independent of a particular architecture. Finally, we address the issues of capabilities versus actual performance and point out results from computational learning theory to show that neural networks can not be used as universal controllers. Although this is a paper on applications of neural networks to systems and control, we focus not on particular experiments but on generic capabilities.