Designing stabilizing controllers is a fundamental challenge in autonomous
systems, particularly for high-dimensional, nonlinear systems that cannot be
accurately modeled using differential equations. Lyapunov theory offers a
robust solution for stabilizing control systems. Still, current methods relying
on Lyapunov functions require access to complete dynamics or samples of system
executions throughout the entire state space. Consequently, they are
impractical for high-dimensional systems. In this paper, we introduce a novel
framework, LYGE, for learning stabilizing controllers specifically tailored to
high-dimensional, unknown systems. LYGE employs Lyapunov theory to iteratively
guide the search for samples during exploration while simultaneously learning
the local system dynamics, control policy, and Lyapunov functions. We
demonstrate its scalability on highly complex systems, including a
high-fidelity F-16 jet model from the Air Force featuring a 16D state space and
a 4D input space. Experimental results indicate that, compared to prior works
in reinforcement learning, imitation learning, and neural certificates, LYGE
reduces the distance to the goal by 50% while requiring only 5% to 32% of the
samples. Furthermore, we demonstrate that our algorithm can be extended to
learn controllers guided by alternative certificate functions for unknown
systems.Comment: 32 pages, 7 figure