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- W4287777332 abstract "We propose a deep neural network architecture and a training algorithm for computing approximate Lyapunov functions of systems of nonlinear ordinary differential equations. Under the assumption that the system admits a compositional Lyapunov function, we prove that the number of neurons needed for an approximation of a Lyapunov function with fixed accuracy grows only polynomially in the state dimension, i.e., the proposed approach is able to overcome the curse of dimensionality. We show that nonlinear systems satisfying a small-gain condition admit compositional Lyapunov functions. Numerical examples in up to ten space dimensions illustrate the performance of the training scheme." @default.
- W4287777332 created "2022-07-26" @default.
- W4287777332 creator A5054568856 @default.
- W4287777332 date "2020-05-18" @default.
- W4287777332 modified "2023-09-29" @default.
- W4287777332 title "Computing Lyapunov functions using deep neural networks" @default.
- W4287777332 doi "https://doi.org/10.48550/arxiv.2005.08965" @default.
- W4287777332 hasPublicationYear "2020" @default.
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