Graph-Convolutional Reinforcement Learning for Finite-Time Stabilization of a Chaotic Chua Circuit via Unified Flexible Terminal Sliding-Mode Control
Abstract
This paper introduces a graph convolutional reinforcement learning framework for the finite-time stabilization of chaotic dynamics in a physical Chua circuit. The circuit is modeled directly in terms of capacitor voltages, inductor current, and physical component parameters. This preserves the connection between the mathematical model and the underlying electrical system. A unified, flexible terminal sliding-mode controller is developed to achieve stabilization within a finite time in the presence of uncertainties in the lumped model, external disturbances, and bounded control inputs. The controller incorporates state-dependent nonlinear exponents to provide flexible convergence characteristics while avoiding singular terms near equilibrium. To minimize dependence on manual controller tuning, the admissible controller parameters are optimized using an actor-critic reinforcement learning scheme with a graph convolutional network that leverages the circuit dynamics' coupling structure. The learned parameters are constrained to the ranges required by the theoretical stability conditions. Numerical experiments demonstrate the rapid suppression of chaotic oscillations and the finite-time convergence of the state and sliding variables while respecting the prescribed input-saturation limits. Compared to a reference control method, the proposed approach reduces the IAE, ISE, ITAE, and ITSE by 56.27\,\%, 56.40\,\%, 61.69\,\%, and 64.70\,\%, respectively. These results suggest that graph-based reinforcement learning can effectively tune parameters while retaining the robustness and analytical structure of the underlying sliding-mode controller.
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BibTeX
@misc{fatoorehchi2026graphconvolutional,
title = {{Graph-Convolutional Reinforcement Learning for Finite-Time Stabilization of a Chaotic Chua Circuit via Unified Flexible Terminal Sliding-Mode Control}},
author = {Hooman Fatoorehchi and Majid Roohi and Rasmus Kold and Matthias Ehrhardt and Andreas Basse-O'Connor and Sebastian Nis Bay Villadsen and Philip L. Fosbøl},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35613},
eprint = {2610.35613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35613},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Graph-Convolutional Reinforcement Learning for Finite-Time Stabilization of a Chaotic Chua Circuit via Unified Flexible Terminal Sliding-Mode Control
AU - Hooman Fatoorehchi
AU - Majid Roohi
AU - Rasmus Kold
AU - Matthias Ehrhardt
AU - Andreas Basse-O'Connor
AU - Sebastian Nis Bay Villadsen
AU - Philip L. Fosbøl
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35613
UR - https://arxiv.org/abs/2610.35613
AB - This paper introduces a graph convolutional reinforcement learning framework for the finite-time stabilization of chaotic dynamics in a physical Chua circuit. The circuit is modeled directly in terms of capacitor voltages, inductor current, and physical component parameters. This preserves the connection between the mathematical model and the underlying electrical system. A unified, flexible terminal sliding-mode controller is developed to achieve stabilization within a finite time in the presence of uncertainties in the lumped model, external disturbances, and bounded control inputs. The controller incorporates state-dependent nonlinear exponents to provide flexible convergence characteristics while avoiding singular terms near equilibrium. To minimize dependence on manual controller tuning, the admissible controller parameters are optimized using an actor-critic reinforcement learning scheme with a graph convolutional network that leverages the circuit dynamics' coupling structure. The learned parameters are constrained to the ranges required by the theoretical stability conditions. Numerical experiments demonstrate the rapid suppression of chaotic oscillations and the finite-time convergence of the state and sliding variables while respecting the prescribed input-saturation limits. Compared to a reference control method, the proposed approach reduces the IAE, ISE, ITAE, and ITSE by 56.27\,\%, 56.40\,\%, 61.69\,\%, and 64.70\,\%, respectively. These results suggest that graph-based reinforcement learning can effectively tune parameters while retaining the robustness and analytical structure of the underlying sliding-mode controller.
ER -