  Designing stabilizing controllers is a fundamental challenge in autonomous
systems, particularly for high-dimensional, nonlinear systems that can hardly
be accurately modeled with differential equations. The Lyapunov theory offers a
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. This paper introduces a novel
framework, LYapunov-Guided Exploration (LYGE), for learning stabilizing
controllers 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 featuring a 16D state space and a 4D
input space. Experiments 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 other certificate functions for unknown systems.
