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Optimal avoidance strategy based on nonlinear approximate analytic solution of non-cooperative differential game

Published online by Cambridge University Press:  18 September 2024

S.J. Zhao Open the ORCID record for S.J. Zhao [Opens in a new window] ,
H.R. Zhang ,
R. Lyu ,
J. Yang  and
C.C. Xue
S.J. Zhao*
Affiliation:
China Academy of Launch Vehicle Technology, Beijing, China
H.R. Zhang
Affiliation:
China Academy of Launch Vehicle Technology, Beijing, China
R. Lyu
Affiliation:
China Academy of Launch Vehicle Technology, Beijing, China
J. Yang
Affiliation:
China Academy of Launch Vehicle Technology, Beijing, China
C.C. Xue
Affiliation:
China Academy of Launch Vehicle Technology, Beijing, China
*
Corresponding author: Shenjia Zhao; Email: [email protected]
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Abstract

This study examines the pursuit-evasion game involving unmanned aerial vehicles (UAVs), with a specific focus on the scenario of N-pursuers-one-escapee. The primary objective is to develop an optimal strategy for the escapee when the pursuers possess superior capabilities. To obtain this objective, we conduct the following study. Firstly, to enhance realism, a non-cooperative differential game model is formulated, incorporating multiple motion characteristics, including aerodynamics, overloading, and imposed constraints. Secondly, the end-value performance index is subsequently converted to an integral one, simplifying the solution process of the Hamilton-Jacobi-Bellman (HJB) equation. An iterative method is utilised to determine the covariates using the Cauchy initial value problem, and its convergence and uniqueness are established. The optimal avoidance strategy is subsequently derived from the covariates. Finally, the superiority of the proposed strategy is validated through simulation experiments and compared to three advanced optimal avoidance strategies. A total of 1,000 anti-jamming simulation experiments are conducted to verify the robustness of the proposed strategy.

Keywords

aircraft evasion-pursuit gamenon-cooperative differential gameHamilton-Jacobi-Bellman equationCauchy initial value problem
Type
Research Article
Information
The Aeronautical Journal , Volume 128 , Issue 1330 , December 2024 , pp. 2906 - 2923
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Royal Aeronautical Society

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References

Weintraub, I., Pachter, M. and Garcia, E. An introduction to pursuit-evasion differential games, 2020 American Control Conference (ACC), IEEE, 2020.CrossRefGoogle Scholar
Liu, Y., Qi, N. and Wang, T. Capture condition for endo-atmospheric interceptors steered by alcs and arcs, Control Theory Technol., 2014, 12, (1), pp 56–67.CrossRefGoogle Scholar
Vrabie, D. and Lewis, F. Adaptive dynamic programming for online solution of a zero-sum differential game, J. Control Theory Appl., 2011, 9, (3), pp 353–360.CrossRefGoogle Scholar
Perelman, A., Shima, T. and Rusnak, I. Cooperative differential games strategies for active aircraft protection from a homing missile, J. Guid. Control Dyn., 2011, 34, (3), pp 761–773.CrossRefGoogle Scholar
Shaferman, V. and Shima, T.Y. A cooperative differential game for imposing a relative intercept angle, AIAA Guidance, Navigation, and Control Conference, 2017, p 1015.CrossRefGoogle Scholar
Liang, H., Li, Z., Wu, J., Zheng, Y., Chu, H. and Wang, J. Optimal guidance laws for a hypersonic multiplayer pursuit-evasion game based on a differential game strategy, Aerospace, 2022, 9, (2), p 97.CrossRefGoogle Scholar
Garcia, E., Casbeer, D.W. and Pachter, M. Design and analysis of state-feedback optimal strategies for the differential game of active defense, IEEE Trans. Autom. Control, 2018, 64, (2), pp 553–568.Google Scholar
Kang, Y., Yu, J., Dong, X. and Ren, Z. Cooperative differential games guidance laws for multiple missiles against an active defense target with multiple defenders, International Conference on Guidance, Navigation and Control, Springer, 2022, pp 4601–4610.CrossRefGoogle Scholar
Pachter, M., Garcia, E. and Casbeer, D.W. Active target defense differential game, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton), IEEE, 2014, pp 46–53.CrossRefGoogle Scholar
Zhang, H., Zhang, Y. and Zhang, P. Optimal guidance law for intercepting the active defense aircraft with terminal angle constraint, J. Phys. Conf. Ser., 2021, 1828, (1), p 012160 (15 pp).CrossRefGoogle Scholar
Li, Y. and Qi, N. Logic-based guidance law for interceptor missiles steered by aerodynamic lift and divert thruster, IEEE Trans. Control Syst. Technol., 2011, 19, (4), pp 884–890.CrossRefGoogle Scholar
Humin, L., Xu, Z., Feiyao, D. and Jiong, L.I. Finite time convergent zero-effort miss guidance law, J. Natl. Univ. Def. Technol., 2015, 37, (3), pp 136–141.Google Scholar
Liwei, Z., Wuxing, J. and Jianying, Z. [IEEE 2007 Chinese Control Conference - zhangjiajie, china (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - Zero Effort Miss Formulation for Longer Range Targeting, 2006, pp 414–417.CrossRefGoogle Scholar
Su Shan, B.Y.L.Y., Yongjie, X. and Yongzhi, S. Research on cooperative countermeasure guiding law methods for differential countermeasures, Air Space Def., 2022, 002, pp 58–64.Google Scholar
Weintraub, I., Garcia, E. and Pachter, M. Optimal guidance strategy for the defense of a non-manoeuvrable target in 3-dimensions, IET Control Theory Appl., 2020, 14, (11), pp 1531–1538.CrossRefGoogle Scholar
Yan, R., Shi, Z. and Zhong, Y. Reach-avoid games with two defenders and one attacker: An analytical approach, IEEE Trans. Cybern., 2018, 49, (3), pp 1035–1046.CrossRefGoogle ScholarPubMed
Bakolas, E. and Tsiotras, P. Optimal pursuit of moving targets using dynamic voronoi diagrams, IEEE Conference on Decision and Control, Atlanta, GA, IEEE, 2010, pp 7431–7436.CrossRefGoogle Scholar
Zhou, Z., Zhang, W., Ding, J., Huang, H., Stipanovicć, D.M. and Tomlin, C.J. Cooperative pursuit with voronoi partitions, Automatica, 2016, 72, pp 64–72.CrossRefGoogle Scholar
Chipade, V.S. and Panagou, D. Multiplayer target-attacker-defender differential game: Pairing allocations and control strategies for guaranteed intercept, AIAA Scitech 2019 Forum, 2019, p 0658.CrossRefGoogle Scholar
Coon, M. and Panagou, D. Control strategies for multiplayer target-attacker-defender differential games with double integrator dynamics, 2017 IEEE 56th Annual Conference on Decision and Control (CDC), IEEE, 2017, pp 1496–1502.CrossRefGoogle Scholar
Makkapati, V.R. and Tsiotras, P. Optimal evading strategies and task allocation in multi-player pursuit–evasion problems, Dyn. Games Appl., 2019, 9, pp 1168–1187.CrossRefGoogle Scholar
Ninyu, W., Shan, S., Naigang, C., Yongzhi, S. and Shengli, X. Multi-vehicle cooperative optimal allocation method based on differential countermeasures, Tactical Missile Technol., 2021, 6, pp 130–138.Google Scholar
Wei, X. and Yang, J. Optimal strategies for multiple unmanned aerial vehicles in a pursuit/evasion differential game, J. Guid. Control Dyn. A Publ. Am. Inst. Aeronaut. Astronaut. Devoted Technol. Dyn. Control, 2018, 41, (8), pp1798–1805.Google Scholar
Chen, S. and Li, X. Viscous solutions of the Hamilton-Jacobi equation discounted on a non-tight space, J. East China Normal Univ. Nat. Sci. Ed., 2022, (002).Google Scholar
Kawohl, B. and Kutev, N. A study on gradient blow up for viscosity solutions of fully nonlinear, uniformly elliptic equations, Acta Math. Sci., 2012, 32, (1), pp 15–40.CrossRefGoogle Scholar
Wang, K. Exponential convergence to time-periodic viscosity solutions in time-periodic hamilton-jacobi equations, Chin. Ann. Math. Ser. B, 2018, 39, (1), pp 69–82.CrossRefGoogle Scholar
Li, X. and Yan, J. Weak kam theory and Hamilton-Jacobi equations, Sci. Sinica Phys. Mech. Astron., 2014, 44, (12), p 1286.CrossRefGoogle Scholar
Hamadène, S. Mixed zero-sum stochastic differential game and american game options, SIAM J. Control Optim., 2006, 45, (2), pp 496–518.CrossRefGoogle Scholar
Chen, C., Wang, Y.-N. and Yan, J. Convergence of the viscosity solution of non-autonomous hamilton-jacobi equations, Sci. China Math., 2021, 64, pp 1789–1800.CrossRefGoogle Scholar
Xing, G. Research on hypersonic vehicle game breaching strategy, PhD dissertation, Northwestern Polytechnical University.Google Scholar
Bressan, A. and Shen, W. Small bv solutions of hyperbolic noncooperative differential games, SIAM J. Control Optim., 2004, 43, (1), pp 194–215.CrossRefGoogle Scholar
Youness, E.A., Megahed, A.E.-M.A., Eladdad, E.E. and Madkour, H.F. Min-max differential game with partial differential equation, AIMS Math., 2022, 7, (8), pp 13777–13789.CrossRefGoogle Scholar
Makkapati, V.R., Sun, W. and Tsiotras, P. Pursuit-evasion problems involving two pursuers and one evader, 2018 AIAA Guidance, Navigation, and Control Conference, 2018, p 2107.CrossRefGoogle Scholar
Zheng-Ping, L., Hui-Cai, L., Zhi-Qiang, W., Kai-Feng, H. and Ze-Xuan, Z. Dynamic multi-objective evolutionary algorithm with adaptive change response, Acta Automatica Sinica, 2023, 49, (8), pp 1688–1706.Google Scholar
Zhou Hongyu, S.Y.Z.Y.C.N. and Xiaogang, W. Cooperative trajectory planning for aircraft based on improved particle swarm algorithm, J. Automat., 2022, 48, pp 2670–2676.Google Scholar