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

Leonardo R S Rodrigues

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arXiv · 2610.17563

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

Leonardo R S Rodrigues

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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.

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BibTeX RIS

Leonardo R S Rodrigues. 2026-10-13. Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning. https://arxiv.org/abs/2610.17563

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