Adaptive 3-Dimensional Differential Game Guidance for Hypersonic Attack and Defense

doi:10.12382/bgxb.2022.0425

Abstract

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

CLC Number:

V448

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.

Figures/Tables 13

Fig.1 Diagram of an HGV intercepting a hypersonic target

Fig.2 Engagement geometry

Fig.3 Structure of critic neural network

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

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

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

Fig.6 Values of the Hamilton functions estimated by ADP

Fig.7 Weights of the critic neural network in ADP

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

Fig.9 Velocities of both sides under differential game guidance

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

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

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

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