## 1 Introduction  
As the \"brain\" of an aeroengine, the role of the control system is to make the engine work stably and reliably under any changing conditions and give full play to its performance benefits [1]. Visible, stability and reliability are the fundamental guarantee of all other higher control requirements. Modern aero engines adopt a full authority digital electronic control (FADEC) system responsible for complex tasks including control, monitoring and management. Its structure consists of numerous sensors, actuators and electronic control components. Due to the long-term work in high temperature, high pressure and intense vibration, these components are prone to failure during system operation. Once a fault occurs, the whole control system may collapse, resulting in severe consequences. According to the data, the sensor fault of aeroengine is higher than 80% of the total system fault [2]. Fault-tolerant control (FTC) means that when the system fails, the remaining control tasks can be completed safely according to the specified performance index, or the performance index can be reduced but still within the acceptable range. At present, the most fault-tolerant design of engine control systems is based on hardware redundancy. The development of non-hardware redundancy is mainly focused on sensor fault diagnosis and signal reconstruction. In the 1970s, [PERSON] and [PERSON] proposed a passive FTC technology with analytic redundancy to reconstruct the fault system for engines with sensor faults [3]. Since the 1980s, NASA has designed an analytical redundancy scheme to improve engine control reliability, which can detect and distinguish between hard and soft faults of the control system and reconstruct the system for sensor faults [4]. Around the 90s, [PERSON] et al. used a set of Kalman estimators in fault detection and isolation. By monitoring the residuals of each estimator, specific faults that have occurred can be detected and isolated [5; 6]. Since the end of the last century, intelligent algorithms have been applied in sensor fault diagnosis and FTC systems and successfully verified in turbojet, turbofan and other engines [7; 8]. [PERSON] used a self-association neural network to construct the analysis redundancy of sensors to ensure the reliability of aircraft engine closed-loop control [9]. [PERSON] et al. used wavelet transform to diagnose sensor faults, and used BP neural network to predict the output data of fault sensors [10]. [PERSON] et al. obtained a set of modal functions by empirical mode decomposition of the output signal of the sensor, and took its sample entropy as the fault feature of the sensor, and classified the fault state of the sensor by sparse representation-based classifier [11]. [PERSON] and [PERSON] used radial basis function (RBF) neural network and general regression neural network (GRNN) respectively to predict timing data. If the difference between the predicted value and the actual output value of the sensor exceeds the set threshold, the sensor is considered to be faulty, and the sensor signal is reconstructed with the predicted value [12; 13]. [PERSON] et al. proposed an intelligent FTC system based on an Online Sequential Extreme Learning Machine (OS-ELM) for sensor faults. The system can realize online fault diagnosis and signal reconstruction without establishing a system model [14]. These latest research results are mostly combined with artificial intelligence algorithm for sensor fault diagnosis, most of them stay at the theoretical level. The complexity of the algorithm reduces the speed of diagnosis and makes it difficult to apply it in engineering practice. Besides, most of the research on sensor FTC is based on steady-state control. In the process of engine transition, because the speed and other parameters are sensitive parameters closely related to the engine performance, to improve the stability and reliability of the transition, closed-loop control is often carried out.