Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation
Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation
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DOI：
10.1109/cdc51059.2022.9993006
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Nathan Gaby;Fumin Zhang;X. Ye
中科院分区：
文献类型：
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作者：
Nathan Gaby;Fumin Zhang;X. Ye
我们开发了一个通用的深度神经网络架构，称为Lyapunov- net，以在高维上近似动力系统的Lyapunov函数。Lyapunov-Net保证了正确定性，因此可以很容易地训练到满足负轨道导数条件，在实践中经验风险函数只呈现单一项。这大大简化了参数调整，并大大提高了网络训练和近似质量的收敛性。我们还对李亚普诺夫网的逼近精度和认证保证提供了全面的理论论证。我们证明了所提出的方法在高维状态空间非线性动力系统上的有效性，并表明所提出的方法显着优于最先进的方法。
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 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 simplifies parameter tuning and results in greatly improved convergence during network training and approximation quality. We also provide comprehensive theoretical justifications on the approximation accuracy and certification guarantees of Lyapunov-Nets. We demonstrate the efficiency of the proposed method on nonlinear dynamical systems in high dimensional state spaces, and show that the proposed approach significantly outperforms the state-of-the-art methods.