Computing Lyapunov functions using deep neural networks-Reference-Cited by-同舟云学术

Computing Lyapunov functions using deep neural networks

Published:2021 Issue:2 Volume:8 Page:131
ISSN:2158-2505
Container-title:Journal of Computational Dynamics
language:
Short-container-title:JCD

Author:

Grüne Lars

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Computational Mathematics,Computational Mechanics,General Medicine

Reference45 articles.

1. M. Abadi, A. Agarwal, P. Barham, E. Brevdo and Z. Chen, et al., TensorFlow: Large-scale machine learning on heterogeneous systems, 2015., Available from: https://www.tensorflow.org/.

2. M. Abu-Khalaf, F. L. Lewis.Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach, Automatica J. IFAC, 41 (2005), 779-791.

3. J. Anderson, A. Papachristodoulou.Advances in computational Lyapunov analysis using sum-of-squares programming, Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), 2361-2381.

4. J. Berner, P. Grohs, A. Jentzen.Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations, SIAM J. Math. Data Sci., 2 (2020), 631-657.

5. L. Bottou, Large-scale machine learning with stochastic gradient descent, in Proceedings of COMPSTAT'2010, Physica-Verlag/Springer, Heidelberg, 2010, 177-186.

Cited by 20 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Solving optimal control problems governed by nonlinear PDEs using a multilevel method based on an artificial neural network;Computational and Applied Mathematics;2024-08-06

2. Zubov-Koopman Learning of Maximal Lyapunov Functions;2024 American Control Conference (ACC);2024-07-10

3. Compositionally Verifiable Vector Neural Lyapunov Functions for Stability Analysis of Interconnected Nonlinear Systems;2024 American Control Conference (ACC);2024-07-10

4. A Physics-Informed Neural Network Method to Approximate Homogeneous Lyapunov Functions;2024 European Control Conference (ECC);2024-06-25

5. A Data-Driven Approach for Certifying Asymptotic Stability and Cost Evaluation for Hybrid Systems;Proceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control;2024-05-14