一种基于凸优化的高速飞行器轨迹优化方法  

A Hypersonic Vehicle Trajectory Optimization Method Based on Convex Optimization

作　　者：顾嘉耀 贾世伟 郑天宇 钟继鸿 陈好 GU Jiayao;JIA Shiwei;ZHENG Tianyu;ZHONG Jihong;CHEN Hao(Shanghai Electro-Mechanical Engineering Institute,Shanghai 201109)

机构地区：[1]上海机电工程研究所,上海201109

出　　处：《飞控与探测》2025年第1期67-76,共10页Flight Control & Detection

摘　　要：针对基于能量管理的高速飞行器轨迹优化问题,考虑发动机工作过程对飞行状态严格的约束要求,提出一种基于凸优化的高速飞行器轨迹优化方法。即认为发动机燃油耗尽关机、飞行器动力一定的前提下,求解射程最远的优化轨迹以满足高速长远距离飞行任务需求。首先,在飞行器纵向动力学质点模型基础上进行简化处理,得到以飞行器质量为变量的四阶动力学方程,将考虑发动机工作约束的飞行器射程的最优轨迹求解问题,转化为一系列非线性规划问题;接着,将非线性规划问题转化为二阶锥规划(Second Order Cone Program,SOCP)问题,对动力学方程以及不等式约束线性化、离散化处理后,采用原对偶内点法求解,获得最优轨迹;最后,仿真验证了所提优化方法在发动机工作约束范围内,解得了射程最大的最优轨迹。Aiming at the problem of trajectory optimization of high-speed aircraft based on energy management,this paper proposes a trajectory optimization method of high-speed aircraft based on convex optimization,considering the strict constraints of the engine working process on flight state.It is considered that under the premise that the engine runs out of fuel and shuts down.The total impulse of the aircraft is certain,and the optimal trajectory with the longest range can be solved to meet the needs of hypersonic long-distance flight missions.First,based on the particle model of aircraft longitudinal dynamics,the fourth-order dynamic equation with aircraft mass as variable is obtained,and the problem of solving the optimal trajectory of aircraft range considering engine working constraints is transformed into a series of nonlinear programming problems.Second,the nonlinear programming problem is transformed into a second-order cone programming problem.After linearization and discretization of the dynamic equation and inequality constraints,the primal-dual interior point method is used to solve the problem,and the optimal trajectory is obtained.Finally,the simulation results show that the proposed optimization method is within the engine working constraints and the optimal trajectory based on the least energy is obtained.

关 键 词：凸优化 非线性规划 轨迹优化 约束条件 二阶锥规划 

分 类 号：V19[航空宇航科学与技术—人机与环境工程]