## 1 Introduction
(2018) proposed a steam generator pipeline degradation prediction method based on particle filter (PF), aiming to solve the problems existing in the aging management of nuclear power plant systems, such as the contradiction between the general aging model and the individual differences of the system, the insufficient accuracy of degradation prediction, and the uncertainty of measurement data affecting the reliability of evaluation. Meanwhile, machine learning have proven to be highly effective in modeling complex system behaviors ([PERSON], 1964; [PERSON], 2018), surpassing traditional methods like transfer functions and state-space models. By training on extensive operational data, neural networks accurately replicate the intricate dynamics of supercritical plants, providing a solid foundation for control improvements. There are also many studies on predictive control based on machine learning ([PERSON], 2018; [PERSON], 2018; [PERSON], 2018). For example, [PERSON] et al. (2018) built a predictive model for nuclear superheated-steam supply systems (Su-NSSS) through multi-layer perceptron, and combined the model predictive control method to dynamically optimize the thermal power response of nuclear power plant Su-NSSS. [PERSON] et al. (2018) employed LSTM to accurately model the dynamic characteristics of supercritical power plants, and combined ESKF-EMPC to optimize the thermal power response. These combined advancements in filtering and identification have demonstrated tangible benefits in enhancing MPC's adaptability and precision. Despite these advancements, current MPC strategies, even when bolstered by advanced filtering techniques, encounter significant hurdles in meeting the dynamic control needs of supercritical coal plants. For instance, while the EKF and its extended-state variant enhance disturbance rejection, their static parameter configurations struggle to cope with rapid operational shifts, such as those driven by fluctuating grid demands or aging infrastructure. Existing MPC variants, including distributed and dual-timescale approaches,often face trade-offs between computational efficiency and responsiveness, particularly under wide-ranging load conditions or when confronted with strong multivariable coupling and large inertia. These shortcomings reveal a critical gap in achieving real-time adaptability without sacrificing control precision or stability. For rapid changes in the operating conditions of supercritical power plants, a single filtering or modeling technique may still not be sufficient to fully optimize the control performance. Therefore, the complex, dynamic and variable operating conditions of supercritical power plants require the control strategy to have higher adaptability. Adaptive control provides an effective way to achieve accurate and stable multivariable control by dynamically adjusting parameters to deal with nonlinearity, disturbance and parameter drift. [PERSON] et al. [27] combined digital twins with augmented state-extended Kalman Filters to model industrial system energy consumption and predict power consumption more accurately by dynamically updating parameters. [PERSON] et al. [28] analyzed the quality of biomass fuel through image processing and machine learning, adaptively adjusted furnace setpoints to more accurately adapt to fuel changes, and improved the adaptive control ability of industrial furnaces. [PERSON] et al. [5] used adaptive second-order non-singular terminal sliding mode control to dynamically estimate nuclear power plant disturbances and adjust control inputs to stabilize power more accurately. In this study, backpropagation neural networks were used to create high-fidelity simulations of supercritical power plants that accurately reflect their complex properties.