Complete controllability of continuous-time recurrent neural networks

This paper studies controllability for the class of control systems commonly called (continuous-time) recurrent neural networks. It is shown that, under a generic condition on the input matrix, the system is controllable, for every possible state matrix. The result holds when the activation function is the hyperbolic tangent.

[1]  Rafal Zbikowski.  Lie Algebra of Recurrent Neural Networks and Identifiability , 1993, 1993 American Control Conference.

[2]  Eduardo D. Sontag,et al.  Sample complexity for learning recurrent perceptron mappings , 1995, IEEE Trans. Inf. Theory.

[3]  Eduardo D. Sontag,et al.  Neural Networks for Control , 1993 .

[4]  Ah Chung Tsoi,et al.  FIR and IIR Synapses, a New Neural Network Architecture for Time Series Modeling , 1991, Neural Computation.

[5]  Richard J. Mammone,et al.  Artificial neural networks for speech and vision , 1994 .

[6]  Eduardo D. Sontag,et al.  NEURAL NETS AS SYSTEMS MODELS AND CONTROLLERS , 1992 .

[7]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[8]  Eduardo D. Sontag,et al.  Vapnik-Chervonenkis Dimension of Recurrent Neural Networks , 1997, Discret. Appl. Math..

[9]  Hava T. Siegelmann,et al.  On the Computational Power of Neural Nets , 1995, J. Comput. Syst. Sci..

[10]  Kenneth J. Hunt,et al.  Neural Adaptive Control Technology , 1996 .

[11]  Eduardo D. Sontag,et al.  UNIQUENESS OF WEIGHTS FOR NEURAL NETWORKS , 1993 .

[12]  Hava T. Siegelmann,et al.  On the computational power of neural nets , 1992, COLT '92.

[13]  Eduardo D. Sontag,et al.  State observability in recurrent neural networks , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[14]  Eduardo D. Sontag,et al.  For neural networks, function determines form , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[15]  Héctor J. Sussmann,et al.  Uniqueness of the weights for minimal feedforward nets with a given input-output map , 1992, Neural Networks.

[16]  Harry L. Trentelman,et al.  Essays on control : perspectives in the theory and its applications , 1993 .

[17]  Yoshua Bengio,et al.  Neural networks for speech and sequence recognition , 1996 .

[18]  P. D. Pra,et al.  Forward accessibility for recurrent neural networks , 1995, IEEE Trans. Autom. Control..

[19]  Eduardo D. Sontag,et al.  Using Fourier-neural recurrent networks to fit sequential input/output data , 1997, Neurocomputing.

[20]  Eduardo D. Sontag,et al.  Vapnik-Chervonenkis Dimension of Recurrent Neural Networks , 1998, Discret. Appl. Math..