The field of heat recovery steam generator (HRSG) control is moving towards the development of innovative, fault-tolerant control strategies that can adapt to operational disturbances and valve leakage faults. Recent research has focused on integrating physics-informed neural networks (PINNs) with traditional control methodologies to improve the reliability and efficiency of HRSG systems. These advanced control frameworks have shown strong potential for industrial deployment, ensuring autonomous fault recovery and enhanced performance. Noteworthy papers in this area include: Fault-Tolerant Temperature Control of HRSG Superheaters, which introduced a fault-tolerant temperature control framework using PINNs, demonstrating significantly improved response times and reduced temperature deviations. Fault-Tolerant Control of Steam Temperature in HRSG Superheater under Actuator Fault, which presented a novel fault-tolerant control framework using a sliding mode observer and PINN, demonstrating effective fault adaptation and reduced temperature overshoot. PINN vs LSTM, which compared the performance of PINNs and LSTMs for adaptive steam temperature control, concluding that embedding physical knowledge into data-driven control is essential for developing reliable, fault-tolerant autonomous control systems.