# 通过降阶强化学习对改进 Timoshenko-Ehrenfest 梁进行边界控制

> 原文链接：https://robotics.hellobike.com/papers/2026-10-13-2610-17563
> 频道：papers | 更新日期：2026-10-13 | 标签：arxiv, cs.RO
> 核心摘要：研究弹性梁主动振动控制，将偏微分方程约化为 ROM，并用 PPO 在边界控制问题上与 LQR 数值比较。

# 通过降阶强化学习对改进 Timoshenko-Ehrenfest 梁进行边界控制

::: v-pre
> 原文链接：[Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning](https://arxiv.org/abs/2610.17563)（arXiv 2610.17563 · 发布日期：2026-10-13）

**Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning**

研究弹性梁主动振动控制，将偏微分方程约化为 ROM，并用 PPO 在边界控制问题上与 LQR 数值比较。

## 核心要点

- 面向弹性梁主动振动控制，系统由简支边界条件下的线性偏微分方程建模。
- 通过特征值展开和截断 Galerkin 投影构建 ROM，并采用边界作动施加控制。
- 将有限维系统表述为连续时间马尔可夫决策过程，并用 PPO 数值求解。
- 系统比较 PPO 控制器与 LQR，讨论能量耗散机制和作动器约束下的优劣。

**验证范围与局限**：验证范围限于该梁模型的 ROM 数值求解及与 LQR 的系统比较。

## 英文摘要 (Abstract)

In this paper, we study the active vibration control of an elastic beam using reinforcement learning (RL). The physical system is modeled by a modified Timoshenko-Ehrenfest type linear partial differential equation with simply supported boundary conditions. The dynamics are approximated by a reduced-order model (ROM) obtained through eigenvalue expansion and truncated Galerkin projection. Control is applied through boundary actuation. The resulting finite-dimensional system is formulated as a continuous-time Markov decision process and solved numerically using the Proximal Policy Optimization (PPO) algorithm. All modeling steps, from physical formulation to temporal discretization and control design, are explicitly described. A systematic comparison is performed between the controller learned via PPO and the classical linear quadratic (LQR) regulator. The analysis highlights the strengths and limitations of each approach, both from a theoretical and practical point of view, with particular emphasis on energy dissipation mechanisms and actuator constraints.

作者：Leonardo R. S. Rodrigues
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## 原始参考来源 (Sources)

- [arXiv 2610.17563：Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning](https://arxiv.org/abs/2610.17563)