TY - GEN
T1 - State observability in recurrent neural networks
AU - Albertini, Francesca
AU - Sontag, Eduardo
N1 - Funding Information:
to each coordinate of an n-vector, a(Xl ..... x,) = (a(xl) ..... a(x,)). See Figure 1 for a block diagram, where A indicates either a unit delay or integration. The complete model is specified once that a and the triple (A, B, C) are given. (In continuous time, one needs to assume also that a is at least locally Lipschitz, so that existence and local uniqueness of the differential equation holds.) Many questions, mirroring those for linear systems (for which a is the identity) can be posed. In the recent work \[1\]w, e explored realization questions, and in particular the fact that all the entries of the matrices A, B, and C can be recovered (up to a small number of symmetries) from the zero-initial state input/output behavior, assuming suitable minimality assumptions, and as long as a is nonlinear enough. This is somewhat surprising, since for the linear case one can only recover the parameters up to basis changes, and it is reminiscent of old work of Rugh and coworkers, as well as Boyd and Chua (see for instance \[5, 3\]) on uniqueness of interconnections containing nonlinearities. (Reference I-2\] explains the relation between those more classical facts and the result in \[1\].) Correspondence to." Prof. E.D. Sontag, Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. E-mail: [email protected]. * This research was supported in part by US Air Force Grant AFOSR-91-0346, and also by an INDAM (Istituto Nazionale di Alta Matematica Francesco Severi, Italy) fellowship. ** Also: Universita' di Padova, Dipartimento di Matematica, Via Belzoni 7, 35100 Padova, Italy.
PY - 1993
Y1 - 1993
N2 - We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research.
AB - We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research.
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M3 - Conference contribution
AN - SCOPUS:0027851970
SN - 0780312988
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3706
EP - 3707
BT - Proceedings of the IEEE Conference on Decision and Control
PB - Publ by IEEE
T2 - Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4)
Y2 - 15 December 1993 through 17 December 1993
ER -