助推—滑翔式飞行器弹道设计与制导技术研究
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摘要
助推-滑翔式飞行器以其增加射程、提高突防能力的独特优势正成为当前的研究热点。本文以解决助推-滑翔式飞行器弹道优化与再入制导关键技术为目标，系统研究了全弹道基本特性、弹道优化技术、再入弹道在线生成和跟踪制导、弹道在线优化与预测制导等问题，主要研究成果如下：
基于平面再入运动模型，对助推-滑翔式飞行器的全弹道特性进行了分析。分析了平衡滑翔弹道特性，得到了高度、倾角、射程等弹道参数与升阻比、滑翔速度的关系；分析了助推-滑翔式飞行器被动段射程与主动段终点参数的关系并与弹道导弹的相关结果进行比较；根据飞行器任务进行了火箭助推方案设计，完成了主动段弹道的分析与设计。
建立了再入弹道优化问题的数学模型，阐述了Gauss伪谱方法求解最优控制问题的基本框架，并应用Gauss伪谱方法对助推-滑翔式飞行器的飞行性能进行了分析，计算了针对全弹道的最大射程弹道、针对给定再入点的飞行器目标覆盖范围、考虑禁飞区约束的最优弹道。
对再入滑翔弹道的在线生成与跟踪制导方法进行了研究，将再入制导分为纵向和侧向制导，纵向采用在线生成与跟踪制导的方式，侧向则采用方位误差走廊控制弹道。主要做了两方面的研究工作：一是提出了基于高度-速度(H-V)飞行剖面的再入弹道在线生成方法，在再入走廊内将整个滑翔段弹道设计为二段三次H-V曲线，根据待飞射程的要求确定H-V曲线，基于反馈线性化方法设计了弹道跟踪制导律，通过跟踪H-V曲线获得其他弹道参数，引入射程更新技术，实现了高精度的再入制导；二是改进了基于平衡滑翔弹道的再入弹道在线生成方法，利用平衡滑翔条件建立了弹道参数间的近似关系，并将弹道约束转换为控制量约束，建立攻角的参数化模型，根据待飞射程要求迭代确定攻角曲线，利用弹道参数间的近似关系，得到其他纵向弹道参数，采用线性二次调节器方法计算弹道跟踪的最优增益系数，通过弹道跟踪实现了高精度的再入制导。
针对目前数值预测-校正制导方法的局限性，提出了基于伪谱法弹道在线优化的预测制导技术。较系统的讨论了以伪谱法进行弹道在线优化来进行预测-校正的可行性和实现方法，通过对控制更新时间间隔以及在线优化计算节点数的合理选择，保证了较高制导精度和在线计算效率，为实现数值预测-校正制导的应用提供了一条可行的途径。
采用一种满足落角约束的最优导引律来解决滑翔式飞行器下压段制导问题，并进行仿真验证。
本文工作是最优控制理论在助推-滑翔式飞行器弹道设计与再入制导技术上的一次创新性应用，所作工作能对发展未来新型助推-滑翔式飞行器及相关技术问题的进一步研究提供有益的理论依据和技术支持。
Based on augmenting the range and excellent penetration ability, the boost-glidevehicle becomes one of the focuses currently. For the purpose of developingtrajectory optimization and reentry guidance technology of the boost-glide vehicle,this dissertation studies the properties of the whole trajectory, trajectory optimizationmethod, on-board trajectory generation and tracking guidance, trajectory onlineoptimization and predictor-corrector guidance. The main work and results achieved inthis dissertation are summarized as follows:
Based on the planar reentry dynamic model, the rudimentary properties of theboost-glide trajectory are studied. The characteristics of the equilibrium glidetrajectory are analyzed. The influences of burnout trajectory parameters on range areanalyzed comparing with ballistic vehicle. Based on two stage rocket-boost launchingmode, booster parameter is evaluated for mission; the trajectory of boost phase isdesigned.
A trajectory optimization approach using Gauss Pseudospectral Method (GPM)for boost-glide vehicle is developed. The optimization models for the boost-glidetrajectory are presented and the principle of GPM is described. Then the GPM isapplied to compute the optimal trajectory of Max range of whole trajectory, theattainable region of reentry flight and the optimal trajectory considering the restrictionof “no-fly zone”.
A scheme of reentry trajectory on-board generation and tracking guidance forboost-glide vehicle is discussed. The reentry guidance is divided into longitudinalguidance and lateral guidance, the vehicle’s longitudinal motion is controlled bytrajectory on-board generation and tracking guidance, lateral motion is controlled byheading error corridor. The main contributions of this research are:1. A method ofheight vs velocity(H-V) profile online generation is proposed. The trajectory isdesigned to two segments of cubic curve in reentry corridors, the curve is determinedby terminate range constraint. A nonlinear tracking law is designed using thefeedback linearization method. The reference trajectory is obtained by trajectorytracking, with the range updating method, the H-V profile generation and trackingguidance performed well.2. An improved equilibrium glide trajectory generationmethod is proposed. The equilibrium glide condition is presented and utilized toestablish the approximate relationship between trajectory parameters and convert allpath constraints to the constraints of control variables. The control variables areparameterized, the parameters of control variable and longitudinal reference trajectorycan be solved with terminate range constraint. The corresponding tracking law is designed using linear quadratic regulator theory. Then the3DOF trajectory iscompleted by longitudinal trajectory tracking control and the heading error corridorcontrol in lateral motion. The equilibrium glide trajectory generation and LQRtracking guidance can overcome the disturbances of initial states and aerodynamicsparameters.
To improve the performances of conventional numerical predictor-correctorguidance, a pseudospectral-based online trajectory optimization and feedbackguidance algorithm has been developed and evaluated. The feasibility of using onlinetrajectory optimization to predict the trajectory instead of using numerical integrationis discussed. The good performance is obtained by reasonably choose of the controlupdating period and the number of nodes in optimization calculation. This canprovide an approach for apply the numerical predictor-corrector guidance.
The guidance laws with terminal angular constraint in dive phase are studied.
The research of this dissertation is an innovative application of optimal controltheory on trajectory design and reentry guidance of Boost-Glide vehicle, which willprovide theoretical support for the overall design and key technology development ofthis kind of vehicle.
基于平面再入运动模型，对助推-滑翔式飞行器的全弹道特性进行了分析。分析了平衡滑翔弹道特性，得到了高度、倾角、射程等弹道参数与升阻比、滑翔速度的关系；分析了助推-滑翔式飞行器被动段射程与主动段终点参数的关系并与弹道导弹的相关结果进行比较；根据飞行器任务进行了火箭助推方案设计，完成了主动段弹道的分析与设计。
建立了再入弹道优化问题的数学模型，阐述了Gauss伪谱方法求解最优控制问题的基本框架，并应用Gauss伪谱方法对助推-滑翔式飞行器的飞行性能进行了分析，计算了针对全弹道的最大射程弹道、针对给定再入点的飞行器目标覆盖范围、考虑禁飞区约束的最优弹道。
对再入滑翔弹道的在线生成与跟踪制导方法进行了研究，将再入制导分为纵向和侧向制导，纵向采用在线生成与跟踪制导的方式，侧向则采用方位误差走廊控制弹道。主要做了两方面的研究工作：一是提出了基于高度-速度(H-V)飞行剖面的再入弹道在线生成方法，在再入走廊内将整个滑翔段弹道设计为二段三次H-V曲线，根据待飞射程的要求确定H-V曲线，基于反馈线性化方法设计了弹道跟踪制导律，通过跟踪H-V曲线获得其他弹道参数，引入射程更新技术，实现了高精度的再入制导；二是改进了基于平衡滑翔弹道的再入弹道在线生成方法，利用平衡滑翔条件建立了弹道参数间的近似关系，并将弹道约束转换为控制量约束，建立攻角的参数化模型，根据待飞射程要求迭代确定攻角曲线，利用弹道参数间的近似关系，得到其他纵向弹道参数，采用线性二次调节器方法计算弹道跟踪的最优增益系数，通过弹道跟踪实现了高精度的再入制导。
针对目前数值预测-校正制导方法的局限性，提出了基于伪谱法弹道在线优化的预测制导技术。较系统的讨论了以伪谱法进行弹道在线优化来进行预测-校正的可行性和实现方法，通过对控制更新时间间隔以及在线优化计算节点数的合理选择，保证了较高制导精度和在线计算效率，为实现数值预测-校正制导的应用提供了一条可行的途径。
采用一种满足落角约束的最优导引律来解决滑翔式飞行器下压段制导问题，并进行仿真验证。
本文工作是最优控制理论在助推-滑翔式飞行器弹道设计与再入制导技术上的一次创新性应用，所作工作能对发展未来新型助推-滑翔式飞行器及相关技术问题的进一步研究提供有益的理论依据和技术支持。
Based on augmenting the range and excellent penetration ability, the boost-glidevehicle becomes one of the focuses currently. For the purpose of developingtrajectory optimization and reentry guidance technology of the boost-glide vehicle,this dissertation studies the properties of the whole trajectory, trajectory optimizationmethod, on-board trajectory generation and tracking guidance, trajectory onlineoptimization and predictor-corrector guidance. The main work and results achieved inthis dissertation are summarized as follows:
Based on the planar reentry dynamic model, the rudimentary properties of theboost-glide trajectory are studied. The characteristics of the equilibrium glidetrajectory are analyzed. The influences of burnout trajectory parameters on range areanalyzed comparing with ballistic vehicle. Based on two stage rocket-boost launchingmode, booster parameter is evaluated for mission; the trajectory of boost phase isdesigned.
A trajectory optimization approach using Gauss Pseudospectral Method (GPM)for boost-glide vehicle is developed. The optimization models for the boost-glidetrajectory are presented and the principle of GPM is described. Then the GPM isapplied to compute the optimal trajectory of Max range of whole trajectory, theattainable region of reentry flight and the optimal trajectory considering the restrictionof “no-fly zone”.
A scheme of reentry trajectory on-board generation and tracking guidance forboost-glide vehicle is discussed. The reentry guidance is divided into longitudinalguidance and lateral guidance, the vehicle’s longitudinal motion is controlled bytrajectory on-board generation and tracking guidance, lateral motion is controlled byheading error corridor. The main contributions of this research are:1. A method ofheight vs velocity(H-V) profile online generation is proposed. The trajectory isdesigned to two segments of cubic curve in reentry corridors, the curve is determinedby terminate range constraint. A nonlinear tracking law is designed using thefeedback linearization method. The reference trajectory is obtained by trajectorytracking, with the range updating method, the H-V profile generation and trackingguidance performed well.2. An improved equilibrium glide trajectory generationmethod is proposed. The equilibrium glide condition is presented and utilized toestablish the approximate relationship between trajectory parameters and convert allpath constraints to the constraints of control variables. The control variables areparameterized, the parameters of control variable and longitudinal reference trajectorycan be solved with terminate range constraint. The corresponding tracking law is designed using linear quadratic regulator theory. Then the3DOF trajectory iscompleted by longitudinal trajectory tracking control and the heading error corridorcontrol in lateral motion. The equilibrium glide trajectory generation and LQRtracking guidance can overcome the disturbances of initial states and aerodynamicsparameters.
To improve the performances of conventional numerical predictor-correctorguidance, a pseudospectral-based online trajectory optimization and feedbackguidance algorithm has been developed and evaluated. The feasibility of using onlinetrajectory optimization to predict the trajectory instead of using numerical integrationis discussed. The good performance is obtained by reasonably choose of the controlupdating period and the number of nodes in optimization calculation. This canprovide an approach for apply the numerical predictor-corrector guidance.
The guidance laws with terminal angular constraint in dive phase are studied.
The research of this dissertation is an innovative application of optimal controltheory on trajectory design and reentry guidance of Boost-Glide vehicle, which willprovide theoretical support for the overall design and key technology development ofthis kind of vehicle.
引文
[1]刘桐林.美国高超声速技术的发展与展望[J].航天控制,2004,22(4):36-41.
[2]刘桐林.国外高超声速技术发展探析[J].飞航导弹,2002,(6):30-40.
[3]廖少英.高超声速跳跃飞行武器研究[J].上海航天,2005,(4):27-30.
[4]雍恩米,陈磊,唐国金.助推--滑翔弹道的发展史及基于该弹道的制导武器方案设想[J].飞航导弹,2006,(3).
[5]李瑜,崔乃刚,郭继峰.助推-滑翔导弹发展概况及关键技术分析[J].战术导弹技术,2008,(5):13-19.
[6]关世义.基于钱学森弹道的新概念飞航导弹[J].飞航导弹,2003:1-4.
[7]徐玮,孙丕忠,夏智勋.助推-滑翔导弹总体一体化优化设计[J].固体火箭技术2008,31(4):317-319.
[8]张永军.跳跃式导弹总体优化设计与性能分析[D].国防科学技术大学,2006.
[9] Bredt S, Irene. The Silver Bird Story[J]. Spaceflight,1973,15:166-181.
[10]陈小庆.高超声速滑翔飞行器机动技术研究[D].国防科学技术大学,2011.
[11] Peebles, Curtis. The Origins of the U.S. Space Shuttle-1[J]. Spaceflight,1979,21:435-442.
[12] Peebles, Curtis. On Wings into Space[J]. Spaceflight,1986,28:276-280.
[13]胡建学,陈克俊,赵汉元. RLV再入标准轨道制导与轨道预测制导方法比较分析研究[J].国防科学技术大学学报,2007,29(1).
[14]胡建学.可重复使用跨大气层飞行器再入制导技术研究[D].国防科学技术大学,2007.
[15] Richie George. The Common Aero Vehicle-Space delivery system of thefuture[C]. AIAA Space Technology Conference&Exposition,1999Albuquerque,NM:
[16] Philips. A Common Aero Vehicle (CAV) Model, Description, andEmploymentGuide[J]. Report from Schafer Corporation for AFRL and AFSPC,2003.
[17] Agency B. FALCON force application and launch from CONUS[J].2003.
[18]刘美霞.跳跃的死神——美国“猎鹰”空天轰炸机计划情报[J].国际瞭望,2007,(4).
[19]童雄辉.美国“猎鹰”计划及其最新进展[J].中国航天,2005,(2).
[20] Steven H Walker, Fredrick Rodgers. Falcon Hypersonic TechnologyOverview[J]. AIAA2005-3253,2005.
[21]康开华,才满瑞,伍赣湘.美国高超声速技术飞行器[J].航天制造技术,2010,(1):7-11.
[22]战培国,赵昕.美国高超声速巡航飞行器研发进展[J].航空科学技术,2010,(1).
[23] Steven Walker, Ming Tang, Sue Morris. Falcon HTV-3X--a reusable hypersonictest bed[J]. AIAA一2008-2544,2008.
[24] Steven H Walker, Jefrey Sherk, Dale Shell. The DARPA/AF falcon program:thehypersonic technology vehicle#2(HTV-2) flight demonstration phase[J]. AIAA2008-2539,2008.
[25]李文杰,钱开耘,古雨田. HTV-2项目取得重大进展[J].飞航导弹,2010,(9).
[26]牛文,车易. DARPA完成HTV-2飞行器第二次试飞[J].飞航导弹,2011,(9).
[27]牛文,郭朝邦,叶蕾.美国成功完成AHW首次试飞[J].飞航导弹,2011,(12).
[28]刘晓恩.美俄新一代战略导弹技术分析[J].中国航天,2005.
[29]江山.从X-31到X-50盘点美国的X系列飞行器研究[J].国际航空,2002,(11).
[30]乔阿光. X-38—国际空间站未来的救生船[J].航天技术,2002,(1).
[31] Lu Ping. Inverse Dynamics Approach to Trajectory Optimization for anAerospace Plane[J]. Journal of Guidance,Control and Dynamics,1993,16(4):726-732.
[32] Verma Ajay, Junkins John L. Inverse dynamics approach for real-timedetermination of feasible aircraft reference trajectories[C]. AIAA AtmosphericFlight Mechanics Conference and Exhibit. Portland,OR,1999.
[33] Verma Ajay, Oppenheimer Michael W, Doman David B. On-Line AdaptiveEstimation and Trajectory Reshaping[C]. AIAA Guidance, Navigation, andControl Conference and Exhibit. San Francisco, CA, USA,2005.
[34] Lu Ping, Pierson Bion L. Optimal Aircraft Terrain-Following Analysis andTrajectory Generation[J]. Journal of Guidance,Control and Dynamics,1995,18(3):555-560.
[35]谢愈,刘鲁华,汤国建.高超声速滑翔飞行器摆动式机动突防弹道设计[J].航空学报,2011,32(12):2174-2181.
[36] Andrzej Zyluk. An Inverse Simulation Study On Wing Adapter Kit Dynamicsand Control in Prescribed Trajectory Flight[C].44th AIAA AerospaceSciences Meeting and Exhibit Reno, Nevada,9-12January,2006.
[37] Rick G Drury, James F Whidborne. A Quaternion-based Inverse DynamicsModel for Real-time UAV Trajectory Generation[C]. AIAA Guidance,Navigation, and Control Conference. Chicago, Illinois,10-13August,2009.
[38] Fahroo F, Ross I M. Direct trajectory optimization by a chebyshevpseudospectral method[J]. Journal of Guidance,Control and Dynamics,2002,25(1):160-166.
[39] Fahroo F, Ross I M. On discrete-time optimality conditions for pseudopectralmethods[C]. AIAA/AAS Astrodynamics Specialist Conference and Exhibit.Keystone, CO,2006.
[40] Fahroo F, Ross I M. Costate estimation by a Legendre pseudospectralmethod[[C]. Guidance, Navigation, and Control Conference and Exhibit.Boston, MA,1998.
[41] Ross I M, Fahroo F. A pseudospectral transformation of the covectors of optimalcontrol systems[C]. Proceedings of the1st IFAC/IEEE Symposium on Structureand Control,2001Prague, Czech Republic:
[42] Ross I M, Fahroo F. Pseudospectral knotting methods for solving optimal controlproblems[J]. Journal of Guidance,Control and Dynamics,2004,27(3):397-405.
[43]徐明亮,刘鲁华,汤国建.高超声速临近空间飞行器铰链力矩最小俯冲弹道设计[J].弹道学报,2011,23(3).
[44]宗群,田栢苓,窦立谦.基于Gauss伪谱法的临近空间飞行器上升段轨迹优化[J].宇航学报,2010,31(7).
[45]彭祺擘,李海阳,沈红新.基于高斯—伪谱法的月球定点着陆轨道快速优化设计[J].宇航学报,2010,31(4).
[46]雍恩米,唐国金,磊陈.基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化[J].宇航学报,2008,29(6).
[47]杨希祥,张为华.基于Gauss伪谱法的固体运载火箭上升段轨迹快速优化研究[J].宇航学报,2011,32(1).
[48] Rao Anil V, Clarke Kimberley A. Performance optimization of a maneuveringreentry vehicle using a legendre pseudospectral method[C]. AIAAAtmospheric Flight Mechanics Conference and Exhibit. Monterey, California,2002.
[49] Huntington Geoffrey Todd. Advancement and Analysis of a GaussPseudospectral Transcription for Optimal Control Problems[D]. MassachusettsInstitute of Technology,2007.
[50] Huntington Geoffrey Todd, Rao Anil V. Optimal configuration of spacecraftformation via a Gauss Pseudospectral Method[C]. AAS spaceflight MechanicsMeeting. Mountain, CO,2005.
[51] Benson D. A Gauss Pseudospectral Transcription for Optimal Control[D].Massachusetts Institute of Technology,2004.
[52]谢克明.现代控制理论[M].北京:清华大学出版社,2007.
[53]席裕庚.预测控制[M].北京:国防工业出版社,1993.
[54] Mayne D, Rawling J, Rao C. Constrained model predictive control: Stability andoptimality[J]. Automatica,1987,36(6):789-814
[55] Bellingham J, Richards A, How J. Receding Horizon Control of AutonomousAerial Vehicles[C]. American Control Conference,2002
[56]任怀庆,粱艳春,孙亮.基于神经网络的滚动时域优化控制[J].北京邮电大学学报,2009,32(1).
[57]曾剑新,周焰,何彦杰.一种飞行器在线航路重规划方法[J].空军雷达学院学报,2010,24(5).
[58] Kuwata Yoshiaki, Schouwenaars Tom, Richards Arthur. Robust ConstrainedReceding Horizon Control for Trajectory Planning[C]. AIAA Guidance,Navigation, and Control Conference and Exhibit. San Francisco, CA; USA,2005.
[59] Tam′As Keviczky, Gary J Balas. Flight Test of a Receding Horizon Controllerfor Autonomous UAV Guidance[C]. American Control Conference. Portland,OR, USA, June8-10,2005.
[60]张胜祥,裴海龙,刘保罗.基于滚动时域优化的无人飞行器轨迹规划[J].计算机工程与应用,2008,44(35).
[61]唐强,张新国,刘锡成.一种用于低空飞行的在线航迹重规划方法[J].西北工业大学学报,2005,23(4):271-275.
[62] Wingrove Rodney C. Survey of Atmosphere Re-entry Guidance and ControlMethods[J]. AIAA Journal,1963,1(9):2019-2029.
[63] Hanson J. Advanced Guidance and Control Project for Reusable LaunchVehicles[C]. Proceedings of the2000AIAA GN&C Conference,2000
[64]南英,陈士橹,吕学富.航天器再入轨迹与控制进展[J].导弹与航天运载技术,1994,(5):1-11.
[65]赵汉元.航天器再入制导方法综述[J].航天控制,1994,(1):26-33.
[66] Harpold J.C, Graves C.A. Shuttle Entry Guidance[J]. Journal of theAstronautical Science,1979,27(3).
[67] Lu Ping. Entry Guidance and Trajectory Control for Reusable LaunchVehicle.[J]. Journal of Guidance, Control and Dynamics,1997,20(1):143-149.
[68] Mease K D, Kremer J P. Shuttle Entry Guidance Revisited[J]. AIAA Paper92-4450,1992.
[69] Mease K D, Kremer J P. Shuttle Entry Guidance Revisited Using NonlinearGeometric Methods[J]. Journal of Guidance, Control and Dynamics,,1994,17(6):1350-1356.
[70] Roenneke A J, Markl A. Re-Entry Control to a Drag-vs-Energy Profile[J].Journal of Guidance, Control, and Dynamics,1997,17(5):916-920.
[71] Roenneke A J, Well K H. Nonlinear Drag-Tracking Control Applied to OptimalLow-Lift Re-Entry Guidance[J]. AIAA Paper96-3698,1996.
[72] Lu Ping, Hanson J M, Bharadwaj S. An Alternative Entry Guidance Scheme forthe X-33[J]. AIAA Paper98-4255,1988.
[73] Hanson J M, Coughlin D J, Dukeman G A. Ascent, Transition, Entry and AbortGuidance Algorithm Design for the X-33Vehicle[J]. AIAA Paper98-4409,1998.
[74] Bharadwaj S, Rao A V, Mease K D. Entry Trajectory Tracking Law viaFeedback Linearization[J]. Journal of Guidance, Control and Dynamics,1998,21(5):726-732.
[75] Hu J, Chen K, Zhao H. An Evolved Entry Guidance and Performance Analysisfor Reusable Launch Vehicles[J]. Journal of Astronautics,2006,27(6):1409-1413.
[76] Mease K D, Chen D T, Tandon S. A Three-Dimensional Predictive GuidanceApproach[J]. AIAA Paper2000-3959,2000.
[77] Hanson J. A Plan for Advanced Guidance and Control Technology for2ndGeneration Reusable Launch Vehicles[C]. Proceedings of the2002AIAAGN&C Conference,2002
[78] Hanson J. New Guidance for New Launchers[J]. Aerospace America,2003,3:36-41.
[79] Hanson J, Jones R. Test Results for Entry Guidance Methods for SpaceVehicles[J]. Journal of Guidance,Control and Dynamics,2004,27(6):960-966.
[80] Dukeman Greg. Profile-following entry guidance using linear quadratic regulatortheory[C]. AIAA Guidance, Navigation, and Control Conference and Exhibit.Monterey, CA,2002.
[81] Schierman J D, Ward D G, J F Monaco. On-Line Trajectory CommandReshaping for Reusable Launch Vehicles[J]. AIAA Paper AIAA-2003-5439,2003.
[82] Mease K D, Teufel P. Reentry Trajectory Planning for a Reusable LaunchVehicle[J]. AIAA-99-4160,1999.
[83] Saraf A., Leavitt J.A, Chen D.T. Design and Evaluation of an AccelerationGuidance Algorithm for Entry[J]. Journal of Spacecraft and Rockets,2004,41(6).
[84] Verma Ajay, Vadakkeveedu Kalyan. Smooth Function Modeling for On-LineTrajectory Reshaping Application.[C]. AIAA Guidance, Navigation, andControl Conference and Exhibit. Keystone, Colorado,21-24August,2006.
[85] Zimmerman C, Dukeman G, Hanson J. Automated Method to Compute OrbitalReentry Trajectories with Heating Constraints[J]. Journal of Guidance, Control,and Dynamics,2003,26(4):523-529.
[86] Shen Z, Lu Ping. On-Board Generation of Three-Dimensional Constrained EntryTrajectories[J]. Journal of Guidance, Control, and Dynamics,2003,26(1):111-121.
[87] Shen Z, Lu Ping. Onboard entry trajectory planning expanded to sub-orbitalflight[J]. AIAA2003-5736,2003.
[88] Tigges M, Ling L. A Predictive Guidance Algorithm for Mars Entry[J].AIAA-89-0632,1989.
[89] Jean De Lafontaine, Jean-Fran ois Lévesque, Aymeric Kron. Robust Guidanceand Control Algorithms Using Constant Flight Path Angle for Precision Landingon Mars[C]. AIAA Guidance, Navigation, and Control Conference andExhibit. Keystone, Colorado,21-24August,2006.
[90] Jean-Francois Levesque, Jean De Lafontaine. Optimal Guidance UsingDensity-Proportional Flight path Angle Profile for Precision Landing onMars[C]. AIAA Guidance, Navigation, and Control Conference and Exhibit.Keystone,Colorado,21-24August,2006.
[91] Powell R W. Numerical Roll Reversal Predictor-Corrector Aerocapture andPrecision Landing Guidance Algorithm for the Mars Surveyor Program2001Missions[J]. AIAA-98-4574,1998.
[92] Fuhry D P. Adaptive Atmospheric Reentry Guidance for the Kistler K-1OrbitalVehicle[J]. AIAA-99-4211,1999.
[93] Youssef H, Chowdhry R.S, Lee H. Predictor-Corrector Entry Guidance forReusable Launch Vehicles[J]. AIAA Paper2001-4043,2001.
[94] Ashok Joshi, Sivan K, Amma S S. Predictor-Corrector Reentry GuidanceAlgorithm with Path Constraints for Atmospheric Entry Vehicles[J]. Journal ofGuidance, Control and Dynamics,2007,30(5):1307-1318.
[95] Schierman J D, Hull J R, Gandhi Neha. Flight Test Results of an AdaptiveGuidance System for Reusable Launch Vehicles[C]. AIAA Guidance,Navigation, and Control Conference and Exhibit. Providence, Rhode Island,16-19August,2004.
[96] Schierman J D, Ward D G, Monaco J F. A Reconfigurable Guidance Approachfor Reusable Launch Vehicles[J]. AIAA Paper2001-4429,2001.
[97] Schierman J D, Ward D G, Hull J R. Intelligent Guidance and TrajectoryCommand Systems for Autonomous Space Vehicles[C]. AIAA1st IntelligentSystems Technical Conference. Chicago, Illinois,20-22September,2004.
[98] Schierman J D, Ward D G, Hull J R. Integrated Adaptive Guidance and Controlfor Re-entry Vehicles with Flight-Test Results[J]. Journal of Guidance,Dynamics, and Control,2004,20(1):975-988.
[99] Schierman J D, Hull J R, Ward D G. ON-LINE TRAJECTORY COMMANDRESHAPING FOR REUSABLE LAUNCH VEHICLES[C]. AIAA Guidance,Navigation, and Control Conference and Exhibit. Austin, Texas,11-14August,2003.
[100]Schierman J D, Hull J R, Ward D G. Adaptive Guidance with TrajectoryReshaping for Reusable Launch Vehicles[C]. AIAA Guidance, Navigation, andControl Conference and Exhibit. Monterey, California,5-8August,2002.
[101]Schierman J D, Hull J R. In-Flight Entry Trajectory Optimization for ReusableLaunch Vehicles[C]. AIAA Guidance, Navigation, and Control Conferenceand Exhibit. San Francisco, California,15-18August,2005.
[102]Burken J, Lu Ping, Wu Z. Reconfigurable Flight Control Designs WithApplication to the X-33Vehicle[J]. AIAA Paper99-4134,1999.
[103]Oppenheimer M W, Doman D B. Reconfigurable Control Design for the X-40Awith In-Flight Simulation Results[J]. AIAA Paper2004-5017,2004.
[104]Johnson E N, Jcalise A. Reusable Launch Vehicle Adaptive Guidance andControl using Neural Networks[J]. AIAA Paper2001-4381,2001.
[105]Sharma M, Ward D G. Flight-Path Angle Control via Neuro-AdaptiveBackstepping[J]. AIAA Paper2002-4451,2002.
[106]贾沛然,陈克俊,何力.远程火箭弹道学[M].长沙:国防科学技术大学出版社,1993.
[107]瞿章华,刘伟,曾明.高超声速空气动力学[M].长沙:国防科技大学出版社,2011.
[108]赵吉松,谷良贤,龚春林.高超声速飞行器起飞质量的解析估算[J].固体火箭技术,2008,31(6).
[109]雍恩米,唐国金,陈磊.基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化[J].宇航学报,2008,29(6):1766-1772.
[110]Huntington G T, Benson D A, How J P. Computation of boundary controlsusing a gauss pseudospectral method[C]. Astrodynamics SpecialistConference. Mackinac Island，Michigan,2007.
[111]Rao A V. Extension of a pseudospectral Legendre method to nonsequentialmultiple-phase optimal control problems[C]. AIAA Guidance，Navigation，andControl Conference. Austin, TX,2003.
[112]Han S P. A Globally Convergent Method For Nonlinear Programming[J].Journal of Optimization Theory and Applications,1977,22:297-309.
[113]Ross I Michael, Sekhavaty Pooya, Flemingz Andrew. Pseudospectral FeedbackControl: Foundations, Examples and Experimental Results[C]. AIAAGuidance, Navigation, and Control Conference and Exhibit. Keystone, Colorado,21-24August,2006.
[114]崔锋.采用伪谱法的再入飞行器最优反馈制导方法[J].中国制造业信息化,2011,40(19).
[115]水尊师,军周,葛致磊.基于高斯伪谱方法的再入飞行器预测校正制导方法研究[J].宇航学报,2011,32(6).
[116]解永锋,唐硕.基于伪谱法的亚轨道返回轨迹在线重构方法[J].飞行力学,2011,29(6).
[117]Bollino Kevin P, Ross I Michael. Optimal Nonlinear Feedback Guidance forReentry Vehicles[C]. AIAA Guidance, Navigation, and Control Conferenceand Exhibit. Keystone, Colorado,21-24August,2006.
[118]Sekhavat Pooya, Fleming Andrew, Ross I Michael. Time-Optimal NonlinearFeedback Control for the NPSAT1Spacecraft[C]. Proceedings of the2005IEEE/ASME International Conference on Advanced Intelligent Mechatronics,2005Monterey, California, USA:
[119]赵云.关于Gronwall不等式的一个注记[J].高等数学研究,2011,14(4).
[120]赵汉元.飞行器再入动力学和制导[M].长沙:国防科技大学出版社,1997.
[2]刘桐林.国外高超声速技术发展探析[J].飞航导弹,2002,(6):30-40.
[3]廖少英.高超声速跳跃飞行武器研究[J].上海航天,2005,(4):27-30.
[4]雍恩米,陈磊,唐国金.助推--滑翔弹道的发展史及基于该弹道的制导武器方案设想[J].飞航导弹,2006,(3).
[5]李瑜,崔乃刚,郭继峰.助推-滑翔导弹发展概况及关键技术分析[J].战术导弹技术,2008,(5):13-19.
[6]关世义.基于钱学森弹道的新概念飞航导弹[J].飞航导弹,2003:1-4.
[7]徐玮,孙丕忠,夏智勋.助推-滑翔导弹总体一体化优化设计[J].固体火箭技术2008,31(4):317-319.
[8]张永军.跳跃式导弹总体优化设计与性能分析[D].国防科学技术大学,2006.
[9] Bredt S, Irene. The Silver Bird Story[J]. Spaceflight,1973,15:166-181.
[10]陈小庆.高超声速滑翔飞行器机动技术研究[D].国防科学技术大学,2011.
[11] Peebles, Curtis. The Origins of the U.S. Space Shuttle-1[J]. Spaceflight,1979,21:435-442.
[12] Peebles, Curtis. On Wings into Space[J]. Spaceflight,1986,28:276-280.
[13]胡建学,陈克俊,赵汉元. RLV再入标准轨道制导与轨道预测制导方法比较分析研究[J].国防科学技术大学学报,2007,29(1).
[14]胡建学.可重复使用跨大气层飞行器再入制导技术研究[D].国防科学技术大学,2007.
[15] Richie George. The Common Aero Vehicle-Space delivery system of thefuture[C]. AIAA Space Technology Conference&Exposition,1999Albuquerque,NM:
[16] Philips. A Common Aero Vehicle (CAV) Model, Description, andEmploymentGuide[J]. Report from Schafer Corporation for AFRL and AFSPC,2003.
[17] Agency B. FALCON force application and launch from CONUS[J].2003.
[18]刘美霞.跳跃的死神——美国“猎鹰”空天轰炸机计划情报[J].国际瞭望,2007,(4).
[19]童雄辉.美国“猎鹰”计划及其最新进展[J].中国航天,2005,(2).
[20] Steven H Walker, Fredrick Rodgers. Falcon Hypersonic TechnologyOverview[J]. AIAA2005-3253,2005.
[21]康开华,才满瑞,伍赣湘.美国高超声速技术飞行器[J].航天制造技术,2010,(1):7-11.
[22]战培国,赵昕.美国高超声速巡航飞行器研发进展[J].航空科学技术,2010,(1).
[23] Steven Walker, Ming Tang, Sue Morris. Falcon HTV-3X--a reusable hypersonictest bed[J]. AIAA一2008-2544,2008.
[24] Steven H Walker, Jefrey Sherk, Dale Shell. The DARPA/AF falcon program:thehypersonic technology vehicle#2(HTV-2) flight demonstration phase[J]. AIAA2008-2539,2008.
[25]李文杰,钱开耘,古雨田. HTV-2项目取得重大进展[J].飞航导弹,2010,(9).
[26]牛文,车易. DARPA完成HTV-2飞行器第二次试飞[J].飞航导弹,2011,(9).
[27]牛文,郭朝邦,叶蕾.美国成功完成AHW首次试飞[J].飞航导弹,2011,(12).
[28]刘晓恩.美俄新一代战略导弹技术分析[J].中国航天,2005.
[29]江山.从X-31到X-50盘点美国的X系列飞行器研究[J].国际航空,2002,(11).
[30]乔阿光. X-38—国际空间站未来的救生船[J].航天技术,2002,(1).
[31] Lu Ping. Inverse Dynamics Approach to Trajectory Optimization for anAerospace Plane[J]. Journal of Guidance,Control and Dynamics,1993,16(4):726-732.
[32] Verma Ajay, Junkins John L. Inverse dynamics approach for real-timedetermination of feasible aircraft reference trajectories[C]. AIAA AtmosphericFlight Mechanics Conference and Exhibit. Portland,OR,1999.
[33] Verma Ajay, Oppenheimer Michael W, Doman David B. On-Line AdaptiveEstimation and Trajectory Reshaping[C]. AIAA Guidance, Navigation, andControl Conference and Exhibit. San Francisco, CA, USA,2005.
[34] Lu Ping, Pierson Bion L. Optimal Aircraft Terrain-Following Analysis andTrajectory Generation[J]. Journal of Guidance,Control and Dynamics,1995,18(3):555-560.
[35]谢愈,刘鲁华,汤国建.高超声速滑翔飞行器摆动式机动突防弹道设计[J].航空学报,2011,32(12):2174-2181.
[36] Andrzej Zyluk. An Inverse Simulation Study On Wing Adapter Kit Dynamicsand Control in Prescribed Trajectory Flight[C].44th AIAA AerospaceSciences Meeting and Exhibit Reno, Nevada,9-12January,2006.
[37] Rick G Drury, James F Whidborne. A Quaternion-based Inverse DynamicsModel for Real-time UAV Trajectory Generation[C]. AIAA Guidance,Navigation, and Control Conference. Chicago, Illinois,10-13August,2009.
[38] Fahroo F, Ross I M. Direct trajectory optimization by a chebyshevpseudospectral method[J]. Journal of Guidance,Control and Dynamics,2002,25(1):160-166.
[39] Fahroo F, Ross I M. On discrete-time optimality conditions for pseudopectralmethods[C]. AIAA/AAS Astrodynamics Specialist Conference and Exhibit.Keystone, CO,2006.
[40] Fahroo F, Ross I M. Costate estimation by a Legendre pseudospectralmethod[[C]. Guidance, Navigation, and Control Conference and Exhibit.Boston, MA,1998.
[41] Ross I M, Fahroo F. A pseudospectral transformation of the covectors of optimalcontrol systems[C]. Proceedings of the1st IFAC/IEEE Symposium on Structureand Control,2001Prague, Czech Republic:
[42] Ross I M, Fahroo F. Pseudospectral knotting methods for solving optimal controlproblems[J]. Journal of Guidance,Control and Dynamics,2004,27(3):397-405.
[43]徐明亮,刘鲁华,汤国建.高超声速临近空间飞行器铰链力矩最小俯冲弹道设计[J].弹道学报,2011,23(3).
[44]宗群,田栢苓,窦立谦.基于Gauss伪谱法的临近空间飞行器上升段轨迹优化[J].宇航学报,2010,31(7).
[45]彭祺擘,李海阳,沈红新.基于高斯—伪谱法的月球定点着陆轨道快速优化设计[J].宇航学报,2010,31(4).
[46]雍恩米,唐国金,磊陈.基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化[J].宇航学报,2008,29(6).
[47]杨希祥,张为华.基于Gauss伪谱法的固体运载火箭上升段轨迹快速优化研究[J].宇航学报,2011,32(1).
[48] Rao Anil V, Clarke Kimberley A. Performance optimization of a maneuveringreentry vehicle using a legendre pseudospectral method[C]. AIAAAtmospheric Flight Mechanics Conference and Exhibit. Monterey, California,2002.
[49] Huntington Geoffrey Todd. Advancement and Analysis of a GaussPseudospectral Transcription for Optimal Control Problems[D]. MassachusettsInstitute of Technology,2007.
[50] Huntington Geoffrey Todd, Rao Anil V. Optimal configuration of spacecraftformation via a Gauss Pseudospectral Method[C]. AAS spaceflight MechanicsMeeting. Mountain, CO,2005.
[51] Benson D. A Gauss Pseudospectral Transcription for Optimal Control[D].Massachusetts Institute of Technology,2004.
[52]谢克明.现代控制理论[M].北京:清华大学出版社,2007.
[53]席裕庚.预测控制[M].北京:国防工业出版社,1993.
[54] Mayne D, Rawling J, Rao C. Constrained model predictive control: Stability andoptimality[J]. Automatica,1987,36(6):789-814
[55] Bellingham J, Richards A, How J. Receding Horizon Control of AutonomousAerial Vehicles[C]. American Control Conference,2002
[56]任怀庆,粱艳春,孙亮.基于神经网络的滚动时域优化控制[J].北京邮电大学学报,2009,32(1).
[57]曾剑新,周焰,何彦杰.一种飞行器在线航路重规划方法[J].空军雷达学院学报,2010,24(5).
[58] Kuwata Yoshiaki, Schouwenaars Tom, Richards Arthur. Robust ConstrainedReceding Horizon Control for Trajectory Planning[C]. AIAA Guidance,Navigation, and Control Conference and Exhibit. San Francisco, CA; USA,2005.
[59] Tam′As Keviczky, Gary J Balas. Flight Test of a Receding Horizon Controllerfor Autonomous UAV Guidance[C]. American Control Conference. Portland,OR, USA, June8-10,2005.
[60]张胜祥,裴海龙,刘保罗.基于滚动时域优化的无人飞行器轨迹规划[J].计算机工程与应用,2008,44(35).
[61]唐强,张新国,刘锡成.一种用于低空飞行的在线航迹重规划方法[J].西北工业大学学报,2005,23(4):271-275.
[62] Wingrove Rodney C. Survey of Atmosphere Re-entry Guidance and ControlMethods[J]. AIAA Journal,1963,1(9):2019-2029.
[63] Hanson J. Advanced Guidance and Control Project for Reusable LaunchVehicles[C]. Proceedings of the2000AIAA GN&C Conference,2000
[64]南英,陈士橹,吕学富.航天器再入轨迹与控制进展[J].导弹与航天运载技术,1994,(5):1-11.
[65]赵汉元.航天器再入制导方法综述[J].航天控制,1994,(1):26-33.
[66] Harpold J.C, Graves C.A. Shuttle Entry Guidance[J]. Journal of theAstronautical Science,1979,27(3).
[67] Lu Ping. Entry Guidance and Trajectory Control for Reusable LaunchVehicle.[J]. Journal of Guidance, Control and Dynamics,1997,20(1):143-149.
[68] Mease K D, Kremer J P. Shuttle Entry Guidance Revisited[J]. AIAA Paper92-4450,1992.
[69] Mease K D, Kremer J P. Shuttle Entry Guidance Revisited Using NonlinearGeometric Methods[J]. Journal of Guidance, Control and Dynamics,,1994,17(6):1350-1356.
[70] Roenneke A J, Markl A. Re-Entry Control to a Drag-vs-Energy Profile[J].Journal of Guidance, Control, and Dynamics,1997,17(5):916-920.
[71] Roenneke A J, Well K H. Nonlinear Drag-Tracking Control Applied to OptimalLow-Lift Re-Entry Guidance[J]. AIAA Paper96-3698,1996.
[72] Lu Ping, Hanson J M, Bharadwaj S. An Alternative Entry Guidance Scheme forthe X-33[J]. AIAA Paper98-4255,1988.
[73] Hanson J M, Coughlin D J, Dukeman G A. Ascent, Transition, Entry and AbortGuidance Algorithm Design for the X-33Vehicle[J]. AIAA Paper98-4409,1998.
[74] Bharadwaj S, Rao A V, Mease K D. Entry Trajectory Tracking Law viaFeedback Linearization[J]. Journal of Guidance, Control and Dynamics,1998,21(5):726-732.
[75] Hu J, Chen K, Zhao H. An Evolved Entry Guidance and Performance Analysisfor Reusable Launch Vehicles[J]. Journal of Astronautics,2006,27(6):1409-1413.
[76] Mease K D, Chen D T, Tandon S. A Three-Dimensional Predictive GuidanceApproach[J]. AIAA Paper2000-3959,2000.
[77] Hanson J. A Plan for Advanced Guidance and Control Technology for2ndGeneration Reusable Launch Vehicles[C]. Proceedings of the2002AIAAGN&C Conference,2002
[78] Hanson J. New Guidance for New Launchers[J]. Aerospace America,2003,3:36-41.
[79] Hanson J, Jones R. Test Results for Entry Guidance Methods for SpaceVehicles[J]. Journal of Guidance,Control and Dynamics,2004,27(6):960-966.
[80] Dukeman Greg. Profile-following entry guidance using linear quadratic regulatortheory[C]. AIAA Guidance, Navigation, and Control Conference and Exhibit.Monterey, CA,2002.
[81] Schierman J D, Ward D G, J F Monaco. On-Line Trajectory CommandReshaping for Reusable Launch Vehicles[J]. AIAA Paper AIAA-2003-5439,2003.
[82] Mease K D, Teufel P. Reentry Trajectory Planning for a Reusable LaunchVehicle[J]. AIAA-99-4160,1999.
[83] Saraf A., Leavitt J.A, Chen D.T. Design and Evaluation of an AccelerationGuidance Algorithm for Entry[J]. Journal of Spacecraft and Rockets,2004,41(6).
[84] Verma Ajay, Vadakkeveedu Kalyan. Smooth Function Modeling for On-LineTrajectory Reshaping Application.[C]. AIAA Guidance, Navigation, andControl Conference and Exhibit. Keystone, Colorado,21-24August,2006.
[85] Zimmerman C, Dukeman G, Hanson J. Automated Method to Compute OrbitalReentry Trajectories with Heating Constraints[J]. Journal of Guidance, Control,and Dynamics,2003,26(4):523-529.
[86] Shen Z, Lu Ping. On-Board Generation of Three-Dimensional Constrained EntryTrajectories[J]. Journal of Guidance, Control, and Dynamics,2003,26(1):111-121.
[87] Shen Z, Lu Ping. Onboard entry trajectory planning expanded to sub-orbitalflight[J]. AIAA2003-5736,2003.
[88] Tigges M, Ling L. A Predictive Guidance Algorithm for Mars Entry[J].AIAA-89-0632,1989.
[89] Jean De Lafontaine, Jean-Fran ois Lévesque, Aymeric Kron. Robust Guidanceand Control Algorithms Using Constant Flight Path Angle for Precision Landingon Mars[C]. AIAA Guidance, Navigation, and Control Conference andExhibit. Keystone, Colorado,21-24August,2006.
[90] Jean-Francois Levesque, Jean De Lafontaine. Optimal Guidance UsingDensity-Proportional Flight path Angle Profile for Precision Landing onMars[C]. AIAA Guidance, Navigation, and Control Conference and Exhibit.Keystone,Colorado,21-24August,2006.
[91] Powell R W. Numerical Roll Reversal Predictor-Corrector Aerocapture andPrecision Landing Guidance Algorithm for the Mars Surveyor Program2001Missions[J]. AIAA-98-4574,1998.
[92] Fuhry D P. Adaptive Atmospheric Reentry Guidance for the Kistler K-1OrbitalVehicle[J]. AIAA-99-4211,1999.
[93] Youssef H, Chowdhry R.S, Lee H. Predictor-Corrector Entry Guidance forReusable Launch Vehicles[J]. AIAA Paper2001-4043,2001.
[94] Ashok Joshi, Sivan K, Amma S S. Predictor-Corrector Reentry GuidanceAlgorithm with Path Constraints for Atmospheric Entry Vehicles[J]. Journal ofGuidance, Control and Dynamics,2007,30(5):1307-1318.
[95] Schierman J D, Hull J R, Gandhi Neha. Flight Test Results of an AdaptiveGuidance System for Reusable Launch Vehicles[C]. AIAA Guidance,Navigation, and Control Conference and Exhibit. Providence, Rhode Island,16-19August,2004.
[96] Schierman J D, Ward D G, Monaco J F. A Reconfigurable Guidance Approachfor Reusable Launch Vehicles[J]. AIAA Paper2001-4429,2001.
[97] Schierman J D, Ward D G, Hull J R. Intelligent Guidance and TrajectoryCommand Systems for Autonomous Space Vehicles[C]. AIAA1st IntelligentSystems Technical Conference. Chicago, Illinois,20-22September,2004.
[98] Schierman J D, Ward D G, Hull J R. Integrated Adaptive Guidance and Controlfor Re-entry Vehicles with Flight-Test Results[J]. Journal of Guidance,Dynamics, and Control,2004,20(1):975-988.
[99] Schierman J D, Hull J R, Ward D G. ON-LINE TRAJECTORY COMMANDRESHAPING FOR REUSABLE LAUNCH VEHICLES[C]. AIAA Guidance,Navigation, and Control Conference and Exhibit. Austin, Texas,11-14August,2003.
[100]Schierman J D, Hull J R, Ward D G. Adaptive Guidance with TrajectoryReshaping for Reusable Launch Vehicles[C]. AIAA Guidance, Navigation, andControl Conference and Exhibit. Monterey, California,5-8August,2002.
[101]Schierman J D, Hull J R. In-Flight Entry Trajectory Optimization for ReusableLaunch Vehicles[C]. AIAA Guidance, Navigation, and Control Conferenceand Exhibit. San Francisco, California,15-18August,2005.
[102]Burken J, Lu Ping, Wu Z. Reconfigurable Flight Control Designs WithApplication to the X-33Vehicle[J]. AIAA Paper99-4134,1999.
[103]Oppenheimer M W, Doman D B. Reconfigurable Control Design for the X-40Awith In-Flight Simulation Results[J]. AIAA Paper2004-5017,2004.
[104]Johnson E N, Jcalise A. Reusable Launch Vehicle Adaptive Guidance andControl using Neural Networks[J]. AIAA Paper2001-4381,2001.
[105]Sharma M, Ward D G. Flight-Path Angle Control via Neuro-AdaptiveBackstepping[J]. AIAA Paper2002-4451,2002.
[106]贾沛然,陈克俊,何力.远程火箭弹道学[M].长沙:国防科学技术大学出版社,1993.
[107]瞿章华,刘伟,曾明.高超声速空气动力学[M].长沙:国防科技大学出版社,2011.
[108]赵吉松,谷良贤,龚春林.高超声速飞行器起飞质量的解析估算[J].固体火箭技术,2008,31(6).
[109]雍恩米,唐国金,陈磊.基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化[J].宇航学报,2008,29(6):1766-1772.
[110]Huntington G T, Benson D A, How J P. Computation of boundary controlsusing a gauss pseudospectral method[C]. Astrodynamics SpecialistConference. Mackinac Island，Michigan,2007.
[111]Rao A V. Extension of a pseudospectral Legendre method to nonsequentialmultiple-phase optimal control problems[C]. AIAA Guidance，Navigation，andControl Conference. Austin, TX,2003.
[112]Han S P. A Globally Convergent Method For Nonlinear Programming[J].Journal of Optimization Theory and Applications,1977,22:297-309.
[113]Ross I Michael, Sekhavaty Pooya, Flemingz Andrew. Pseudospectral FeedbackControl: Foundations, Examples and Experimental Results[C]. AIAAGuidance, Navigation, and Control Conference and Exhibit. Keystone, Colorado,21-24August,2006.
[114]崔锋.采用伪谱法的再入飞行器最优反馈制导方法[J].中国制造业信息化,2011,40(19).
[115]水尊师,军周,葛致磊.基于高斯伪谱方法的再入飞行器预测校正制导方法研究[J].宇航学报,2011,32(6).
[116]解永锋,唐硕.基于伪谱法的亚轨道返回轨迹在线重构方法[J].飞行力学,2011,29(6).
[117]Bollino Kevin P, Ross I Michael. Optimal Nonlinear Feedback Guidance forReentry Vehicles[C]. AIAA Guidance, Navigation, and Control Conferenceand Exhibit. Keystone, Colorado,21-24August,2006.
[118]Sekhavat Pooya, Fleming Andrew, Ross I Michael. Time-Optimal NonlinearFeedback Control for the NPSAT1Spacecraft[C]. Proceedings of the2005IEEE/ASME International Conference on Advanced Intelligent Mechatronics,2005Monterey, California, USA:
[119]赵云.关于Gronwall不等式的一个注记[J].高等数学研究,2011,14(4).
[120]赵汉元.飞行器再入动力学和制导[M].长沙:国防科技大学出版社,1997.
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