Strengthened stability analysis of discrete-time Lurie systems involving ReLU neural networks
Strengthened stability analysis of discrete-time Lurie systems involving ReLU neural networks
This paper addresses the stability analysis of a discrete-time (DT) Lurie system featuring a static repeated ReLU nonlinearity. Such systems often arise in the analysis of recurrent neural networks and other neural feedback loops. Custom quadratic constraints, satisfied by the repeated ReLU, are employed to strengthen the standard Circle and Popov Criteria for this specific Lurie system. The criteria can be expressed as a set of linear matrix inequalities (LMIs) with less restrictive conditions on the matrix variables. It is further shown that if the Lurie system under consideration has a unique equilibrium point at the origin, then this equilibrium point is in fact globally stable or unstable, meaning that local stability analysis will provide no additional benefit. Numerical examples demonstrate that the strengthened criteria achieve a desirable balance between reduced conservatism and complexity when compared to existing criteria.
Lyapunov methods, Neural networks, semi-definite programming, stability of nonlinear systems
209-221
Richardson, Carl R.
3406b6af-f00d-410b-8051-a0ecc27baba5
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Gunn, Steve R.
306af9b3-a7fa-4381-baf9-5d6a6ec89868
11 June 2024
Richardson, Carl R.
3406b6af-f00d-410b-8051-a0ecc27baba5
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Gunn, Steve R.
306af9b3-a7fa-4381-baf9-5d6a6ec89868
Richardson, Carl R., Turner, Matthew C. and Gunn, Steve R.
(2024)
Strengthened stability analysis of discrete-time Lurie systems involving ReLU neural networks.
Abate, A., Cannon, M., Margellos, K. and Papachristodoulou, A.
(eds.)
In Proceedings of the 6th Annual Conference on Learning for Dynamics and Control.
vol. 242,
PMLR.
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
This paper addresses the stability analysis of a discrete-time (DT) Lurie system featuring a static repeated ReLU nonlinearity. Such systems often arise in the analysis of recurrent neural networks and other neural feedback loops. Custom quadratic constraints, satisfied by the repeated ReLU, are employed to strengthen the standard Circle and Popov Criteria for this specific Lurie system. The criteria can be expressed as a set of linear matrix inequalities (LMIs) with less restrictive conditions on the matrix variables. It is further shown that if the Lurie system under consideration has a unique equilibrium point at the origin, then this equilibrium point is in fact globally stable or unstable, meaning that local stability analysis will provide no additional benefit. Numerical examples demonstrate that the strengthened criteria achieve a desirable balance between reduced conservatism and complexity when compared to existing criteria.
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Published date: 11 June 2024
Venue - Dates:
6th Annual Learning for Dynamics & Control Conference, , Oxford, United Kingdom, 2024-07-15 - 2024-07-17
Keywords:
Lyapunov methods, Neural networks, semi-definite programming, stability of nonlinear systems
Identifiers
Local EPrints ID: 492285
URI: http://eprints.soton.ac.uk/id/eprint/492285
ISSN: 2640-3498
PURE UUID: b2054aca-7cfa-4783-97aa-f6f36aebcbf2
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Date deposited: 23 Jul 2024 17:02
Last modified: 24 Jul 2024 02:04
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Contributors
Author:
Carl R. Richardson
Author:
Matthew C. Turner
Author:
Steve R. Gunn
Editor:
A. Abate
Editor:
M. Cannon
Editor:
K. Margellos
Editor:
A. Papachristodoulou
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