Lyapunov Function

Lyapunov functions are mathematical tools used to analyze the stability of dynamical systems, primarily aiming to prove the convergence of a system to a desired equilibrium point. Current research focuses on leveraging Lyapunov functions within machine learning contexts, particularly for designing stable controllers and analyzing the convergence of algorithms like stochastic gradient descent and reinforcement learning, often employing neural networks to approximate these functions. This work has significant implications for robotics, control systems, and optimization problems, enabling the development of more robust and reliable algorithms with provable stability guarantees.