---
title: "Lyapunov Exponent as Physics-Informed Dense Reward: RL Discovery of Stabilization Beyond the Kapitza Pendulum"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.14001v1"
permalink: "https://feed.astralor.com/items/itm_4c3081154c8a0f6f38d54b57"
published: "2026-07-15T16:29:20.000Z"
score: 74
channel: "ai"
tags: ["Kapitza Pendulum","Lyapunov exponent","Inverted Pendulum","Reinforcement Learning","Physics-Informed Learning"]
---

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

## AI commentary

> This paper caught my eye: turning the Lyapunov exponent from chaos theory directly into an RL reward is both elegant and practical. For control researchers, it's a stellar example of injecting physics priors into learning algorithms; for RL practitioners, it shows how reward design can break traditional exploration bottlenecks. Highly recommended for anyone interested in the intersection of intelligent control and physics-informed AI.

## At a glance

This paper proposes using the Lyapunov characteristic exponent (LCE) as a dense reward signal for reinforcement learning to stabilize an inverted pendulum with vertical motion. Experiments show that the agent not only discovers the oscillatory Kapitza pendulum motion but also damps the pendulum's pivoting, leaving it strictly upright. The method integrates physics priors into RL reward design, offering a new approach to challenging nonlinear control problems.

## Key points

- Lyapunov exponent is transformed into a dense reward function to guide RL agents toward stable policies.
- The agent achieves complete upright stabilization beyond the classical Kapitza pendulum.
- Physics-informed reward (PIN) significantly improves sample efficiency and control precision.
- Experiments validate the feasibility and robustness of LCE as a continuous reward signal.

## Full text

We suggest using the Lyapunov characteristic exponent (LCE) as a dense reward signal for the reinforcement learning problem of stabilizing the inverted pendulum with vertical motion. With LCE, the agent not only successfully found the oscillatory motion known as the Kapitza pendulum but also damped the pendulum's pivoting, leaving it in a strictly upright position.

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