Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation

• URL: http://arxiv.org/abs/2109.13359v1
• Date: Mon, 27 Sep 2021 21:42:19 GMT
• Title: Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation
• Authors: Nathan Gaby and Fumin Zhang and Xiaojing Ye
• Abstract summary: We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to satisfy the negative orbital derivative condition.
• Score: 7.469944784454579
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to satisfy the negative orbital derivative condition, which only renders a single term in the empirical risk function in practice. This significantly reduces the number of hyper-parameters compared to existing methods. We also provide theoretical justifications on the approximation power of Lyapunov-Net and its complexity bounds. We demonstrate the efficiency of the proposed method on nonlinear dynamical systems involving up to 30-dimensional state spaces, and show that the proposed approach significantly outperforms the state-of-the-art methods.

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