提出可证明稳定的神经网络控制方法，解决非线性系统控制的可靠性难题。
Provably-Stable Neural Network-Based Control of Nonlinear Systems
- 基于神经网络设计闭环稳定控制，理论保证系统不发散。
- 状态渐近收敛至目标点附近，可调逼近精度。
- 适用于对稳定性要求高的实际系统，如无人机、机械臂。
近年来，神经网络（NNs）因其处理传统非线性控制方案难以应对场景的潜力，被用于控制非线性系统。然而，据我们所知，现有基于神经网络的控制研究缺乏稳定性与跟踪性能的理论保障，限制了其在需严格稳定性保证系统中的应用。为此，本文提出一种系统且全面的方法，为仿射非线性系统设计可证明稳定的神经网络控制方案。通过严格分析，证明所提方法能保证闭环系统稳定性。同时，结果表明该神经网络控制方案确保系统状态渐近收敛至期望平衡点附近的邻域，且邻域大小可通过参数调节。该方法在倒立摆系统仿真和Parrot Bebop 2无人机实验中得到验证与评估。
原文摘要 · Abstract (English)
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.
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