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Stability in dynamical systems

Lyapunov exponents and ilk

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Refs

Berkenkamp, Felix, and Angela P. Schoellig. 2015. “Safe and Robust Learning Control with Gaussian Processes.” In 2015 European Control Conference (ECC), 2496–2501. Linz, Austria: IEEE. https://doi.org/10.1109/ECC.2015.7330913.

Chang, Bo, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, and Elliot Holtham. 2018. “Reversible Architectures for Arbitrarily Deep Residual Neural Networks.” In. http://arxiv.org/abs/1709.03698.

Haddad, Wassim M, and VijaySekhar Chellaboina. 2011. Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach. Princeton: Princeton University Press. http://public.eblib.com/choice/publicfullrecord.aspx?p=768552.

Mohammed, Salah-Eldin A., and Michael K. R. Scheutzow. 1997. “Lyapunov Exponents of Linear Stochastic Functional-Differential Equations. II. Examples and Case Studies.” The Annals of Probability 25 (3): 1210–40. https://doi.org/10.1214/aop/1024404511.

Pathak, Jaideep, Zhixin Lu, Brian R. Hunt, Michelle Girvan, and Edward Ott. 2017. “Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data.” Chaos: An Interdisciplinary Journal of Nonlinear Science 27 (12): 121102. https://doi.org/10.1063/1.5010300.

Smith, Leonard A. 2000. “Disentangling Uncertainty and Error: On the Predictability of Nonlinear Systems.” In Nonlinear Dynamics and Statistics.