arXiv:2610.35613v1 Announce Type: cross 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.