高超声速攻防博弈自适应微分对策三维制导

doi:10.12382/bgxb.2022.0425

摘要/Abstract

摘要：

针对高超声速拦截器精确打击高超声速机动目标的攻防博弈制导问题,提出一种基于自适应动态规划(ADP)的微分对策三维制导律。将高超声速攻防博弈三维制导问题分解在纵向平面和侧向平面分别进行制导律设计。在纵向平面内建立高超声速二人零和微分博弈问题模型,设计非二次型代价函数以满足控制约束,并通过Hamilton-Jacobi-Isaacs(HJI)方程得到高超声速拦截器和目标的微分博弈最优策略。由于HJI方程无法直接得到解析解,利用ADP方法,引入评价神经网络逼近最优代价函数,进而得到攻防博弈双方的倾侧角幅值最优指令。在侧向平面内建立平行接近倾侧角反转逻辑实现侧向制导。仿真结果表明,该制导律能够在攻防博弈双方的控制约束内,实现高超声速拦截器在高超声速目标机动躲避拦截情况下的精确打击。

关键词: 高超声速, 攻防博弈, 自适应动态规划, 平行接近

Abstract:

A 3-dimensional (3D) differential game guidance law based on adaptive dynamic programming (ADP) is proposed to solve the attack and defense problem in hypersonic interceptors attacking hypersonic maneuvering targets. Firstly, the 3D guidance problem in hypersonic attack and defense game is decomposed into the longitudinal plane and lateral plane. Then, the problem model of a hypersonic two-person zero-sum differential game is established in the longitudinal plane. A non-quadratic cost function is designed to satisfy the control constraints. The optimal differential game strategy of the hypersonic interceptor and the target is obtained by the Hamilton-Jacobi-Isaacs (HJI) equation. Since the HJI equation can not be solved analytically, the ADP method is used and a critic neural network is introduced to approximate the optimal cost function to obtain the bank angle amplitudes of both sides. Finally, the lateral guidance is realized by establishing the bank angle reversal logic in the lateral plane by the parallel approach. The simulation results show that the guidance law can achieve precision strike by a hypersonic interceptor under the condition of a maneuvering hypersonic target avoiding interception within the control constraints of both sides of the attack and defense game.

Key words: hypersonic velocity, attack and defense, adaptive dynamic programming, parallel approach

中图分类号:

V448

王子瑶, 唐胜景, 郭杰, 阎宏磊, 葛健豪. 高超声速攻防博弈自适应微分对策三维制导[J]. 兵工学报, 2023, 44(8): 2342-2353.

WANG Ziyao, TANG Shengjing, GUO Jie, YAN Honglei, GE Jianhao. Adaptive 3-Dimensional Differential Game Guidance for Hypersonic Attack and Defense[J]. Acta Armamentarii, 2023, 44(8): 2342-2353.

图/表 13

图1 HGV拦截高超声速目标的作战流程示意图

Fig.1 Diagram of an HGV intercepting a hypersonic target

图2 攻防博弈几何关系

Fig.2 Engagement geometry

图3 评价神经网络结构图

Fig.3 Structure of critic neural network

表1 攻防博弈双方的初始状态

Table 1 Initial states of both sides of the game

飞行器	x/km	高度/ km	速度/ (m·s^-1)	航迹角/ (°)	航向角/ (°)
拦截器	0	35	3000	-1	90
任务1目标	500	30	2200	0	-90
任务2目标	500	30	2200	-0.5	-90
任务3目标	500	30	2200	-0.5	-80

图4 攻防博弈双方的三维轨迹

Fig.4 3D trajectories of both sides of the game

图5 攻防博弈双方的纵向法向加速度

Fig.5 Longitudinal normal accelerations of both sides of the game

图6 ADP算法估计的Hamilton函数值

Fig.6 Values of the Hamilton functions estimated by ADP

图7 ADP算法评价神经网络权值

Fig.7 Weights of the critic neural network in ADP

图8 微分对策制导下攻防博弈双方的相对关系

Fig.8 Relative relation between both sides under differential game guidance

图9 微分对策制导下攻防博弈双方的速度

Fig.9 Velocities of both sides under differential game guidance

图10 微分对策制导下攻防博弈双方的航迹角

Fig.10 Flight path angles of both sides under differential game guidance

图11 微分对策制导下攻防博弈双方的航向角

Fig.11 Heading angles of both sides under differential game guidance

图12 微分对策制导下攻防博弈双方的倾侧角

Fig.12 Bank angles of both sides under differential game guidance

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