标题： 基于神经网络的非线性系统的可证明稳定控制 显示英文标题

标题： Provably-Stable Neural Network-Based Control of Nonlinear Systems

摘要： 近年来，由于神经网络（NNs）在处理传统非线性控制方案可能难以应对的情况方面具有潜在能力，它们被用于控制非线性系统。 然而，据我们所知，当前基于NN的控制文献中缺乏对稳定性和跟踪性能的理论保证。 这限制了基于NN的控制方案在需要严格稳定性和性能保证的系统中的应用。 为解决这一差距，本文提出了一种系统且全面的方法，以设计可证明稳定的基于NN的控制方案，适用于仿射非线性系统。 提供了严格的分析，以表明所提出的方法保证了闭环系统在环中的NN的稳定性。 此外，还表明所得到的基于NN的控制方案确保系统状态渐近收敛到期望平衡点附近的邻域，并具有可调节的接近阈值。 所提出的方法通过倒立摆的仿真研究和Parrot Bebop 2无人机的实验研究进行了验证和评估。 显示英文摘要

摘要： In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of our knowledge, the current literature on NN-based control lacks theoretical guarantees for stability and tracking performance. This precludes the application of NN-based control schemes to systems where stringent stability and performance guarantees are required. To address this gap, this paper proposes a systematic and comprehensive methodology to design provably-stable NN-based control schemes for affine nonlinear systems. Rigorous analysis is provided to show that the proposed approach guarantees stability of the closed-loop system with the NN in the loop. Also, it is shown that the resulting NN-based control scheme ensures that system states asymptotically converge to a neighborhood around the desired equilibrium point, with a tunable proximity threshold. The proposed methodology is validated and evaluated via simulation studies on an inverted pendulum and experimental studies on a Parrot Bebop 2 drone.