## 1 Introduction
However, the MPC method needs to compute optimal control online at each step, which means it is computationally expensive [16; 17]. This is also verified in the above literature. The real-time performance of the MPC method cannot be guaranteed in practice, especially when the hardware resource is poor. To deal with this drawback, the explicit MPC method is proposed to resolve the multiparametric programming problem corresponding to MPC. The EMPC method expresses the optimal solution as a piecewise affine (PWA) equation of the state space of the system, and divides the state space of the system convexly to obtain different regions, which are called state partitions by offline calculation [16]. Online calculation only needs to determine the PWA equation in the state partition according to the current system state, and calculate the corresponding feedback control rate solution through the PWA equation, which is called the location problem [17]. Therefore, online optimization is replaced with offline calculation and online parameter positioning, which improves the real-time performance of MPC and expands its application range. [PERSON] et al. [18] show the digital hardware architecture design results for that explicit MPC solutions, which means it can be implemented in a standard field programmable gate array, or an application specific integrated circuit. However, the regions for storing the explicit solution increases exponentially as the number of constraints increase. The larger the number of regions, the longer it takes to locate the parameters [19]. In order to deal with location problem, many algorithms were proposed. Most of them focus on new data structures and data searching methods, which are introduced to balance online location time and storage requirements. [PERSON] et al. [20] impose an orthogonal search tree structure on the partition to determine an approximate explicit PWA state feedback solution. The number of the regions for storing the explicit solution is reduced significantly, and the control error is bounded and small. [PERSON] et al. [21] firstly use a binary search tree (BST) to evaluate the PWA solution. Through the optimization of a location algorithm, the number of the regions for storing the explicit solution is within the acceptable range, even if the prediction horizon is large. [PERSON] et al. [22] utilize the hash tables and the associated hash functions to an aggregated point location problem that overcomes prohibitive complexity growth with the number of polyhedral regions, and propose scaling parameters to reduce the storage complexities. Considering the limits of embedded control systems, [PERSON] et al. [23] deal with a wider class of problems for which the BST method becomes prohibitive in terms of preprocessing time or memory requirements, by combining an orthogonal truncated binary search tree and lattice representation for PWA functions in a unified structure. The above studies show that the real-time performance of an explicit MPC controller is greatly improved. However, it has not been discussed how to apply a binary search tree to an explicit MPC method for aero-engine real-time control, especially for active jet noise control. Based on the above discussion, this paper designed an active jet noise controller based on explicit model predictive control. The main contributions of this paper can be summarized as follows:  
1. To calculate the engine parameters and jet noise in real time, an integrated model of turbofan engine and jet noise was established. The integrated model used the semi-empirical model to calculate the jet noise, and used the component level model of the turbofan engine to calculate the performance parameters. The relationship of parameter transmission between two models was determined. 2. Based on the integrated model of the turbofan engine and jet noise, the explicit MPC controller of active jet noise control was proposed.