| 引用本文: | 雷虎民,李宁波,周觐,等.临近空间拦截弹最优弹道跟踪制导律.[J].国防科技大学学报,2018,40(1):24-31.[点击复制] |
| LEI Humin,LI Ningbo,ZHOU Jin,et al.Optimal trajectory tracking guidance law for near space interceptor[J].Journal of National University of Defense Technology,2018,40(1):24-31[点击复制] |
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| 临近空间拦截弹最优弹道跟踪制导律 |
| 雷虎民1, 李宁波1,2, 周觐1, 邵雷1, 王斌1 |
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(1. 空军工程大学 防空反导学院， 陕西 西安 710051;2.
2. 西安交通大学 电子信息与工程学院， 陕西 西安 710049)
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| 摘要: |
| 针对拦截临近空间高超声速飞行器的弹道跟踪过程，基于线性二次型调节器理论和高斯伪谱法设计一种跟踪制导律。为了对标称弹道进行精确跟踪，考虑线性二次型跟踪问题，应用最优控制理论推导最优解的充要条件，得到带时变增益的线性状态反馈控制量的表达式；基于高斯伪谱法，在离散的勒让德-高斯点上利用标称弹道数据计算差分矩阵和系数矩阵，求得状态扰动反馈控制律。仿真结果表明，与基于求解矩阵黎卡提方程的方法相比，该方法选取较少的节点即可获得高精度的反馈控制量，且运算效率大幅提高，满足在线实施要求。 |
| 关键词: 临近空间 拦截 弹道跟踪 最优控制 高斯伪谱法 |
| DOI：10.11887/j.cn.201801004 |
| 投稿日期：2016-06-22 |
| 基金项目:国家自然科学基金资助项目（61573374，61503408）；航空科学基金资助项目（20150196006） |
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| Optimal trajectory tracking guidance law for near space interceptor |
| LEI Humin1, LI Ningbo1,2, ZHOU Jin1, SHAO Lei1, WANG Bin1 |
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(1. Air and Missile Defense College, Air Force Engineering University, Xi′an 710051, China;2.
2. School of Electronic and Information Engineering, Xi′an Jiaotong University, Xi′an 710049, China)
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| Abstract: |
| In allusion to the trajectory tracking process of interception against hypersonic targets in near space, a novel tracking guidance law based on linear quadratic regulator theory and Gauss pseudospectral method was designed. In order to track the nominal trajectory accurately, the linear quadratic tracking problem was considered, while the sufficient and necessary conditions for optimal solutions were deduced with the optimal control theory to acquire the expression of linear state feedback control variables. Based on Gauss pseudospectral method, the time-varying difference matrixes and coefficient matrixes were calculated by using the information of the nominal trajectory on the Legendre-Gauss points to obtain the state disturbances feedback control law. Simulation results show that, compared with the method by solving Riccati equation, this method can obtain the feedback control variables with high accuracy and computation efficiency by less nodes and satisfy the requirement of on-line implementation. |
| Keywords: near space interception trajectory tracking optimal control Gauss pseudospectral method |
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