Lyapunov Exponent as Physics-Informed Dense Reward: RL Discovery of Stabilization Beyond the Kapitza Pendulum

The authors propose using the Lyapunov characteristic exponent (LCE) as a dense reward signal for stabilizing an inverted pendulum with vertical motion. This approach enables reinforcement learning agents to discover complex stabilization behaviors beyond standard oscillatory solutions.

• The LCE serves as a physics-informed dense reward for the reinforcement learning task.
• The agent successfully identifies the oscillatory motion characteristic of the Kapitza pendulum.
• The method allows the agent to damp the pendulum's pivoting, achieving a strictly upright position.