带有控制变量变化率约束的伪谱轨迹优化方法  

Pseudo-spectral Trajectory Optimization Method with Constraint on the Change Rate of Control Variables

作　　者：赵吉松 尚腾[2] 张金明[1] 程晓明 刘蛟龙[2] ZHAO Jisong;SHANG Teng;ZHANG Jinming;CHENG Xiaoming;LIU Jiaolong(College of Astronautics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;Beijing Aerospace Automatic Control Institute,Beijing 100854,China)

机构地区：[1]南京航空航天大学航天学院,南京210016 [2]北京航天自动控制研究所,北京100854

出　　处：《宇航学报》2022年第10期1368-1377,共10页Journal of Astronautics

基　　金：国家自然科学基金(11602107);中央高校基本科研业务费(NS2021059)。

摘　　要：基于伪谱法提出一种能够求解带有控制变量变化率约束的轨迹优化方法。首先,应用伪谱法将轨迹优化转化为非线性规划;其次,引入有限差分法将控制量变化率约束转化为相邻离散点处控制量的线性约束;然后,应用非线性规划算法求解带有线性约束的非线性规划;最后,采用带有控制量变化率约束的轨迹优化问题对方法进行了验证。仿真结果表明,此方法能够快速求解带有控制量变化率约束的轨迹优化问题,与引入控制量导数作为虚拟控制量的传统控制量变化率约束处理方法相比,此方法计算量更小,并且避免了虚拟控制量振荡问题,更容易收敛,综合效果是能够将优化耗时减少大约80%。Based on pseudo-spectral method,a trajectory optimization method with the constraint on the change rate of control variables is proposed.Firstly,the trajectory optimization problem is converted into nonlinear programming using the pseudo-spectral method.Secondly,the finite difference method is introduced to transform the constraint on the change rate of the control variables into the linear constraints of the discretized control variables at adjacent mesh points.Then,the nonlinear programming algorithm is applied to solve the nonlinear programming with linear constraints.Finally,the trajectory optimization problem with change rate constraint is used to verify the method.The simulation results show that the method can rapidly solve this kind of trajectory optimization problems.Compared with the traditional processing method that introduces the derivative of control variables as the virtual control variables,the proposed method has less computational cost,avoids the oscillation problem of virtual control quantity and is easier to converge,and the comprehensive effect is to reduce the optimization time by about 80%.

关 键 词：导弹制导 轨迹优化 伪谱法 变化率约束 

分 类 号：V412[航空宇航科学与技术—航空宇航推进理论与工程]