A method for Designing a Guidance Law Utilizing Linear Quadratic Forms based on Differential Games in 3-Dimensional Space

DOI: https://doi.org/10.62517/jiem.202403214

Author(s)

Baiming Liu*, Xiaoggang Song, Guang Hu, Qiwen Fang

Affiliation(s)

Technical Center, Guizhou Aerospace Nanhai Science & Technology Co., Ltd., Zunyi, Guizhou, China *Corresponding Author.

Abstract

Consider a T-A-D game scenario in space: the target strives to evade the attacker, the defender intercepts the target, and the attacker must both avoid the target's counterattack and attempt to hit the target. It is assumed that all entities are intelligent, anticipating the next state of their adversaries and making the most suitable maneuvering strategy based on this prediction. This paper presents a 3-dimensional linear-quadratic differential game guidance law for target-attacker-defender scenarios, which is more intelligent than traditional guidance laws and is suitable for future intelligent environments.

Keywords

Differential Game; Linear-Quadratic; Target-Attacker-Defender

References

[1]. Isaacs, R., Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization[J]. Physics Bulletin, 1966. 2(17): 60. [2]. Pachter, M. and Y. Yavin, One pursuer and two evaders on the line: A stochastic pursuit-evasion differential game[J]. Journal of optimization theory and applications, 1983. 39(4): 513-539. [3]. Turetsky, V. and J. Shinar, Missile guidance laws based on pursuit–evasion game formulations[J]. Automatica, 2003. 39(4): 607-618. [4]. Weintraub, I.E., M. Pachter and E. Garcia, An Introduction to Pursuit-evasion Differential Games. 2020: Denver, CO, USA. 1049-1066. [5]. Cockayne, E., Plane Pursuit with Curvature Constraints Author(s): Ernest Cockayne Source: SIAM Journal on Applied Mathematics[J], 1967. 15(6):1511-1516. [6]. Shinar, J. and S. Gutman, 3-Dimensional Optimal Pursuit and Evasion with Bounded Controls[J]. IEEE Transactions on Automatic Control, 1980. 25(3): 492-496. [7]. Moritz, K., R. Polis and K.H. Well, Pursuit-evasion in medium-range air-combat scenarios[J]. Computers & mathematics with applications (1987), 1987. 13(1): 167-180. [8]. Green, A., J. Shinar and M. Guelman, Game Optimal Guidance Law Synthesis for Short-Range Missiles[J]. Journal of Guidance Control and Dynamics, 1992. 15(1): 191-197. [9]. Shinar, J. and G. Silberman, A discrete dynamic game modelling anti-missile defense scenarios[J]. Dynamics and control, 1995. 5(1): 55-67. [10]. Hayoun, S.Y., M. Weiss and T. Shima, A Mixed L-2/L-infinity Differential Game Approach to Pursuit-Evasion Guidance[J]. IEEE Transactions on Aerospace and Electronic Systems, 2016. 52(6): 2775-2788. [11]. Perelman, A., T. Shima and I. Rusnak, Cooperative Differential Games Strategies for Active Aircraft Protection from a Homing Missile[J]. Journal of Guidance Control and Dynamics, 2011. 34(3): 761-773. [12]. Garcia, E., D.W. Casbeer and M. Pachter, Cooperative Strategies for Optimal Aircraft Defense from an Attacking Missile[J]. Journal of guidance, control, and dynamics, 2015. 38(8): 1510-1520. [13]. Kothari, M., J. Manathara and I. Postlethwaite, Cooperative Multiple Pursuers against a Single Evader[J]. Journal of Intelligent & Robotic Systems, 2017. 86(3-4): 551-567. [14]. Hayoun, S.Y. and T. Shima, A Two-on-One Linear Pursuit-Evasion Game with Bounded Controls[J]. Journal of Optimization Theory and Applications, 2017. 174(3): 837-857. [15]. Su, W., K. Li and L. Chen, Coverage-based three-dimensional cooperative guidance strategy against highly maneuvering target[J]. Aerospace Science and Technology, 2019. 85: 556-566.