Stochastic Gradient-Descent Calibration of Pyragas Delayed-Feedback Control for Chaos Suppression in the Sprott Circuit

Abstract

This paper explores chaos control in the Sprott circuit by leveraging Stochastic Gradient Descent (SGD) to calibrate Pyragas delayed feedback control. Using a third-order nonlinear differential equation, we model the circuit and aim to suppress chaos by optimizing control parameters (gain $K$, delay $T_{\text{con}}$) and the variable resistor $R_v$. Experimental voltage data, extracted from published figures via WebPlotDigitizer, serve as the calibration target. We compare two calibration techniques: sum of squared errors (SSE) minimization via grid search and stochastic gradient descent (SGD) with finite differences. Joint optimization of $K$, $T_{\text{con}}$, and $R_v$ using SGD achieves superior alignment with experimental data, capturing both phase and amplitude with high fidelity. Compared to grid search, SGD excels in phase synchronization, though minor amplitude discrepancies persist due to model simplifications. Phase space analysis confirms the model ability to replicate the chaotic attractor geometry, despite slight deviations. We analyze the trade-off between calibration accuracy and computational cost, highlighting scalability challenges. Overall, SGD-based calibration demonstrates significant potential for precise control of chaotic systems, advancing mathematical modeling and applications in electrical engineering.