## 1 Introduction  
Trajectory correction projectiles have gained significant attention both domestically and abroad as a crucial approach for achieving low-cost precision upgrades to traditional standard artillery shells [1]. The main types of trajectory correction projectiles include drag increasing correction projectiles, pulse correction projectiles [2, 3], canard correction projectiles [4], and metamorphic center correction projectiles. These projectiles offer several advantages, such as achieving long-range suppression, enhancing shooting accuracy, efficiently destroying targets, and reducing collateral damage [5]. Modular, low-cost trajectory correction mechanisms can help in maximizing the utilization of the existing inventory of standard ammunition while satisfying the necessary requirements for precision targeting. By utilizing simple detection and control units, these mechanisms can considerably reduce costs while still achieving the desired precision. Currently, both domestic and international scholars primarily focus on the research of dynamic modeling [6], aerodynamic shape, ballistics optimization design [7, 8, 9, 10], and control strategies [11] pertaining to two-dimensional trajectory correction projectiles. Pulse trajectory correction projectiles, in comparison to other correction projectile types, offer several advantages, including shorter response time, streamlined and efficient control, and reduced cost. However, due to the limited design space and various engineering constraints involved in the modification of standardized ammunition, the corrective mechanisms have limited capacity for improvement. As a result, the current trajectory correction projectile with lateral pulses has limited corrective ability and efficiency. Furthermore, given that pulse correction projectiles generally lack attitude stability control systems, it becomes increasingly crucial to enhance the tactical performance of the projectile while ensuring optimal flight stability. Hence, selecting appropriate modeling and design methods is of paramount importance to establish the mapping relationship between design variables and to target performance efficiently and accurately. This will help in reducing the design cycle, enhancing the robustness of the design solution, and ensuring that the pulse-controlled correction projectile achieves the desired correction capability while maintaining stable flight. The comprehensive optimization of aerodynamic layout and external ballistics design has been primarily focused on unguided projectiles in both domestic and international research. Only a few studies have been conducted on guided projectiles, with most of them focusing on canard-controlled trajectory correction projectiles. [PERSON] [12] and [PERSON] [13; 14] are among the researchers who have studied the comprehensive optimization of aerodynamic layout and controlled trajectory for canard-controlled correction projectiles. They have utilized engineering algorithms to efficiently obtain the aerodynamic parameters of the projectile, addressing the issue of high computational costs associated with aerodynamic calculations during the design phase. However, neither of them has considered the issue of maintaining stable performance of the design results when there are small fluctuations in aerodynamic coefficients due to the lack of precision in engineering algorithms during the design process. Previous research on pulse-controlled correction projectiles has predominantly concentrated on optimizing the local parameters of the pulse correction mechanism. However, optimizing solely the local parameters of the correction mechanism cannot guarantee optimal overall performance of the ballistic [15; 16]. In references [4; 5], the parameters of the pulse correction mechanism were used as design variables, and particle swarm optimization and ant colony optimization algorithms were employed, respectively, to minimize energy consumption and maximize the lateral correction capability for the controlled projectile trajectory design.