论文/arXiv 2610.17563·15 天前

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

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。

AI 整理

• 硬件零部件
• 本体 SDK 与控制
• 具身模型

原文链接：Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning（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

来源

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1. arXiv 2610.17563：Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning访问 2026-10-21