Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning
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.
Related
- Carleman estimates for a nonconservative Timoshenko beam involving Dirichlet-Neumann boundary conditions and application to exact controllability
- Lack of exponential stability for thermoelastic Timoshenko and Bresse systems with full homogeneous Dirichlet boundary conditions
- On Equilibrium Problem for Elastic Body with Neumann Boundary Condition and Delaminated Timoshenko Inclusion
- Boundary-aware Reinforcement Learning for Hypercube State Spaces via Deterministic Policy Gradient
- Modified Decomposition Algorithms for Fractional Delay Boundary Value Problems
BibTeX
@misc{rodrigues2026boundary,
title = {{Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning}},
author = {Leonardo R S Rodrigues},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17563},
eprint = {2610.17563},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17563},
}
RIS
TY - UNPB
TI - Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning
AU - Leonardo R S Rodrigues
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17563
UR - https://arxiv.org/abs/2610.17563
AB - 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.
ER -