前置追踪拦截方式的拦截器变结构制导律研究
|
摘要
动能拦截器是为了对付战术导弹而发展起来的一种防空武器,多数采用红外成像寻的探测技术。在大气层内作战时,由于高速飞行会在拦截器头罩周围产生气动加热现象,从而会对红外成像制导系统带来严重的探测干扰。为了降低这种探测干扰的影响,本文针对末制导阶段拦截器采用前置追踪拦截方式进行研究,设计了相应的非线性滑模制导律和跟踪微分器,并进行了全航迹拦截运动仿真。
前置追踪拦截方式是近几年来发展起来的一种导弹拦截技术,该技术是将拦截器导引到目标轨道的前方并和目标沿相同方向飞行,从而在目标轨道的前方拦截目标。在进行了运动分析和相应的模型简化的基础上,根据古典力学理论推导了前置追踪拦截方式拦截器和目标导弹的运动方程,建立了前置追踪拦截的数学模型。同时根据前置追踪拦截方式的工作原理,建立了拦截器前置追踪拦截方式的制导方程,并且通过对拦截条件的分析,给出了满足拦截条件的参数选择和初始条件。
由于弹体气动系数变化、目标机动及外界干扰等因素的影响,拦截器和目标的三维拦截运动方程存在着复杂的非线性关系和不确定性。由于滑模变结构控制具有对干扰不敏感的特点,本文根据李亚普诺夫稳定性理论,设计了一种在有限时间内收敛的非线性变结构控制算法。同时在目标加速度未知的情况下,采用不确定性边界的自适应估计方法,设计了一种非线性自适应算法。针对所建立的前置追踪拦截运动方程,给出了有限时间收敛的非线性变结构制导律。数字仿真结果验证了非线性变结构制导律的有效性。
由微分包含和齐次性理论建立起来的高阶滑模变结构控制能够有效地降低普通变结构控制的抖振现象,实现系统的连续控制,同时保持滑模控制对干扰具有鲁棒性的优点。文中以二阶滑模控制为例设计了一种具有强鲁棒性的二阶滑模控制算法。同时采用一种微分观测器对目标加速度进行观测估计,得到了一种平滑的二阶滑模控制器,从而有效地消除了二阶滑模控制中不确定项的影响。结合前置追踪拦截的拦截器和目标的运动模型设计了前置追踪拦截的二阶滑模制导律,仿真结果进一步验证了二阶滑模制导律的有效性和优越性。
为了实现前置追踪拦截过程中的视线角和视线角速度的跟踪观测,本文对跟踪微分器进行了设计。非线性滑模控制是跟踪微分器设计的一个重要方法,尤其是高阶滑模具有抖振弱、强鲁棒性等特点而得到了广泛应用。为了提高跟踪微分器的鲁棒性,本文在深入分析非线性滑模跟踪微分器的基础上,利用李亚普诺夫稳定性定理提出了一种二阶滑模非线性跟踪微分器,并在此基础上进一步提出了降低了二阶滑模跟踪微分器微分输出抖动的方法。该跟踪微分器综合了线性跟踪微分器和非线性跟踪微分器的优点,可实现任意信号的跟踪和微分,并且结构简单、易于实现。
拦截器的姿态控制系统是一个多输入多输出的非线性系统,文中对拦截器的姿态控制方法进行了研究,针对利用喷气控制的拦截器设计了一种姿态稳定的变结构控制算法。由于描述导弹的空间运动方程组由动力学方程、运动学方程、质量变化方程、几何方程和控制关系方程等组成。因此,本文在导弹刚体运动模型、空气动力、质量变化、目标运动以及轨控和姿控发动机开关控制的分析基础之上,采用非线性变结构制导律和变结构姿态控制算法,根据导弹的实际运行情况进行了前置追踪拦截方式的全航迹拦截数字仿真,从而验证了拦截运动模型、制导律和姿态控制算法的正确性。
KKV(Kinetic Kill Vehicle) is a general interceptor used to intercept the tactic ballistic missile, and infrared sensor is applied to detect the target. To reduce the perturbation of interceptor detection induced by aerodynamic heating which is brought by high speed of the interceptor at the endgame guidance stage at atmosphere, a novel interception method, head pursuit interception is provided in this paper. Based on this advanced interception technology, the corresponing guidance law and tracking differentiator are studied using Lyapunov stability theory. The whole trjectory simulation is performed in the end.
Head pursuit interception is a new missile interception technology which has been developped recently. For head pursuit interception, the interceptor is guided ahead of the target along the target’s flight trajectory, so that the interceptor and the target fly in the same direction. The three-dimensional kinematics model is presented considering the motion of the interceptor and the target based on simplified interception model. According to the performance of head pursuit interception, the head pursuit guidance model is founded and the condition of head pursuit interception is discussed, at the same time the parameters and initial conditions for this kind of interception are provided.
There are many uncertainties for the guidance and control of missile including aerodynamics, target maneuvering and outer disturbance. Three-dimensional head pursuit interception model is a nonlinear and uncertain system, and variable structure control method has the character of robustness for system diturbances. So based on Lyapunov stability theory a nonlinear finite-time stability variable structure control guidance law is designed considering the unknown accelerations of the target, which can satisfy the requirement of head pursuit interception. At the same time, an adaptive variable structure control guidance law is presented to eliminate the effect of uncertain item using the adaptive uncertain boundary method.
High-order sliding mode control method is introduced according to differential inclusions and homogeneity theory. The main advantage of high-order sliding mode is being able to reduce the control discontinuity of sliding mode control while keeping the advantage of the sliding mode control. So a kind of second order sliding modes algorithm and head pursuit interception guidance law are presented, and smooth second order sliding mode head pursuit interception guidance law with an observer is provided to eliminate the control discontinuity. Simulation is performed using smooth second-order sliding mode head pursuit intercepion as an example.
Tracking differentiator is a general method to get signal differentiator information in engineering, which can be used to track the signal of LOS(line of sight) angle and it’s derivative. Nonlinear sliding mode control is an important method for tracking differentiator design, especially high order sliding mode control has been widely used, which has the character of less perturbation and high robustness. A second-order sliding mode tracking differentiator as well as it’s improved algorithm are presented using Lyapunov stability theory on the basis of nonlinear second order sliding mode control theory. Integrating the character of linear and nonlinear tracking differentiator, this tracking differentiator can track and differentiate any signal. At the same time it has a simple form and is easy to be applied.
The mathematic model used to depict the motion of missile is a multi-input multi-output system including dynamical equations, kinematic equations, geometric equations and control equations. So a variable structure control method is designed to control the interceptor attitude stability considering the on-off control of attitude engine. Finally, according to the algorithms designed above, a head pursuit interception numerical simulation is done considering the missile model, aerodynamics, mass variablity and target maneuvering, using second order sliding mode guidance law, variable structure attitude control theory. Simulation results verified the effectiness of the three-dimensional guidance model, the guidance law and the attitude control algorithm.
前置追踪拦截方式是近几年来发展起来的一种导弹拦截技术,该技术是将拦截器导引到目标轨道的前方并和目标沿相同方向飞行,从而在目标轨道的前方拦截目标。在进行了运动分析和相应的模型简化的基础上,根据古典力学理论推导了前置追踪拦截方式拦截器和目标导弹的运动方程,建立了前置追踪拦截的数学模型。同时根据前置追踪拦截方式的工作原理,建立了拦截器前置追踪拦截方式的制导方程,并且通过对拦截条件的分析,给出了满足拦截条件的参数选择和初始条件。
由于弹体气动系数变化、目标机动及外界干扰等因素的影响,拦截器和目标的三维拦截运动方程存在着复杂的非线性关系和不确定性。由于滑模变结构控制具有对干扰不敏感的特点,本文根据李亚普诺夫稳定性理论,设计了一种在有限时间内收敛的非线性变结构控制算法。同时在目标加速度未知的情况下,采用不确定性边界的自适应估计方法,设计了一种非线性自适应算法。针对所建立的前置追踪拦截运动方程,给出了有限时间收敛的非线性变结构制导律。数字仿真结果验证了非线性变结构制导律的有效性。
由微分包含和齐次性理论建立起来的高阶滑模变结构控制能够有效地降低普通变结构控制的抖振现象,实现系统的连续控制,同时保持滑模控制对干扰具有鲁棒性的优点。文中以二阶滑模控制为例设计了一种具有强鲁棒性的二阶滑模控制算法。同时采用一种微分观测器对目标加速度进行观测估计,得到了一种平滑的二阶滑模控制器,从而有效地消除了二阶滑模控制中不确定项的影响。结合前置追踪拦截的拦截器和目标的运动模型设计了前置追踪拦截的二阶滑模制导律,仿真结果进一步验证了二阶滑模制导律的有效性和优越性。
为了实现前置追踪拦截过程中的视线角和视线角速度的跟踪观测,本文对跟踪微分器进行了设计。非线性滑模控制是跟踪微分器设计的一个重要方法,尤其是高阶滑模具有抖振弱、强鲁棒性等特点而得到了广泛应用。为了提高跟踪微分器的鲁棒性,本文在深入分析非线性滑模跟踪微分器的基础上,利用李亚普诺夫稳定性定理提出了一种二阶滑模非线性跟踪微分器,并在此基础上进一步提出了降低了二阶滑模跟踪微分器微分输出抖动的方法。该跟踪微分器综合了线性跟踪微分器和非线性跟踪微分器的优点,可实现任意信号的跟踪和微分,并且结构简单、易于实现。
拦截器的姿态控制系统是一个多输入多输出的非线性系统,文中对拦截器的姿态控制方法进行了研究,针对利用喷气控制的拦截器设计了一种姿态稳定的变结构控制算法。由于描述导弹的空间运动方程组由动力学方程、运动学方程、质量变化方程、几何方程和控制关系方程等组成。因此,本文在导弹刚体运动模型、空气动力、质量变化、目标运动以及轨控和姿控发动机开关控制的分析基础之上,采用非线性变结构制导律和变结构姿态控制算法,根据导弹的实际运行情况进行了前置追踪拦截方式的全航迹拦截数字仿真,从而验证了拦截运动模型、制导律和姿态控制算法的正确性。
KKV(Kinetic Kill Vehicle) is a general interceptor used to intercept the tactic ballistic missile, and infrared sensor is applied to detect the target. To reduce the perturbation of interceptor detection induced by aerodynamic heating which is brought by high speed of the interceptor at the endgame guidance stage at atmosphere, a novel interception method, head pursuit interception is provided in this paper. Based on this advanced interception technology, the corresponing guidance law and tracking differentiator are studied using Lyapunov stability theory. The whole trjectory simulation is performed in the end.
Head pursuit interception is a new missile interception technology which has been developped recently. For head pursuit interception, the interceptor is guided ahead of the target along the target’s flight trajectory, so that the interceptor and the target fly in the same direction. The three-dimensional kinematics model is presented considering the motion of the interceptor and the target based on simplified interception model. According to the performance of head pursuit interception, the head pursuit guidance model is founded and the condition of head pursuit interception is discussed, at the same time the parameters and initial conditions for this kind of interception are provided.
There are many uncertainties for the guidance and control of missile including aerodynamics, target maneuvering and outer disturbance. Three-dimensional head pursuit interception model is a nonlinear and uncertain system, and variable structure control method has the character of robustness for system diturbances. So based on Lyapunov stability theory a nonlinear finite-time stability variable structure control guidance law is designed considering the unknown accelerations of the target, which can satisfy the requirement of head pursuit interception. At the same time, an adaptive variable structure control guidance law is presented to eliminate the effect of uncertain item using the adaptive uncertain boundary method.
High-order sliding mode control method is introduced according to differential inclusions and homogeneity theory. The main advantage of high-order sliding mode is being able to reduce the control discontinuity of sliding mode control while keeping the advantage of the sliding mode control. So a kind of second order sliding modes algorithm and head pursuit interception guidance law are presented, and smooth second order sliding mode head pursuit interception guidance law with an observer is provided to eliminate the control discontinuity. Simulation is performed using smooth second-order sliding mode head pursuit intercepion as an example.
Tracking differentiator is a general method to get signal differentiator information in engineering, which can be used to track the signal of LOS(line of sight) angle and it’s derivative. Nonlinear sliding mode control is an important method for tracking differentiator design, especially high order sliding mode control has been widely used, which has the character of less perturbation and high robustness. A second-order sliding mode tracking differentiator as well as it’s improved algorithm are presented using Lyapunov stability theory on the basis of nonlinear second order sliding mode control theory. Integrating the character of linear and nonlinear tracking differentiator, this tracking differentiator can track and differentiate any signal. At the same time it has a simple form and is easy to be applied.
The mathematic model used to depict the motion of missile is a multi-input multi-output system including dynamical equations, kinematic equations, geometric equations and control equations. So a variable structure control method is designed to control the interceptor attitude stability considering the on-off control of attitude engine. Finally, according to the algorithms designed above, a head pursuit interception numerical simulation is done considering the missile model, aerodynamics, mass variablity and target maneuvering, using second order sliding mode guidance law, variable structure attitude control theory. Simulation results verified the effectiness of the three-dimensional guidance model, the guidance law and the attitude control algorithm.
引文
1王定超.反动能拦截器拦截方案设计.四川兵工学报. 2008, 29(5):36~38
2王静.动能拦截弹技术发展现状与趋势.现代防御技术. 2008,36(4):23~27
3 H. K. Armenian, J. D. Collier. TMD Defense Planning. AIAA Missile Science Conference. 1997
4徐世禄,侯振宁.弹道导弹防御系统的现状与发展.情报指挥控制系统与仿真技术. 2004, 26(1):32~37
5谷良贤,龚春林,郝波.动能拦截器姿控与轨控方案设计及仿真.西北工业大学学报. 2007, 25(3):402~405
6齐艳丽.美国导弹防御系统动能拦截弹研制与部署现状.中国航天. 2009, 1:31~37
7高红卫,谢良贵,文树梁.弹道导弹目标微动特性的微多普勒分析与仿真研究.系统仿真学报. 2009, 21(4):954~958
8周艳萍.侧窗探测下的姿态变结构控制.现代防御技术. 2006, 34(1):29~33
9尹海波,王敏,王科.战术弹道导弹防御的手段与发展分析.船舶电子工程. 2007, 5:47~51
10张巍,苏鹏辉,李成.美国战区导弹防御系统的现状与发展趋势.船舶电子工程. 2007, 4:33~38
11范晋祥.美国弹道导弹防御系统的红外系统与技术的发展.红外与激光工程. 2006, 35(5):536~541
12周林,张文.多通道地空导弹武器系统拦截决策模型研究.系统仿真学报. 2002,14(6):698~699
13李群章.美国战区高空区域防御系统拦截导弹红外寻的技术分析.红外与激光工程. 1998, 27(2):25~28
14 O. M. Golan, T. Shima. Head Pursuit Guidance for Hypervelocity Interception. Navigation and Control Conference. CP-4885, AIAA. 2004 Washington: 1~12
15 O. M. Golan, T. Shima. Precursor Interceptor Guidance Using the Sliding Mode Approach. Navigation and Control Conference. CP-4885, AIAA, 2005, Washington: 1~15
16李超勇,荆武兴.空间微分几何制导律应用研究.宇航学报. 2007, 28(5):1235~1240
17杨凯,曹小军.比例导引规律在导弹控制系统设计中的应用.弹箭与制导学报. 2007, 27(5):105~107
18 Abolghasem Naghash, Reza Esmaelzadeh, Mehdi Mortazavi. Near optimal guidance law for descent to a point using inverse problem approach. Aerospace Science and Technology. 2008, 12: 241-247
19陈宇强,赵育善.导弹最优制导律弹道仿真分析.指挥控制与仿真. 2007, 29(3):91~93.
20左斌,杨长波,李静.基于微分对策的导弹攻击策略.海军筑空工程学院学报. 2005, 20(5):524~526
21 Vladimir Turetsky, Josef Shinar. Missile guidance laws based on pursuit evasion game formulations. Automatica. 2003, 39:607~618
22 Han Yanhua, Xu Bo. Variable structure guidance law for attacking surface maneuver targets Journal of Systems Engineering and Electronics. 2008, 19(2):337~341
23钟书辉.变结构控制在空空导弹控制系统中的应用研究.航空兵器. 2006,(4): 14~17
24 Y. Z. Elhalwagy, M. Tarbouchi. Fuzzy logic sliding mode control for command guidance law design. ISA Transactions. 2004, 43(4):231~242
25 Rafael Yanushevsky, Warren Boord. Lyapunov approach to guidance laws design. Nonlinear Analysis. 2005, 63:743~749
26 LI H X, TONG S C. A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. IEEE Trans. on Fuzzy Systems. 2003, 11(1):24~34
27郑守军,姜长生.空空导弹三维自适应模糊滑模制导律设计.电光与控制. 2008, 15(1):12~16
28张汝川,顾文锦,于进勇.基于Hopfield神经网络的最优滑模制导律研究.宇航学报. 2009, 30(1):220~225
29孙未蒙,郑志强.一种多约束条件下的三维变结构制导律.宇航学报. 2007, 28(2):344~349
30 S. D. Brierley, R. Longchamp. Application of Sliding Mode Control to Air-Air Interception Problem. IEEE Transactions on Aerospace and Electronic Systems. 1990, 26(2):306~325
31 K. R. Babu, J. G. Sarmah, K. N. Swamy. Switched Bias Proportional Navigation for Homing Guidance against Highly Maneuvering Target. Journal of Guidance, Control and Dynamics. 1994, 17(6):1357~1363
32郭建国,周凤岐,周军.基于零脱靶量设计的变结构末制导律.宇航学报. 2005, 26(2):152~156
33张邦楚,杨剑影,王少锋.飞航导弹智能自适应滑模制导律设计.战术导弹技术. 2006, 7:68~72
34周荻,邹昕光,孙德波.导弹机动突防滑模制导律.宇航学报. 2006, 27(2):213~216
35 Shubhi Purwa. Higher Order Sliding Mode Controller for Robotic Manipulator. 22nd IEEE International Symposium on Intelligent Control. 2007:556~561
36 Zhou Jun, Wang Ting. Integrated Guidance-Control System for Beam-riding Guidance Missiles Based on Second Order Sliding Mode Control. Journal of Astronautics. 2007, 28(6):1632~1637
37宋建梅,张天桥.带末端落角约束的变结构导引律.弹道学报. 2001, 13(1):16~19
38郭鸿武,林维菘,刘明俊.基于相对速度偏角的变结构导引律.宇航学报. 2001, 22(3):33~37
39 Y. J. Huang, K. S. Yeung. A Robust Control Scheme Against All Parameter Variations and Disturbances. International Journal of Systems Science. 1994,25:1621~1629
40 K. Ravindra Babu, J. G. Sarmah and K. N. Swamy. Switched Bias Proportional Navigation for Homing Guidance Against Highly Maneuvering Targets. Journal of Guidance, Control and Dynamics. 1994, 17(6) : 1357~1363
41 K. Ravindra Babu, J. G. Sarmah and K. N. Swamy. Two Robust Homing Missile Guidance Laws Based on Sliding Mode Control Theory. Proceedings of Naecon. Dayton. 1994,24:540~547
42 M. Kim, K. V. Grider. Terminal Guidance for Impact Attitude Angle Constrained Flight Trajectories. IEEE Transaction Aerospace and Electronics Systems. 1973, 9(6):852~859
43 R. J. York, H. L. Pastrick. Optimal Terminal Guidance with Constraints atFinal Time. Journal of Spacecraft and Rockets. 1977, 14(6) :381~391
44 Ryoo C K, Cho H J, Tahk M J. Closed form solutions of optimal guidance with terminal impact angle constraint. Proceedings of the 2003 Conference on Control Application. 2003: 504~509
45 Byung. Soo. Kim, Jang. Gyu. Lee, Homing Guidance with Terminal Angular Constraint against Noman-wevering and Maneuvering Target. AIAA-97-3474: 189~199
46 Mario. Innocenti, Fabio. Pelleegrini, Francesco Nasuti. AVSS Guidance Law for Agile Missile. AIAA-97-3473: 381~391
47 D. G. Benshabat, A. BarGill. Robust Command to Line-of-Sight Guidance via Variable Structure Control. IEEE Transactions on Control Systems Technology. 1995,3:356~361
48高为炳.变结构控制理论基础.中国科学技术出版社. 1990
49顾文锦,赵红超.变结构控制在导弹制导中的应用综述.飞行力学. 2005, 23(1):1~4
50 Antonios Tsourdos, Brian A. White. Adaptive flight control design for nonlinear missile. Control Engineering Practice. 2005, 13:373~382
51 Aiay. Thukral, Mario. Innocenti. Variable Structure Autopilot for High Attack Maneuvers Using on-off Thrusters. IEEE Proceedings of the 33rdConference on Decision and Control. 1994, Lake Buena Vista: 3850~3851
52朱民雄.非线性空间飞行器系统的解耦滑模控制.北京航天航空大学学报. 2000, 26(5):509~913
53张云鹏,缪栋,刘云峰.基于特征点分段的导弹姿态全程滑态变结构控制研究.战术导弹技术. 2005, 4:48~51
54 Emmanuel Duflos, Patrick Penel, Philippe Vanheeghe. 3D Guidance Law Modeling. IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS. 1999, 35(1): 72~83
55武立军.三维末制导律的鲁棒动态逆设计方法研究.系统工程与电子技术. 2007, 29(8):1331~1333
56张友安,杨华东.空空导弹三维导引模型和机动目标导引规律研究.现代防御技术. 2003, 31(3):19~23
57钱杏芳,林瑞雄,赵亚男.导弹飞行力学.北京理工大学出版社, 2000
58马清华,王明海.弹道导弹常用坐标系及其转换.火力与指挥控制. 2004,(29):89~91
59李延秋,葛连正.侧窗探测控制技术研究报告.哈尔滨工业大学控制科学与工程系. 2003
60 Jaehyuk Oh, Injoong Ha. Capturabiliy of the 3Dimensional Pure PNG Law. IEEE Transactions on Aerospase and Electronic Systems. 1999. 35 (2): 490~512
61 S. H. Song, HA. Ij. A Lyapunov-like Approach to Performance Analysis of 3-dimensional Pure PNG Laws. IEEE Trans on Aerospace and Electronic Systems. 1994, 30(1); 239~247
62 Yusun Fu, Zuohua Tian, Songjiao Shi. Robust H∞control of uncertain nonlinear systems. Automatica. 2006, 42:1547~1552
63 Roger Skjetne, Thor Fossena, Petar V. Kokotovi. Robust output maneuvering for a class of nonlinear systems. Automatica. 2004,40: 373~383
64 Mehmet Onder Efea, Cem Unsalb, Okyay Kaynak. Variable structure control of a class of uncertain systems. Automatica. 2004,40:59~64
65 Fang Wei, Jiang Changsheng, Nonlinear predictive control of an aerospace vehicle based on adaptive fuzzy systems. Acta Aeronautica et Astronautica Sinica. 2008, 29(4): 988~994
66刘金琨,孙富春.滑模变结构控制理论及其算法研究与进展.控制理论与应用. 2007, 24(3):407~418
67 Deutscher Joachim, Schmid Christian. A state space embedding approach to approximate feedback linearization of single input nonlinear control systems. International Journal of Robust and Nonlinear Control. 2006, 16(9):421~440
68 Meshksar Sina, Jenabali Mahda, Dehzangi, Omid. Nonlinear control of distillation column using feedback linearization. MIC, 2007: 277~284
69关为群,殷兴良.导弹大攻角高机动飞行特性分析与仿真.现代防御技术. 2006,4:12~16
70佘文学,周凤岐.一类不确定非线性系统变结构自适应鲁棒控制.西北工业大学学报. 2004, 22(1):25~28
71 Nersesov Sergey G, Haddad Wassim M. On the stability and control of nonlinear dynamical systems via vector Lyapunov functions. IEEE Transactions on Automatic Control. 2006, 51(2): 203~215
72 Hassen. Mekki, Mohamed. Chtourou. Variable Structure Neural Networks forAdaptive Control of Nonlinear Systems Using the Stochastic Approximation. Simulation Modelling Practice and Theory. 2006,14:1000~1009
73 Bouzaouache, Hajer; Braiek, Naceur Benhadj. On the stability analysis of nonlinear systems using polynomial Lyapunov functions. Mathematics and Computers in Simulation. 2008, 76(5):316~329
74佘文学,周凤岐.非线性变结构制导律.宇航学报. 2003, 24(6):638~641
75孙胜,周荻.有限时间收敛变结构导引律.宇航学报. 2008,29(4): 1258~1262
76 Nersesov Sergey G, Haddad Wassim M, Hui, Qing. Finite-time stabilization of nonlinear dynamical systems via control vector Lyapunov functions. Proceedings of the American Control Conference. 2007:4810~4816
77 Nersesov Sergey G, Haddad Wassim M, Hui, Qing. Finite-time stabilization of nonlinear dynamical systems via control vector Lyapunov functions. Journal of the Franklin Institute. 2008, 345(7): 819~837
78 Shtessel Y, Shkolnikov I. Integrated guidance and control of advanced interceptors using second order slidingmodes. IEEE Conference on Decision and Control, Maui, USA, December 2003: 4587~4592
79 Sanjay.P.Bhat, Dennis S. Bernstein. Finite-Time Stability of Homogeneous Systems.Proceedings of the American Control Conference Albuquerque, 1997: 2513~2514
80佘文学,周凤岐.三维非线性变结构寻的制导律.宇航学报. 2004, 25(6):681~684
81汤善同,李忠应.变结构自适应制导规律研究.系统工程与电子技术. 2002, 24(7):68~72.
82 J. Davila, L. Fridman. Second-order Sliding Mode Observer for Mechanical Systems. IEEE Transactions of Automatic Control. 2005, 50(11):1785~1789
83 V. I. Utkin. Sliding Mode in Control and Optimization. Berlin. Germany: Springer-Verlan, 1992
84 Sane, Harshad S. Sussmann, Hector J. Bernstein, Dennis S. Output feedback adaptive stabilization of second-order systems. Proceedings of the American Control Conference. 2000,5:3138~3142
85 Vucic Mladen, Molnar Goran. Time-domain synthesis of continuous-time systems based on second-order cone programming. IEEE Transactions onCircuits and Systems. 2008, 55 (10):3110~3118
86 Ferrara Antonella, Giacomini Luisa, Vecchio Claudio. Adaptive second order sliding mode control of uncertain nonholonomic systems. IEEE 10th International Workshop on Variable Structure Systems. 2008, 45(9):191~196
87魏雷,朱江.二阶微分包含的边值问题及其应用.纯粹数学与应用数学. 2007, 23(1): 75~82
88张建雄,唐万生.分段线性微分包含系统的最优控制设计.系统工程学报. 2006, 21(4): 341~346
89 Song Wen. Stability for Differential Inclusions. Journal of Mathematical Research & Exposition. 1997, 17(1):43~49
90宋福民. Banach空间中微分包含解的存在性.应用数学和力学. 1998, 19(11):1021~1030
91 Wang Zhihua. Topological Properties of Viability Solution Sets for Differential Inclusions. Journal of Anhui University Natural Science Edition. 1995, 26(4):7~12
92郭兴明,罗辉.一类具有非线性不连续项的微分包含.上海大学学报. 2000, 6(4):291~297
93 Zhang, Qinghua, Li Gang. Nonlinear boundary value problems for second order differential inclusions. Nonlinear Analysis Theory, Methods and Applications. 2009, 70(9):3390~3406
94俞建.微分包含解的稳定性.贵州工业大学学报. 1997, 26(3):1~5
95 Lionel Rosier. Homogeneous Luapunov function for homogeneous continuous vector field. System Control Letters. 1992:467~473
96 Sanjay.P.Bhat, Dennis S. Bernstein. Finite-Time Stability of Homogeneous Systems.Proceedings of the American Control Conference Albuquerque. 1997: 2513~2514
97 Chairez Isaac, Poznyak Alexander, Poznyak Tatyana. High order sliding mode neurocontrol for uncertain nonlinear SISO systems: Theory and applications. Lecture Notes in Control and Information Sciences. 2008, 375:179~200
98于红芸,顾文锦.一种新的二阶滑模控制规律的研究.控制工程. 2004, 11(1): 112~114
99 Arie Levant. Homogeneity Approach to High-order Sliding Mode Design.Automatica. 2005,41:823~830
100 Arie Levant. Principles of 2-sliding mode design. Automatica. 2007, 43:576~586
101 A.N. Atassi, H .k .Khalil. Separation results for the stabilization of nonlinear system using different high-gain observer designs. Systems &Control letters. 2000, 39: 183~191
102韩京清,袁露林.跟踪微分器的离散形式.系统科学与教学. 1999, 19(3): 268~273
103武利强,林浩,韩京清.跟踪微分器滤波性能研究.系统仿真学报. 2004, 16(4):651~653
104史永丽,侯朝桢.改进的非线性跟踪微分器设计.控制与决策. 2008, 23(6):647~652
105王新华,陈增强,袁著祉.全程快速非线性跟踪微分器.控制理论与应用. 2003, 20(6): 875~878
106王新华,陈增强,袁著祉.非线性跟踪微分器的性能分析及其改进.控制与决策. 2002, 17:752~754
107 Arie Levant. Higher-order sliding modes, differentiation and output-feedback control. INT .J. Control, 2003, 76(9): 924~94
108唐治理,雷虎民.调制器的高阶滑模设计.系统工程与电子技术. 2008, 30(3): 585~588
109周俊.高阶微分器优化设计研究.湖南师范大学自然科学学报. 2002, 25(1): 25~27
110 Davila J. and Fridman L. Second-order sliding mode observer for mechanical systems, IEEE Transactions of Automatic Control. 2005, 50(11):1785~1789
111 Yuri B, Shtessel. Ilya A. Shkolnikov, Arie Levant. Smooth second-order sliding modes: Missile guidance application. Automatica, 2007, 10(10):1~4
112 Arie Levant. Robust Exact Differentiation via Sliding Mode Technique. Automatica. 1998, 34(3): 379~384
113韩京清,王伟.非线性跟踪微分器.系统科学与教学. 1994,14(2):177~183
114马中华,吴国富.利用TD估计目标状态.应用数学学报. 2007, 30(1): 1~9
115张寅孩,张仲超.用Bang-Bang控制策略实现快速定位最优系统.电力电子技术. 2003, 37(1): 22~24
2王静.动能拦截弹技术发展现状与趋势.现代防御技术. 2008,36(4):23~27
3 H. K. Armenian, J. D. Collier. TMD Defense Planning. AIAA Missile Science Conference. 1997
4徐世禄,侯振宁.弹道导弹防御系统的现状与发展.情报指挥控制系统与仿真技术. 2004, 26(1):32~37
5谷良贤,龚春林,郝波.动能拦截器姿控与轨控方案设计及仿真.西北工业大学学报. 2007, 25(3):402~405
6齐艳丽.美国导弹防御系统动能拦截弹研制与部署现状.中国航天. 2009, 1:31~37
7高红卫,谢良贵,文树梁.弹道导弹目标微动特性的微多普勒分析与仿真研究.系统仿真学报. 2009, 21(4):954~958
8周艳萍.侧窗探测下的姿态变结构控制.现代防御技术. 2006, 34(1):29~33
9尹海波,王敏,王科.战术弹道导弹防御的手段与发展分析.船舶电子工程. 2007, 5:47~51
10张巍,苏鹏辉,李成.美国战区导弹防御系统的现状与发展趋势.船舶电子工程. 2007, 4:33~38
11范晋祥.美国弹道导弹防御系统的红外系统与技术的发展.红外与激光工程. 2006, 35(5):536~541
12周林,张文.多通道地空导弹武器系统拦截决策模型研究.系统仿真学报. 2002,14(6):698~699
13李群章.美国战区高空区域防御系统拦截导弹红外寻的技术分析.红外与激光工程. 1998, 27(2):25~28
14 O. M. Golan, T. Shima. Head Pursuit Guidance for Hypervelocity Interception. Navigation and Control Conference. CP-4885, AIAA. 2004 Washington: 1~12
15 O. M. Golan, T. Shima. Precursor Interceptor Guidance Using the Sliding Mode Approach. Navigation and Control Conference. CP-4885, AIAA, 2005, Washington: 1~15
16李超勇,荆武兴.空间微分几何制导律应用研究.宇航学报. 2007, 28(5):1235~1240
17杨凯,曹小军.比例导引规律在导弹控制系统设计中的应用.弹箭与制导学报. 2007, 27(5):105~107
18 Abolghasem Naghash, Reza Esmaelzadeh, Mehdi Mortazavi. Near optimal guidance law for descent to a point using inverse problem approach. Aerospace Science and Technology. 2008, 12: 241-247
19陈宇强,赵育善.导弹最优制导律弹道仿真分析.指挥控制与仿真. 2007, 29(3):91~93.
20左斌,杨长波,李静.基于微分对策的导弹攻击策略.海军筑空工程学院学报. 2005, 20(5):524~526
21 Vladimir Turetsky, Josef Shinar. Missile guidance laws based on pursuit evasion game formulations. Automatica. 2003, 39:607~618
22 Han Yanhua, Xu Bo. Variable structure guidance law for attacking surface maneuver targets Journal of Systems Engineering and Electronics. 2008, 19(2):337~341
23钟书辉.变结构控制在空空导弹控制系统中的应用研究.航空兵器. 2006,(4): 14~17
24 Y. Z. Elhalwagy, M. Tarbouchi. Fuzzy logic sliding mode control for command guidance law design. ISA Transactions. 2004, 43(4):231~242
25 Rafael Yanushevsky, Warren Boord. Lyapunov approach to guidance laws design. Nonlinear Analysis. 2005, 63:743~749
26 LI H X, TONG S C. A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. IEEE Trans. on Fuzzy Systems. 2003, 11(1):24~34
27郑守军,姜长生.空空导弹三维自适应模糊滑模制导律设计.电光与控制. 2008, 15(1):12~16
28张汝川,顾文锦,于进勇.基于Hopfield神经网络的最优滑模制导律研究.宇航学报. 2009, 30(1):220~225
29孙未蒙,郑志强.一种多约束条件下的三维变结构制导律.宇航学报. 2007, 28(2):344~349
30 S. D. Brierley, R. Longchamp. Application of Sliding Mode Control to Air-Air Interception Problem. IEEE Transactions on Aerospace and Electronic Systems. 1990, 26(2):306~325
31 K. R. Babu, J. G. Sarmah, K. N. Swamy. Switched Bias Proportional Navigation for Homing Guidance against Highly Maneuvering Target. Journal of Guidance, Control and Dynamics. 1994, 17(6):1357~1363
32郭建国,周凤岐,周军.基于零脱靶量设计的变结构末制导律.宇航学报. 2005, 26(2):152~156
33张邦楚,杨剑影,王少锋.飞航导弹智能自适应滑模制导律设计.战术导弹技术. 2006, 7:68~72
34周荻,邹昕光,孙德波.导弹机动突防滑模制导律.宇航学报. 2006, 27(2):213~216
35 Shubhi Purwa. Higher Order Sliding Mode Controller for Robotic Manipulator. 22nd IEEE International Symposium on Intelligent Control. 2007:556~561
36 Zhou Jun, Wang Ting. Integrated Guidance-Control System for Beam-riding Guidance Missiles Based on Second Order Sliding Mode Control. Journal of Astronautics. 2007, 28(6):1632~1637
37宋建梅,张天桥.带末端落角约束的变结构导引律.弹道学报. 2001, 13(1):16~19
38郭鸿武,林维菘,刘明俊.基于相对速度偏角的变结构导引律.宇航学报. 2001, 22(3):33~37
39 Y. J. Huang, K. S. Yeung. A Robust Control Scheme Against All Parameter Variations and Disturbances. International Journal of Systems Science. 1994,25:1621~1629
40 K. Ravindra Babu, J. G. Sarmah and K. N. Swamy. Switched Bias Proportional Navigation for Homing Guidance Against Highly Maneuvering Targets. Journal of Guidance, Control and Dynamics. 1994, 17(6) : 1357~1363
41 K. Ravindra Babu, J. G. Sarmah and K. N. Swamy. Two Robust Homing Missile Guidance Laws Based on Sliding Mode Control Theory. Proceedings of Naecon. Dayton. 1994,24:540~547
42 M. Kim, K. V. Grider. Terminal Guidance for Impact Attitude Angle Constrained Flight Trajectories. IEEE Transaction Aerospace and Electronics Systems. 1973, 9(6):852~859
43 R. J. York, H. L. Pastrick. Optimal Terminal Guidance with Constraints atFinal Time. Journal of Spacecraft and Rockets. 1977, 14(6) :381~391
44 Ryoo C K, Cho H J, Tahk M J. Closed form solutions of optimal guidance with terminal impact angle constraint. Proceedings of the 2003 Conference on Control Application. 2003: 504~509
45 Byung. Soo. Kim, Jang. Gyu. Lee, Homing Guidance with Terminal Angular Constraint against Noman-wevering and Maneuvering Target. AIAA-97-3474: 189~199
46 Mario. Innocenti, Fabio. Pelleegrini, Francesco Nasuti. AVSS Guidance Law for Agile Missile. AIAA-97-3473: 381~391
47 D. G. Benshabat, A. BarGill. Robust Command to Line-of-Sight Guidance via Variable Structure Control. IEEE Transactions on Control Systems Technology. 1995,3:356~361
48高为炳.变结构控制理论基础.中国科学技术出版社. 1990
49顾文锦,赵红超.变结构控制在导弹制导中的应用综述.飞行力学. 2005, 23(1):1~4
50 Antonios Tsourdos, Brian A. White. Adaptive flight control design for nonlinear missile. Control Engineering Practice. 2005, 13:373~382
51 Aiay. Thukral, Mario. Innocenti. Variable Structure Autopilot for High Attack Maneuvers Using on-off Thrusters. IEEE Proceedings of the 33rdConference on Decision and Control. 1994, Lake Buena Vista: 3850~3851
52朱民雄.非线性空间飞行器系统的解耦滑模控制.北京航天航空大学学报. 2000, 26(5):509~913
53张云鹏,缪栋,刘云峰.基于特征点分段的导弹姿态全程滑态变结构控制研究.战术导弹技术. 2005, 4:48~51
54 Emmanuel Duflos, Patrick Penel, Philippe Vanheeghe. 3D Guidance Law Modeling. IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS. 1999, 35(1): 72~83
55武立军.三维末制导律的鲁棒动态逆设计方法研究.系统工程与电子技术. 2007, 29(8):1331~1333
56张友安,杨华东.空空导弹三维导引模型和机动目标导引规律研究.现代防御技术. 2003, 31(3):19~23
57钱杏芳,林瑞雄,赵亚男.导弹飞行力学.北京理工大学出版社, 2000
58马清华,王明海.弹道导弹常用坐标系及其转换.火力与指挥控制. 2004,(29):89~91
59李延秋,葛连正.侧窗探测控制技术研究报告.哈尔滨工业大学控制科学与工程系. 2003
60 Jaehyuk Oh, Injoong Ha. Capturabiliy of the 3Dimensional Pure PNG Law. IEEE Transactions on Aerospase and Electronic Systems. 1999. 35 (2): 490~512
61 S. H. Song, HA. Ij. A Lyapunov-like Approach to Performance Analysis of 3-dimensional Pure PNG Laws. IEEE Trans on Aerospace and Electronic Systems. 1994, 30(1); 239~247
62 Yusun Fu, Zuohua Tian, Songjiao Shi. Robust H∞control of uncertain nonlinear systems. Automatica. 2006, 42:1547~1552
63 Roger Skjetne, Thor Fossena, Petar V. Kokotovi. Robust output maneuvering for a class of nonlinear systems. Automatica. 2004,40: 373~383
64 Mehmet Onder Efea, Cem Unsalb, Okyay Kaynak. Variable structure control of a class of uncertain systems. Automatica. 2004,40:59~64
65 Fang Wei, Jiang Changsheng, Nonlinear predictive control of an aerospace vehicle based on adaptive fuzzy systems. Acta Aeronautica et Astronautica Sinica. 2008, 29(4): 988~994
66刘金琨,孙富春.滑模变结构控制理论及其算法研究与进展.控制理论与应用. 2007, 24(3):407~418
67 Deutscher Joachim, Schmid Christian. A state space embedding approach to approximate feedback linearization of single input nonlinear control systems. International Journal of Robust and Nonlinear Control. 2006, 16(9):421~440
68 Meshksar Sina, Jenabali Mahda, Dehzangi, Omid. Nonlinear control of distillation column using feedback linearization. MIC, 2007: 277~284
69关为群,殷兴良.导弹大攻角高机动飞行特性分析与仿真.现代防御技术. 2006,4:12~16
70佘文学,周凤岐.一类不确定非线性系统变结构自适应鲁棒控制.西北工业大学学报. 2004, 22(1):25~28
71 Nersesov Sergey G, Haddad Wassim M. On the stability and control of nonlinear dynamical systems via vector Lyapunov functions. IEEE Transactions on Automatic Control. 2006, 51(2): 203~215
72 Hassen. Mekki, Mohamed. Chtourou. Variable Structure Neural Networks forAdaptive Control of Nonlinear Systems Using the Stochastic Approximation. Simulation Modelling Practice and Theory. 2006,14:1000~1009
73 Bouzaouache, Hajer; Braiek, Naceur Benhadj. On the stability analysis of nonlinear systems using polynomial Lyapunov functions. Mathematics and Computers in Simulation. 2008, 76(5):316~329
74佘文学,周凤岐.非线性变结构制导律.宇航学报. 2003, 24(6):638~641
75孙胜,周荻.有限时间收敛变结构导引律.宇航学报. 2008,29(4): 1258~1262
76 Nersesov Sergey G, Haddad Wassim M, Hui, Qing. Finite-time stabilization of nonlinear dynamical systems via control vector Lyapunov functions. Proceedings of the American Control Conference. 2007:4810~4816
77 Nersesov Sergey G, Haddad Wassim M, Hui, Qing. Finite-time stabilization of nonlinear dynamical systems via control vector Lyapunov functions. Journal of the Franklin Institute. 2008, 345(7): 819~837
78 Shtessel Y, Shkolnikov I. Integrated guidance and control of advanced interceptors using second order slidingmodes. IEEE Conference on Decision and Control, Maui, USA, December 2003: 4587~4592
79 Sanjay.P.Bhat, Dennis S. Bernstein. Finite-Time Stability of Homogeneous Systems.Proceedings of the American Control Conference Albuquerque, 1997: 2513~2514
80佘文学,周凤岐.三维非线性变结构寻的制导律.宇航学报. 2004, 25(6):681~684
81汤善同,李忠应.变结构自适应制导规律研究.系统工程与电子技术. 2002, 24(7):68~72.
82 J. Davila, L. Fridman. Second-order Sliding Mode Observer for Mechanical Systems. IEEE Transactions of Automatic Control. 2005, 50(11):1785~1789
83 V. I. Utkin. Sliding Mode in Control and Optimization. Berlin. Germany: Springer-Verlan, 1992
84 Sane, Harshad S. Sussmann, Hector J. Bernstein, Dennis S. Output feedback adaptive stabilization of second-order systems. Proceedings of the American Control Conference. 2000,5:3138~3142
85 Vucic Mladen, Molnar Goran. Time-domain synthesis of continuous-time systems based on second-order cone programming. IEEE Transactions onCircuits and Systems. 2008, 55 (10):3110~3118
86 Ferrara Antonella, Giacomini Luisa, Vecchio Claudio. Adaptive second order sliding mode control of uncertain nonholonomic systems. IEEE 10th International Workshop on Variable Structure Systems. 2008, 45(9):191~196
87魏雷,朱江.二阶微分包含的边值问题及其应用.纯粹数学与应用数学. 2007, 23(1): 75~82
88张建雄,唐万生.分段线性微分包含系统的最优控制设计.系统工程学报. 2006, 21(4): 341~346
89 Song Wen. Stability for Differential Inclusions. Journal of Mathematical Research & Exposition. 1997, 17(1):43~49
90宋福民. Banach空间中微分包含解的存在性.应用数学和力学. 1998, 19(11):1021~1030
91 Wang Zhihua. Topological Properties of Viability Solution Sets for Differential Inclusions. Journal of Anhui University Natural Science Edition. 1995, 26(4):7~12
92郭兴明,罗辉.一类具有非线性不连续项的微分包含.上海大学学报. 2000, 6(4):291~297
93 Zhang, Qinghua, Li Gang. Nonlinear boundary value problems for second order differential inclusions. Nonlinear Analysis Theory, Methods and Applications. 2009, 70(9):3390~3406
94俞建.微分包含解的稳定性.贵州工业大学学报. 1997, 26(3):1~5
95 Lionel Rosier. Homogeneous Luapunov function for homogeneous continuous vector field. System Control Letters. 1992:467~473
96 Sanjay.P.Bhat, Dennis S. Bernstein. Finite-Time Stability of Homogeneous Systems.Proceedings of the American Control Conference Albuquerque. 1997: 2513~2514
97 Chairez Isaac, Poznyak Alexander, Poznyak Tatyana. High order sliding mode neurocontrol for uncertain nonlinear SISO systems: Theory and applications. Lecture Notes in Control and Information Sciences. 2008, 375:179~200
98于红芸,顾文锦.一种新的二阶滑模控制规律的研究.控制工程. 2004, 11(1): 112~114
99 Arie Levant. Homogeneity Approach to High-order Sliding Mode Design.Automatica. 2005,41:823~830
100 Arie Levant. Principles of 2-sliding mode design. Automatica. 2007, 43:576~586
101 A.N. Atassi, H .k .Khalil. Separation results for the stabilization of nonlinear system using different high-gain observer designs. Systems &Control letters. 2000, 39: 183~191
102韩京清,袁露林.跟踪微分器的离散形式.系统科学与教学. 1999, 19(3): 268~273
103武利强,林浩,韩京清.跟踪微分器滤波性能研究.系统仿真学报. 2004, 16(4):651~653
104史永丽,侯朝桢.改进的非线性跟踪微分器设计.控制与决策. 2008, 23(6):647~652
105王新华,陈增强,袁著祉.全程快速非线性跟踪微分器.控制理论与应用. 2003, 20(6): 875~878
106王新华,陈增强,袁著祉.非线性跟踪微分器的性能分析及其改进.控制与决策. 2002, 17:752~754
107 Arie Levant. Higher-order sliding modes, differentiation and output-feedback control. INT .J. Control, 2003, 76(9): 924~94
108唐治理,雷虎民.调制器的高阶滑模设计.系统工程与电子技术. 2008, 30(3): 585~588
109周俊.高阶微分器优化设计研究.湖南师范大学自然科学学报. 2002, 25(1): 25~27
110 Davila J. and Fridman L. Second-order sliding mode observer for mechanical systems, IEEE Transactions of Automatic Control. 2005, 50(11):1785~1789
111 Yuri B, Shtessel. Ilya A. Shkolnikov, Arie Levant. Smooth second-order sliding modes: Missile guidance application. Automatica, 2007, 10(10):1~4
112 Arie Levant. Robust Exact Differentiation via Sliding Mode Technique. Automatica. 1998, 34(3): 379~384
113韩京清,王伟.非线性跟踪微分器.系统科学与教学. 1994,14(2):177~183
114马中华,吴国富.利用TD估计目标状态.应用数学学报. 2007, 30(1): 1~9
115张寅孩,张仲超.用Bang-Bang控制策略实现快速定位最优系统.电力电子技术. 2003, 37(1): 22~24