用归纳偏置设计神经控制李雅普诺夫函数，实现稳定端到端学习。
Lyapunov Stability Learning with Nonlinear Control via Inductive Biases
- 将李雅普诺夫条件作为归纳偏置，简化优化约束。
- 收敛速度更快，吸引域更大，实验表现优于现有方法。
- 适用于需保证安全性的控制系统设计，如自动驾驶、机器人。
在需要安全保障的应用中，通过控制器寻找控制李雅普诺夫函数（CLF）是确保系统稳定性的重要方法。近年来，深度学习模型被用于构建CLF，并在学习-验证框架中识别可行候选。然而，学习器将李雅普诺夫条件视为复杂优化约束，难以实现全局收敛，且验证过程过于繁琐。为此，本文将李雅普诺夫条件作为归纳偏置，设计了一种神经CLF与基于CLF的控制器。该设计使优化过程更稳定，约束更少，支持端到端联合学习。在大量实验中，本方法相比现有方法具有更高的收敛率和更大的吸引域（ROA）。同时，我们深入揭示了以往方法在学习过程中成功率下降的原因。
原文摘要 · Abstract (English)
Finding a control Lyapunov function (CLF) in a dynamical system with a controller is an effective way to guarantee stability, which is a crucial issue in safety-concerned applications. Recently, deep learning models representing CLFs have been applied into a learner-verifier framework to identify satisfiable candidates. However, the learner treats Lyapunov conditions as complex constraints for optimisation, which is hard to achieve global convergence. It is also too complicated to implement these Lyapunov conditions for verification. To improve this framework, we treat Lyapunov conditions as inductive biases and design a neural CLF and a CLF-based controller guided by this knowledge. This design enables a stable optimisation process with limited constraints, and allows end-to-end learning of both the CLF and the controller. Our approach achieves a higher convergence rate and larger region of attraction (ROA) in learning the CLF compared to existing methods among abundant experiment cases. We also thoroughly reveal why the success rate decreases with previous methods during learning.
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