Lyapunov Stability Learning with Nonlinear Control via Inductive Biases
This work addresses stability issues in safety-critical control applications, offering an incremental improvement over prior learner-verifier frameworks.
The paper tackles the challenge of learning control Lyapunov functions (CLFs) for stability in dynamical systems by treating Lyapunov conditions as inductive biases, enabling end-to-end learning of CLFs and controllers. It achieves a higher convergence rate and larger region of attraction compared to existing methods in experiments.
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.