Dissipative Deep Neural Dynamical Systems

Drgona, Jan; Tuor, Aaron; Vasisht, Soumya; Vrabie, Draguna

doi:10.1109/OJCSYS.2022.3186838

Title: Dissipative Deep Neural Dynamical Systems

Journal Article · 31 December 2021 · IEEE Open Journal of Control Systems

DOI: https://doi.org/10.1109/OJCSYS.2022.3186838 · OSTI ID:1874397

^[1];

^[1]

Pacific Northwest National Laboratory, Richland, WA, USA

Not Available

View Journal Article

Cite

Export

Save

Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 1874397

Report Number(s):: PNNL-SA-174718; 9809789

Journal Information:: IEEE Open Journal of Control Systems, Journal Name: IEEE Open Journal of Control Systems Vol. 1; ISSN 2694-085X

Publisher:: Institute of Electrical and Electronics EngineersCopyright Statement

Country of Publication:: United States

Language:: English

References (37)

Dissipative Dynamical Systems: Basic Input-Output and State Properties Hill, David J.; Moylan, Peter J. Journal of the Franklin Institute, Vol. 309, Issue 5 https://doi.org/10.1016/0016-0032(80)90026-5	journal	May 1980
Online actor–critic algorithm to solve the continuous-time infinite horizon optimal control problem Vamvoudakis, Kyriakos G.; Lewis, Frank L. Automatica, Vol. 46, Issue 5 https://doi.org/10.1016/j.automatica.2010.02.018	journal	May 2010
Eigenvalue decay: A new method for neural network regularization Ludwig, Oswaldo; Nunes, Urbano; Araujo, Rui Neurocomputing, Vol. 124 https://doi.org/10.1016/j.neucom.2013.08.005	journal	January 2014
Neural network approach to continuous-time direct adaptive optimal control for partially unknown nonlinear systems Vrabie, Draguna; Lewis, Frank Neural Networks, Vol. 22, Issue 3 https://doi.org/10.1016/j.neunet.2009.03.008	journal	April 2009
Robust timing and motor patterns by taming chaos in recurrent neural networks Laje, Rodrigo; Buonomano, Dean V. Nature Neuroscience, Vol. 16, Issue 7 https://doi.org/10.1038/nn.3405	journal	May 2013
A characterization of certain classes of matrix norms Malek-Shahmirzadi, Massoud Linear and Multilinear Algebra, Vol. 13, Issue 2 https://doi.org/10.1080/03081088308817508	journal	May 1983
Stable architectures for deep neural networks Haber, Eldad; Ruthotto, Lars Inverse Problems, Vol. 34, Issue 1 https://doi.org/10.1088/1361-6420/aa9a90	journal	December 2017
Nonlinear random matrix theory for deep learning Pennington, Jeffrey; Worah, Pratik Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 12 https://doi.org/10.1088/1742-5468/ab3bc3	journal	December 2019
Eigenvalues of covariance matrices: Application to neural-network learning Cun, Yann Le; Kanter, Ido; Solla, Sara A. Physical Review Letters, Vol. 66, Issue 18 https://doi.org/10.1103/PhysRevLett.66.2396	journal	May 1991
Eigenvalue Spectra of Random Matrices for Neural Networks Rajan, Kanaka; Abbott, L. F. Physical Review Letters, Vol. 97, Issue 18 https://doi.org/10.1103/PhysRevLett.97.188104	journal	November 2006
Lyapunov spectra of chaotic recurrent neural networks Engelken, Rainer; Wolf, Fred; Abbott, L. F. Physical Review Research, Vol. 5, Issue 4 https://doi.org/10.1103/physrevresearch.5.043044	journal	October 2023
An approach to stability criteria of neural-network control systems Tanaka, K. IEEE Transactions on Neural Networks, Vol. 7, Issue 3 https://doi.org/10.1109/72.501721	journal	May 1996
Neural network-based control design: an LMI approach Limanond, S.; Si, J. IEEE Transactions on Neural Networks, Vol. 9, Issue 6 https://doi.org/10.1109/72.728392	journal	January 1998
Losslessness, feedback equivalence, and the global stabilization of discrete-time nonlinear systems Byrnes, C. I. IEEE Transactions on Automatic Control, Vol. 39, Issue 1 https://doi.org/10.1109/9.273341	journal	January 1994
Analysis of gain scheduled control for nonlinear plants Shamma, J. S.; Athans, M. IEEE Transactions on Automatic Control, Vol. 35, Issue 8 https://doi.org/10.1109/9.58498	journal	January 1990
Relationships between positive real, passive dissipative, & positive systems Kottenstette, N.; Antsaklis, P. J. Proceedings of the 2010 American Control Conference https://doi.org/10.1109/ACC.2010.5530779	conference	June 2010
Fundamentals of economic model predictive control Rawlings, James B.; Angeli, David; Bates, Cuyler N. 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC.2012.6425822	conference	December 2012
Parametrical Adjusting of a Hybrid System for the Vehicle Routing Problem with Time Windows Brandao De Oliveira, Humberto; Vasconcelos, Germano; Mesquita, Rafael 2006 Sixth International Conference on Hybrid Intelligent Systems (HIS'06) https://doi.org/10.1109/HIS.2006.264913	conference	December 2006
Gershgorin Loss Stabilizes the Recurrent Neural Network Compartment of an End-to-end Robot Learning Scheme Lechner, Mathias; Hasani, Ramin; Rus, Daniela 2020 IEEE International Conference on Robotics and Automation (ICRA) https://doi.org/10.1109/ICRA40945.2020.9196608	conference	May 2020
A Convex Parameterization of Robust Recurrent Neural Networks Revay, Max; Wang, Ruigang; Manchester, Ian R. IEEE Control Systems Letters, Vol. 5, Issue 4 https://doi.org/10.1109/LCSYS.2020.3038221	journal	October 2021
Training Robust Neural Networks Using Lipschitz Bounds Pauli, Patricia; Koch, Anne; Berberich, Julian IEEE Control Systems Letters, Vol. 6 https://doi.org/10.1109/LCSYS.2021.3050444	journal	January 2022
AI2: Safety and Robustness Certification of Neural Networks with Abstract Interpretation Gehr, Timon; Mirman, Matthew; Drachsler-Cohen, Dana 2018 IEEE Symposium on Security and Privacy (SP) https://doi.org/10.1109/SP.2018.00058	conference	May 2018
A Lyapunov Function for Economic Optimizing Model Predictive Control Diehl, Moritz; Amrit, Rishi; Rawlings, James B. IEEE Transactions on Automatic Control, Vol. 56, Issue 3 https://doi.org/10.1109/TAC.2010.2101291	journal	March 2011
On Necessity and Robustness of Dissipativity in Economic Model Predictive Control Muller, Matthias A.; Angeli, David; Allgower, Frank IEEE Transactions on Automatic Control, Vol. 60, Issue 6 https://doi.org/10.1109/TAC.2014.2361193	journal	June 2015
Dissipativity Theory for Nonlinear Stochastic Dynamical Systems Rajpurohit, Tanmay; Haddad, Wassim M. IEEE Transactions on Automatic Control, Vol. 62, Issue 4 https://doi.org/10.1109/TAC.2016.2598474	journal	April 2017
A Recurrent Neural Network for Solving Bilevel Linear Programming Problem He, Xing; Li, Chuandong; Huang, Tingwen IEEE Transactions on Neural Networks and Learning Systems, Vol. 25, Issue 4 https://doi.org/10.1109/TNNLS.2013.2280905	journal	April 2014
A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks Zhang, Huaguang; Wang, Zhanshan; Liu, Derong IEEE Transactions on Neural Networks and Learning Systems, Vol. 25, Issue 7 https://doi.org/10.1109/TNNLS.2014.2317880	journal	July 2014
$L1$ -Norm Batch Normalization for Efficient Training of Deep Neural Networks Wu, Shuang; Li, Guoqi; Deng, Lei IEEE Transactions on Neural Networks and Learning Systems, Vol. 30, Issue 7 https://doi.org/10.1109/TNNLS.2018.2876179	journal	July 2019
Finite-Time Stability for Differential Inclusions with Applications to Neural Networks Matusik, Radosław; Nowakowski, Andrzej; Plaskacz, Sławomir SIAM Journal on Control and Optimization, Vol. 58, Issue 5 https://doi.org/10.1137/19M1250078	journal	January 2020
Feature selection, L 1 vs. L 2 regularization, and rotational invariance Ng, Andrew Y. Twenty-first international conference on Machine learning - ICML '04 https://doi.org/10.1145/1015330.1015435	conference	January 2004
Efficient projections onto the l ₁ -ball for learning in high dimensions Duchi, John; Shalev-Shwartz, Shai; Singer, Yoram Proceedings of the 25th international conference on Machine learning - ICML '08 https://doi.org/10.1145/1390156.1390191	conference	January 2008
A random matrix approach to neural networks Louart, Cosme; Liao, Zhenyu; Couillet, Romain The Annals of Applied Probability, Vol. 28, Issue 2 https://doi.org/10.1214/17-AAP1328	journal	April 2018
Achieving stable dynamics in neural circuits Kozachkov, Leo; Lundqvist, Mikael; Slotine, Jean-Jacques PLOS Computational Biology, Vol. 16, Issue 8 https://doi.org/10.1371/journal.pcbi.1007659	journal	August 2020
Constrained Block Nonlinear Neural Dynamical Models Skomski, Elliott; Vasisht, Soumya; Wight, Colby 2021 American Control Conference (ACC) https://doi.org/10.23919/ACC50511.2021.9482930	conference	May 2021
Dissipative Dynamical Systems Willems, Jan C. European Journal of Control, Vol. 13, Issue 2-3 https://doi.org/10.3166/ejc.13.134-151	journal	January 2007
On Lyapunov Exponents for RNNs: Understanding Information Propagation Using Dynamical Systems Tools Vogt, Ryan; Puelma Touzel, Maximilian; Shlizerman, Eli Frontiers in Applied Mathematics and Statistics, Vol. 8 https://doi.org/10.3389/fams.2022.818799	journal	March 2022
Attractor network Eliasmith, Chris Scholarpedia, Vol. 2, Issue 10 https://doi.org/10.4249/scholarpedia.1380	journal	January 2007

Similar Records

Energy-dissipative evolutionary deep operator neural networks

Journal Article · 2024 · Journal of Computational Physics · OSTI ID:2576755

Zhang, Jiahao; Zhang, Shiheng; Shen, Jie; +1 more

Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

Journal Article · 2020 · Water Resources Research · OSTI ID:1639036

Tartakovsky, A. M.; Ortiz Marrero, C.; Perdikaris, Paris; +2 more

Smoothed dissipative particle dynamics model for mesoscopic multiphase flows in the presence of thermal fluctuations

Journal Article · 2016 · Physical Review E · OSTI ID:1283427

Lei, Huan; Baker, Nathan A.; Wu, Lei; +3 more

Related Subjects

42 ENGINEERING
deep neural networks
dissipative systems
dynamical systems
stability analysis

Title: Dissipative Deep Neural Dynamical Systems

Citation Formats

References (37)

Similar Records

Related Subjects