Global Asymptotic Stability and Stabilization of Long Short-Term Memory Neural Networks with Constant Weights and Biases

Shankar A. Deka; Dušan M. Stipanović; Boris Murmann; Claire J. Tomlin

doi:10.1007/s10957-018-1447-6

Global Asymptotic Stability and Stabilization of Long Short-Term Memory Neural Networks with Constant Weights and Biases

Shankar A. Deka, Dušan M. Stipanović, Boris Murmann, Claire J. Tomlin

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, a global asymptotic stability condition for Long Short-Term Memory neural networks is presented. Since this condition is formulated in terms of the networks’ weight matrices and biases that are essentially control variables, the same condition can be viewed as a way to globally asymptotically stabilize these networks. The condition and how to compute numerical values for the weight matrices and biases are illustrated by a number of numerical examples.

Original language	English (US)
Pages (from-to)	231-243
Number of pages	13
Journal	Journal of Optimization Theory and Applications
Volume	181
Issue number	1
DOIs	https://doi.org/10.1007/s10957-018-1447-6
State	Published - Apr 15 2019

Keywords

Global asymptotic stability
Neural networks
Stabilization

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

Online availability

10.1007/s10957-018-1447-6

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abstract = "In this paper, a global asymptotic stability condition for Long Short-Term Memory neural networks is presented. Since this condition is formulated in terms of the networks{\textquoteright} weight matrices and biases that are essentially control variables, the same condition can be viewed as a way to globally asymptotically stabilize these networks. The condition and how to compute numerical values for the weight matrices and biases are illustrated by a number of numerical examples.",

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AU - Murmann, Boris

AU - Tomlin, Claire J.

PY - 2019/4/15

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AB - In this paper, a global asymptotic stability condition for Long Short-Term Memory neural networks is presented. Since this condition is formulated in terms of the networks’ weight matrices and biases that are essentially control variables, the same condition can be viewed as a way to globally asymptotically stabilize these networks. The condition and how to compute numerical values for the weight matrices and biases are illustrated by a number of numerical examples.

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Global Asymptotic Stability and Stabilization of Long Short-Term Memory Neural Networks with Constant Weights and Biases

Abstract

Keywords

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