## 1 Introduction  
Jet noise is the main noise source of jet aircraft. It is caused by the strong turbulent pulsation formed by the rapid mixing of the high-speed air jet from the nozzle and the surrounding medium. Relevant government agencies documents of various countries, such as the Federal Aviation Regulations of the United States [1], aircraft type and airworthiness noise certification regulations of the CAAC [2], aircraft noise environment standards around airports of the State Environmental Protection Administration and so on, have made detailed restrictions on aircraft noise [3]. Aircraft noise reduction, especially jet noise reduction technology, has become an important competitive bargaining chip for the development of large passenger aircraft in various countries [4]. At present, most of the jet noise reduction technologies used in aero-engines are passive noise control technologies, which are mainly achieved by increasing the bypass ratio, and adopting optimized nozzles with special shapes (such as lobe-shaped and saw-tooth-shaped nozzles). Due to the limitation of the engine installation size, the bypass ratio lacks the room for improvement, and the noise reduction potential is limited. When leaving the design point, the noise reduction effect is reduced, and there is a negative impact on the engine's thrust and other performance parameters. In recent years, some progress was made in the active control of jet noise [5]. Micro jet technology reduces jet noise by injecting air or water into the tail jet flow field. In 1958, [PERSON] et al. [6] in the Langley Research Center in the United States carried out a water jet noise reduction test. [PERSON] et al. [7] carry out micro-jet noise reduction for core and bypass nozzles at the same time. The overall noise level is reduced by 1.6 dB, and the perceived sound pressure level is reduced by 1.0 dB. [PERSON] et al. [8] conduct part of a jet noise control experiment using the model test method. The guide blade technology changes the condition of the bypass jet flow field, shields the strong noise generated by the central gas in a specific direction, and reduces the noise radiation in that direction. This method was first proposed in 2004. [PERSON] et al. [9] verify its effectiveness with experiments, which reduce the peak overall sound pressure level by 8 dB. However, all the above methods actively control jet noise, but also affect the thrust and stability performance of the engine. Therefore, it is necessary to comprehensively consider the noise reduction and performance requirements, and carry out multivariable control for the practical application. The active jet noise control needs to solve a multivariable control problem [10]. In the closed-loop control structure, the relationship between the speed control loop and the jet noise control loop is strongly coupled, and many constraints need to be considered during the control process. Model predictive control (MPC) is an optimal control method that treats constraints in an efficient way [11]. It has the advantages of prediction and constraint handling, where prediction allows the future dynamics of the system to be considered, and constraint handling capabilities make the output smoother. MPC was successfully applied in the control of an aero-engine. [PERSON] et al. [12] investigate the feasibility of constrained nonlinear MPC with state estimation, and test this output feedback controller on a high-fidelity turbojet aircraft engine model. [PERSON] et al. [13] propose a novel nonlinear MPC method for aero-engine direct thrust control. The deep neural network is designed as a predictive model, which improves the control accuracy. [PERSON] et al. [14] combine a hybrid grey wolf optimizer with a nonlinear MPC method to deal with control constraints and the performance optimization requirements in aircraft engines. [PERSON] et al. [15] propose a wide-range model predictive controller that controls the engine over a wide range within the flight envelope.