过载和攻击时间约束下的非线性最优制导方法

doi:10.12305/j.issn.1001-506X.2024.02.28

摘要/Abstract

摘要：

考虑导弹过载受限条件下, 对以期望时间为攻击目标的非线性最优制导问题进行了研究。首先, 建立了非线性最优制导问题的理论模型, 基于庞特里亚金极大值原理和饱和函数方法建立了最优轨迹的最优性条件。其次, 根据最优性条件和哈密尔顿轨迹参数化方法, 建立了最优轨迹的参数化微分方程组, 使得通过数值积分即可生成从飞行状态到最优制导指令映射关系的数据集。然后, 通过前馈神经网络对上述映射关系进行近似, 实现了非线性最优制导指令的毫秒量级实时生成。最后, 通过数值仿真验证了所提非线性最优制导指令生成方法的有效性。

关键词: 过载约束, 攻击时间控制, 非线性最优制导, 哈密尔顿轨迹参数化, 前馈神经网络

Abstract:

This paper is concerned with devising the nonlinear optimal guidance for overload-constrained interceptor to hit a target at a desired impact time. Firstly, the theoretical model for the nonlinear optimal guidance problem is established, and optimality conditions for the optimal trajectory are derived in virtue of Pontryagin's maximum principle and saturation function method. Secondly, by embedding the optimality conditions into a parameterized family of Hamiltonian trajectories, a parameterized set of differential equation for optimal trajectories is formulated, which allows one to use a simple numerical integration to generate the dataset of the mapping from the flight state to the optimal guidance command. Then, a feedforward neural network is trained by the dataset to approximate the mapping from flight state to the optimal guidance command. As a consequence, the nonlinear optimal guidance command can be generated by the trained neural network within milliseconds. Finally, numerical simulations are performed to demonstrate and verify the effectiveness of the proposed nonlinear optimal guidance law.

Key words: overload constraints, impact time control, nonlinear optimal guidance, parameterization of Hamiltonian trajectories, feedforward neural network

中图分类号:

V448.2

王坤, 段欣然, 陈征, 黎军. 过载和攻击时间约束下的非线性最优制导方法[J]. 系统工程与电子技术, 2024, 46(2): 649-657.

Kun WANG, Xinran DUAN, Zheng CHEN, Jun LI. Nonlinear optimal guidance method with constraints on overload and impact time[J]. Systems Engineering and Electronics, 2024, 46(2): 649-657.

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导弹编号	初始位置/m	初始速度方向角/(°)
1	(-5 000, 5 000)	-90
2	(-4 000, -1 000)	-110
3	(9 500, 0)	170

导弹编号	OTNOG	打靶法
1	5 368.717 5	5 367.365 8
2	11 714.948 4	11 711.977 1
3	1 114.097 9	2 191.015 3

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[2]	吴放, 常思江, 陈升富. 基于终端滑模理论的攻击时间控制制导律[J]. 系统工程与电子技术, 2019, 41(10): 2334-2342.