## 1 Introduction  
Predictive control is a model-based advanced control technique [1]. The working principle mainly includes three modules: the predictive model, receding horizon optimization, and feedback correction. In each control interval, the MPC algorithm attempts to optimize system behaviors, computes a future manipulated variable adjustment sequence, then sends the first input to the system in an optimal order, and repeats the entire calculation in subsequent control intervals. MPC can be divided into linear MPC and nonlinear MPC. Linear MPC is an effective control strategy, widely used in the process industry. However, many systems are essentially nonlinear. Nonlinear model predictive control (NMPC) is the corresponding predictive control scheme for nonlinear systems [2]. Aircraft engines are a class of complicated aerodynamic thermodynamic systems with strong nonlinearity, systems that have a broad working range, complex working conditions, and inevitably many uncertainties such as disturbance and unmodeled dynamics of actual situations. Therefore, aircraft engines are subject to constraints during operation, and model predictive control can deal with constraints excellently. Therefore, an increasing amount of attention has been paid to the application of NMPC in aircraft engines [3; 4; 5]. Traditional NMPC is based on a nonlinear programming (NP) method to solve control law, such as the sequential quadratic programming (SQP) method [6; 7; 8], but the initial condition of an NP method is limited in its solution, and the algorithm easily falls into a local optimum. Existing intelligent algorithms such as the genetic algorithm (GA) [9], the artificial bee colony algorithm (ABC), and the particle swarm optimization algorithm (PSO) have been successfully used for many optimization problems and have achieved results far superior to those of the traditional NP method. However, they suffer from a slow convergence rate and a low computational accuracy for complex problems, and they also easily fall into a local optimum [10; 11; 12]. Therefore, it is necessary to study an optimization method with a strong searching ability, a high convergence speed, a high calculation accuracy, and a good ability to handle constraints. Some bio-heuristic optimization algorithms have been proposed in recent years, including the grey wolf algorithm [13], the whale algorithm [14], the spider monkey algorithm [15], and the polar bear algorithm [16]. The common feature of these newly bio-heuristics is that they optimize by simulating the survival or predation mechanisms of biological populations. The grey wolf optimization (GWO) algorithm is a new intelligent algorithm that was proposed in 2014. Compared with other intelligent algorithms, the GWO has a faster convergence speed and a stronger search ability in solving function optimization problems, so it has been applied to many optimization problems [17; 18; 19]. However, as a swarm intelligence algorithm, it is inevitable that it still has the risk of falling into a local optimum. Therefore, in order to ensure an optimization ability, many scholars have made improvements on the GWO. In [20], EPD (Population Dynamic Evolution Operator) was integrated into the population updating process of the GWO algorithm by combining self-organizing criticality. The search range of the wolf group in the GWO algorithm was extended to the entire solution space in each iteration process, thus increasing the probability of obtaining a global optimal solution. In [21], the population was divided into a local optimization group and a global optimization group, which increased the diversity of the population and improved the search ability. However, the global search was blind and lacked norms, which increased the complexity of the algorithm.