Nephron autoregulation is essential for maintaining stable renal blood flow and glomerular filtration despite variations in arterial pressure. The coupled interactions between the myogenic response and tubuloglomerular feedback constitute a nonlinear physiological system capable of exhibiting oscillatory dynamics under certain operating conditions. In this study, a physiologically grounded four-state nonlinear nephron model is developed to investigate the dynamic behavior of glomerular pressure, renal blood flow, afferent arteriolar resistance, and macula densa sodium concentration. Nonlinear bifurcation analysis performed using MATCONT identifies the existence of a Hopf bifurcation, confirming the transition from stable equilibrium to sustained limit-cycle oscillations. The corresponding analytical and numerical Jacobian matrices are derived, and eigenvalue analysis verifies the onset of instability through the crossing of a pair of complex conjugate eigenvalues across the imaginary axis. An optimal control problem is subsequently formulated in which the control variable simultaneously serves as the bifurcation parameter. The objective function minimizes deviations of glomerular pressure and renal blood flow from desired physiological values while penalizing excessive control eff ort. A neural-network surrogate model of the Hopf boundary is incorporated within a PYOMO. DAE–IPOPT optimization framework to enable computationally efficient stability-aware optimization. Numerical results demonstrate that incorporating the Hopf-bifurcation constraint produces approximately a 20% reduction in the objective function while maintaining stable nephron dynamics. The proposed framework provides a computational approach for integrating renal physiology, nonlinear dynamics, machine learning, and optimal control to improve nephron autoregulation and support future model-based strategies for kidney disease management.