1. R. Koplon and E.D. Sontag. Using Fourier-neural recurrent networks to fit sequential input/output data. Neurocomputing, 15:225-248, 1997. [PDF] Keyword(s): machine learning, neural networks, recurrent neural networks. Abstract:

   This paper suggests the use of Fourier-type activation functions in fully recurrent neural networks. The main theoretical advantage is that, in principle, the problem of recovering internal coefficients from input/output data is solvable in closed form.




2. R. Koplon, E.D. Sontag, and M. L. J. Hautus. Observability of linear systems with saturated outputs. Linear Algebra Appl., 205/206:909-936, 1994. [PDF] Keyword(s): observability, saturation, bounded inputs. Abstract:

   In this paper, we present necessary and sufficient conditions for observability of the class of output-saturated systems. These are linear systems whose output passes through a saturation function before it can be measured.




3. R. Koplon and E.D. Sontag. Linear systems with sign-observations. SIAM J. Control Optim., 31(5):1245-1266, 1993. [PDF] [doi:http://dx.doi.org/10.1137/0331059] Keyword(s): observability. Abstract:

   This paper deals with systems that are obtained from linear time-invariant continuous- or discrete-time devices followed by a function that just provides the sign of each output. Such systems appear naturally in the study of quantized observations as well as in signal processing and neural network theory. Results are given on observability, minimal realizations, and other system-theoretic concepts. Certain major differences exist with the linear case, and other results generalize in a surprisingly straightforward manner.

1. R. Koplon and E.D. Sontag. Techniques for parameter reconstruction in Fourier-Neural recurrent networks. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 213-218, 1994. Keyword(s): machine learning, neural networks, recurrent neural networks.



2. R. Koplon and E.D. Sontag. Sign-linear systems as cascades of automata and continuous variable systems. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 2290-2291, 1993.

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