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Conference Papers-Neural Networks
Note: The papers on this website may differ from the published versions, both in format and in content.
Neural Networks:
D.R. Hush, C. T. Abdallah, G. L. Heileman and D. Docampo,
"Neural Networks in Fault Detection: A Case Study",
Proceedings of the American Control Conference, Albuquerque, NM, 1997.
[pdf] [ps]
Abstract: In this paper we study the applications of neural nets in the area of fault detection. In particular,
neural networks are used for fault detection in real vibrational data. The study is one of the first to include a large set of real vibrational data and to
illustrate the potential as well as to the limitations
of neural networks for fault detetction.
Y.H. Kim, F.L. Lewis,
C. T. Abdallah,
"Nonlinear Observer Design Using Dynamic Recurrent Neural Networks",
Proceedings of the 35th Conference on Decision and Control, pp.949-954, Kobe, Japan, Dec. 1996.
[pdf]
Abstract: A nonlinear observer for a general class of single-output nonlinear systems is proposed based
on a generalized Dynamic Recurrent Neural Network(DRNN). The Neural Network (NN) weights in the observer are tuned on-line,
with no off-line learning phase required. The obserever stability and boundness of the state estimates and NN weights are proven.
No exact knowledge of the nonlinear function in the observed system is required. Furthermore, no linearity with respect to
the unknown system parameters is assumed. The proposed DRNN observer can be considered as a universal and reusable nonlinear
observer because the same observer can be applied to any system in the class of nonlinear systems.
J. Howse, C. T. Abdallah, and G. L. Heileman,
"Some Control Theoretic Issues in Neural Networks",
International Conference on Neural Networks, Special Sessions, IEEE Press, Washington, DC, June, 1996.
[pdf]
Abstract: We have observed that many neural network models can be written as a bilinear system with
a specific form of nonlinear state-to-input feedback. This framework includes the ART architecture among others.
There are two significant results which follow from this observation. First, the parameters of the model determine the
controllability if the system. A systems is controllable if there exists some inout which transfers any initial state to
any desired final state in a finite time. If for a given set of these parameters the system is not controllable, then
there are regions of the state space which the system can never enter in a finite time for any input. Because of this
restriction the learning ability of the system may be severly limited. Second, the multiplicative equation is linear
in all of the parameters, and all of the adjustable weights. This means that a provably convergent learning algorithm can
be devised for all of these quatities. This does not however circumvent the learning limitation since the learning
algorithm is not guaranteed to converge on a finite time. In the paper, we will study these issues as they apply
to the ART architecture.
C.T. Abdallah, W. Yang, E. Schamiloglu,
and L.D. Moreland,
"A Neural-Network Model of the Input/Output Characteristics of a High-Power Backward Wave Oscillator",
IEEE Transactions On Plasma Science, Vol 24, NO. 3, pp.878-882,June 1996.
[pdf]
Abstract: This paper discusses an approach to model the input/output characteristics of the Sinus-6
electron beam accelerator-driven backward wave oscillator. Since the Sinus-6 is extremely fast to warrant the inclusion
of dynamical effects, and since the sampling interval in the experiment is not fixed, a static continuous neural network model
is used to fit the experimental data. Simulation results show that such a simple nonlinear model is sufficient to accurately
describe the input/output behavior of the Sinus-6-driven backward wave oscillator (BWO) and that the fitted output waveforms
are basically noiseless. This model will be used to control the BWO in order to maximize the radiated power and the efficiency.
This paper is also intended to introduce high-power microwave researchers to control concepts that may enhance the outputs of a wide
spectrum of sources.
J. Howse, C. T. Abdallah, and G. L. Heileman,
"Gradient and Hamiltonian Dynamics Applied to Learning in Neural Networks",
Proceedings of Neural Information Processing Systems, Denver, CO, pp.274-280, 1995.
[pdf]
Abstract: The process of machine learning can be considered in two stages: model selection
and parameter estimation. In this paper, a technique is presented for constructing dynamical systems with
desired qualitative properties. The approach is based in the fact that an n-dimensinal nonlinear dynamical
system can be decomposed into one gradient and (n-1) Hamiltonian systems. Thus, the model selection stage consists of
choosing the gradient and Hamiltonian portions appropriately so that a certain behavior is obtainable. To estimate
the parameters, a stably convergent learning rule is presented. This algorithm has been proven to converge to the
desired system trajectory for all initial conditions and system inputs. This technique can be used to design neural
network models which are guaranteed to solve the trajectory learning problem.
J. Howse, C. T. Abdallah, and G. L. Heileman,
"Some System Theoretic Computations when Learning Dynamical Systems with Neural Networks" ,
Proceedings of Neural Information Processing Systems, Denver, CO, pp.274-280, 1995.
[pdf]
Abstract: The process of machine learning can be considered in two stages: model selection
and parameter estimation. In this paper, a technique is presented for constructing dynamical systems with
desired qualitative properties. The approach is based in the fact that an n-dimensinal nonlinear dynamical
system can be decomposed into one gradient and (n-1) Hamiltonian systems. Thus, the model selection stage consists of
choosing the gradient and Hamiltonian portions appropriately so that a certain behavior is obtainable. To estimate
the parameters, a stably convergent learning rule is presented. This algorithm has been proven to converge to the
desired system trajectory for all initial conditions and system inputs. This technique can be used to design neural
network models which are guaranteed to solve the trajectory learning problem.
J. Howse, C. T. Abdallah, and G. L. Heileman,
"A Learning Algorithm for Applying Cohen's Models to System Identification" ,
Neural Networks Journal.
[pdf] Abstract: In this paper, we extend the models discussed by Cohen (1992) by introducing
an input term. This allows the resulting models to be utilized for ayatem identification tasks. We prove that this
model is stable in the sence that a bounded inout leads to a bounded state when a minor restriction is imposed
on the Lyapunov function. By employing this stability result, we are able to find a learning algorithm which
guarantees convergence to a set of parameters for which the error between the model trajectories and the
desired trajectories vanishes.
G. Heileman,M. Georgiopoulos,
C.T. Abdallah,
"A Dynamical Adaptive Resonance Imaging Architecture",
IEEE Transactions On Neural Networks, Vol 5, NO. 6, pp.873-889, San Antonio, TX, Nov. 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 ART1-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.
J.W. Howse, C.T. Abdallah,
G.L. Heileman, M. Georgiopoulos,
"An Application of Gradient-Like Dynamics to Neural Networks", pp.92-96, 1993.
[pdf]
Abstract: This paper reviews a formalism that enables the dynamics of a broad class of neural
networks to be understood. This formalism is then applied to a specific network and the predicted and simulated behavior
of the system are compared. A number of previous works have analysed the lyapunov stability of neural network models.
This type of analysis shows that the excursion of the solutions from a stable point is bounded. The purpose of this work
is to review and then utilize a model of the dynamics that also describes the phase space behavior and structural stability
of the system. In this paper it is demonstrated that a network with additive activation dynamics and Hebbian weight update
dynamics can be expressed as a gradient-like system. An example of a 3-layer network with feedback between adjacent layers is
presented. It is showm that the process of weight learning is stable when the learned weights are asymmetric, provided that
the activation is computed using only the symmetric part of the weights.
D. Hush, C. T. Abdallah, and B. Horne,
"Recursive Neural Networks for Signal Processing and Control", pp. 523-532, 1991.
[pdf]
Abstract: This paper describes a special type of neural network called the Recursive Neural
Network (RNN). The RNN is a single-input single-output nonlinear dynamical system with a nonrecursive subnet and two
recursive subnets arranged in the configuration shown in figure 1. The purpose of this paper is to describe the
architecture of the RNN, present the learning algorithm for the network, and provide some examples of its use.
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