基于伪谱凸优化和L1罚函数的弹道规划方法研究  

Research on Trajectory Programming Method Based on Pseudo-spectral Convex Optimization and L1 Penalty Function

作　　者：王庆海 陈琦[1] 王中原[1] 尹秋霖 WANG Qinghai;CHEN Qi;WANG Zhongyuan;YIN Qiulin(School of Energy and Power Engineering,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学能源与动力工程学院,江苏南京210094

出　　处：《弹道学报》2022年第1期22-30,共9页Journal of Ballistics

基　　金：江苏省自然科学基金项目(BK20200498)。

摘　　要：传统L1惩罚序列凸规划算法(LPSCP)在进行制导炮弹弹道规划时,线性近似误差大,导致目标函数曲线震颤,难以收敛到最优解。针对此问题提出了一种改进的L1惩罚序列凸规划算法(ILPSCP)。ILPSCP算法引入指数衰减的相对信赖域宽度和带上界的惩罚系数,消除了目标函数的震颤。以一般化控制能量最优轨迹规划模型为研究对象,利用Radau伪谱法离散连续变量,线性凸化非线性动态方程,建立标准凸优化模型。以制导炮弹纵向平面内滑翔弹道模型为仿真实例,分别采用传统的LPSCP算法、提出的ILPSCP算法和非线性最优化通用工具箱GPOPS23种方法进行仿真对比。结果表明:ILPSCP算法成功解决了传统LPSCP算法震颤和不稳定等问题;同时ILPSCP算法的仿真结果与GPOPS2的仿真结果高度重合,证明了提出的算法对求解复杂弹道规划问题的有效性。The traditional L1 penalty sequential convex programming algorithm(LPSCP)has a large linear approximation error in trajectory programming of guided projectiles,which leads to the trembling of the objective function curve,and it is difficult to converge to the optimal solution.Aiming at this problem,an improved L1 penalty sequential convex programming algorithm(ILPSCP)was proposed.The ILPSCP algorithm introduces the relative trust region width of exponential attenuation and the penalty coefficient with upper bound to eliminate the tremor of the objective function.Taking the generalized control energy optimal trajectory programming model as the research object,the Radau pseudo-spectral method was used to discretize the continuous variables and linearly convex the nonlinear dynamic equation to establish the standard convex optimization model.Taking the gliding trajectory model of the guided projectile in the longitudinal plane as an example,the traditional LPSCP algorithm,the proposed ILPSCP algorithm and the general nonlinear optimization toolbox GPOPS2 were used to simulate and compare.The simulation results show that the ILPSCP algorithm successfully solves the problems of chatter and instability of the traditional LPSCP algorithm.At the same time,the simulation results of the ILPSCP algorithm are highly consistent with those of the GPOPS2,which proves the effectiveness of the proposed algorithm in solving complex trajectory programming problems.

关 键 词：弹道规划 凸优化 Radau伪谱法 L1罚函数 

分 类 号：TJ303.4[兵器科学与技术—火炮、自动武器与弹药工程]