带有落角约束的间接Gauss伪谱最优制导律

doi:10.3969/j.issn.1000-1093.2015.07.008

兵工学报 ›› 2015, Vol. 36 ›› Issue (7): 1203-1212.doi: 10.3969/j.issn.1000-1093.2015.07.008

带有落角约束的间接Gauss伪谱最优制导律

陈琦，王中原，常思江

（南京理工大学能源与动力工程学院，江苏南京 210094）

收稿日期:2014-09-09 修回日期:2014-09-09 上线日期:2015-09-21
通讯作者: 陈琦 E-mail:qiychan@126.com
作者简介:陈琦(1989—)，男，博士研究生
基金资助:
国家自然科学基金项目（11402117）

Optimal Guidance Law with Impact Angle Constraints Based on Indirect Gauss Pseudospectral Method

CHEN Qi， WANG Zhong-yuan， CHANG Si-jiang

（School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China）

Received:2014-09-09 Revised:2014-09-09 Online:2015-09-21
Contact: CHEN Qi E-mail:qiychan@126.com

摘要/Abstract

摘要： 针对带有落角约束的末制导问题，提出了一种基于极小值原理和Gauss伪谱法的最优制导律。以期望落角方向为坐标轴定义了落角坐标系，并在其中建立了线性化的导引运动关系方程。将控制系统简化为1阶惯性环节，利用极小值原理得到正则方程，然后引入Gauss伪谱法进行离散，将其转化为代数方程，结合边界条件，推导出最优制导律的解析表达式,无需任何积分过程，避免了求解黎卡提微分方程。仿真结果表明，所提出的算法运算量小，计算效率高，同时也能方便地求解出复杂加权矩阵下的最优制导律，能够在满足落角约束的条件下更快地收敛到落角参考线，并且具有更小的末端需用过载。

关键词: 兵器科学与技术, 落角约束, 最优控制, 末制导律, 极小值原理, 间接Gauss伪谱法

Abstract: A novel optimal guidance law is proposed for the terminal guidance with impact angle constraints by using the combination of the minimal principle and Gauss pseudospectral method. An impact angle coordinate system is defined with an coordinate axis in the direction of the desired impact angle, and the linear engagement kinematics is established using this coordinate system. The control system of missile is simplified into a first-order inertial system. The canonical equation is obtained via the minimal principle, and then translated into a set of algebraic equations by employing the Gauss pseudospectral method. According to the boundary conditions, an analytical solution is finally derived for the optimal guidance law with impact angle constraints without any integral process or solving the Riccati differential equation. Numerical simulations show that the proposed guidance law ensures the much fast convergence of impact angle to the reference line, and has smaller required terminal acceleration compared with other guidance laws. In addition, the proposed guidance law can easily tackle with the guidance problem with complex weighting matrices.

Key words: ordnance science and technology, impact angle constraint, optimal control, terminal guidance, minimal principle, indirect Gauss pseudospectral method

中图分类号:

TJ765.3

陈琦，王中原，常思江. 带有落角约束的间接Gauss伪谱最优制导律[J]. 兵工学报, 2015, 36(7): 1203-1212.

CHEN Qi， WANG Zhong-yuan， CHANG Si-jiang. Optimal Guidance Law with Impact Angle Constraints Based on Indirect Gauss Pseudospectral Method[J]. Acta Armamentarii, 2015, 36(7): 1203-1212.

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带有落角约束的间接Gauss伪谱最优制导律

Optimal Guidance Law with Impact Angle Constraints Based on Indirect Gauss Pseudospectral Method

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