针对高速机动目标的三维非线性微分对策制导律
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摘要
为有效拦截高超声速飞行器,提出了一种基于预测控制的三维微分对策制导律。该制导律将高速机动目标拦截末制导过程抽象为以视线角速率和燃料消耗为性能指标的零和微分对策问题,以非线性模型预测控制为框架,采用梯度下降法实时求解决策约束型有限时域微分对策,得到最优决策。该制导律能够在满足动态系统高维非线性、机动能力和燃料消耗等要求下,实现对目标的精确拦截;在与比例导引律燃料消耗相当的情况下,具有末端弹道平直、制导精度高等优点。
To intercept hypersonic aircraft effectively,a 3-dimensional differential game-based guidance law using predictive control was proposed. The terminal interception for high-speed maneuvering target was formulated as a zero-sum differential game with line-of-sight angle rate and fuel consumption as performance index. Under the framework of nonlinear model predictive-control,the decision-constrained finite-horizon differential game was solved in real time by gradient descent algorithm,and the optimal action was obtained. The guidance law enables accurately intercepting target in compliance with highly dimensional nonlinear dynamic systems,maneuverability constraints and fuel consumption limits. With fuel consumption similar to that of proportional guidance law,the proposed guidance law has the advantages of straighter trajectory and higher guidance accuracy.
To intercept hypersonic aircraft effectively,a 3-dimensional differential game-based guidance law using predictive control was proposed. The terminal interception for high-speed maneuvering target was formulated as a zero-sum differential game with line-of-sight angle rate and fuel consumption as performance index. Under the framework of nonlinear model predictive-control,the decision-constrained finite-horizon differential game was solved in real time by gradient descent algorithm,and the optimal action was obtained. The guidance law enables accurately intercepting target in compliance with highly dimensional nonlinear dynamic systems,maneuverability constraints and fuel consumption limits. With fuel consumption similar to that of proportional guidance law,the proposed guidance law has the advantages of straighter trajectory and higher guidance accuracy.
引文
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[3]郭行,符文星,付斌,等.吸气式高超声速飞行器巡航段突防弹道规划[J].宇航学报,2017,38(3):287-295.GUO Hang,FU Wenxing,FU Bin,et al.Penetration trajectory programming for air-breathing hypersonic vehicles during the cruise phase[J].Journal of Astronautics,2017,38(3):287-295.(in Chinese)
[4]鲜勇,李少朋,雷刚,等.弹道导弹中段机动突防技术研究综述[J].飞航导弹,2015,18(9):43-46.XIAN Yong,LI Shaopeng,LEI Gang,et al.Discussion of ballistic missile defense system[J].Aerodynamic Missile Journal,2015,18(9):43-46.(in Chinese)
[5]常新杰,李言俊.空空导弹的微分对策末制导律研究[J].航空兵器,1997(1):29-34.CHANG Xinjie,LI Yanjun.Research on differential game guidance law of air-to-air missile[J].Aero Weaponry,1997(1):29-34.(in Chinese)
[6]KIM Y S,KIM T H,TAHK M J,et al.Performance analysis of pursuit-evasion game based guidance laws[C]//IEEE European Control Conference.Kos,Greece:IEEE,2007.
[7]PONTANI M,CONWAY B A.Optimal interception of evasive missile warheads:numerical solution of the differential game[J].Journal of Guidance,Control,and Dynamics,2008,31(4):1111-1122.
[8]EREN U,PRACH A,KOER B B,et al.Model predictive control in aerospace systems:current state and opportunities[J].Journal of Guidance Control,and Dynamics,2017,40(7):1541-1566.
[9]TZANNETOS G,MARANTOS P,KYRIAKOPOULOS K J,et al.A competitive differential game between an unmanned aerial and a ground vehicle using model predictive control[C]//The 24th Mediterranean Conference on Control and Automation.Athens,Greece:IEEE,2016:1053-1058.
[10]KANG S,KIM H J,TAHK M J.Aerial pursuit-evasion game using nonlinear model predictive guidance[C]//AIAA Guidance,Navigation and Control Conference.Toronto,Ontario:AIAA,2010:7880.
[11]周洋,李刚,吉阳,等.一种三维非线性免疫变结构制导律[J].弹道学报,2016,28(1):92-96.ZHOU Yang,LI Gang,JI Yang,et al.3D nonlinear immune variable-structure guidance law[J].Journal of Ballistics,2016,28(1):92-96.(in Chinese)
[12]魏鹏鑫,荆武兴,高长生.攻防对抗机动过载关系分析[J].宇航学报,2013,34(2):179-185.WEI Pengxin,JING Wuxing,GAO Changsheng.An analysis of maneuvering overloads in attack-defense confrontation[J].Journal of Astronautics,2013,34(2):179-185.(in Chinese)
[13]李登峰.微分对策及其应用[M].北京:国防工业出版社,2000:160-170.LI Dengfeng.Differential games and applications[M].Beijing:National Defense Industry Press,2000:160-170.(in Chinese)