摘要
航天器的姿态与轨道控制是空间任务成功与否的关键。随着空间需求的日益增多，特别是对于以在轨服务、编队飞行、行星软着陆过程的终端着陆和空间拦截等为代表的空间近距离运动任务，航天器在受控飞行过程中，其位姿需要快速地、同时地满足高精度的控制要求。传统的航天器姿轨独立控制方式已逐渐不能满足这些新型空间任务的控制精度及机动性能的需求。相比之下，航天器的姿轨联合控制方式能够充分考虑并利用姿态动力学与轨道动力学之间的耦合关系，将两者视为整体，采用统一的控制算法同时调整星体位姿，从系统和全局角度来处理问题，能够从本质上提高任务的控制精度和机动性能。因此，研究航天器近距离运动的姿轨联合控制具有非常重要的理论意义与工程应用价值。本论文以航天器的两类近距离运动任务——空间近距离操作和空间相对轨道机动为研究背景，对航天器近距离运动的姿态轨道一体化建模与控制进行了研究，主要内容包括：
建立了面向两类空间近距离运动任务的航天器姿轨耦合动力学模型。根据空间近距离操作和空间相对轨道机动的任务特点，分别提出了控制机构的配置方案，在此基础上，分析航天器姿态与轨道之间的耦合关系，建立了对应的姿轨耦合动力学模型。根据执行机构配置方式的不同，两类动力学模型分别表现为全驱动系统和欠驱动系统。
针对空间近距离操作任务，为充分利用执行机构全驱动控制特点，以提高系统的机动性能及控制精度，研究了航天器姿轨联合有限时间控制问题。针对这一问题，本文提出了基于轨迹跟踪思想的鲁棒姿轨联合有限时间控制律，通过设计一类动态性能良好且有限时间收敛的运动轨迹，将有限时间控制问题等价地转化为对设计轨迹的跟踪问题，并利用自适应Backstepping技术设计了控制律，使得航天器的位姿在星体质量特性未知，推力器安装误差和外界干扰存在的情况下，在预定的时间内达到期望值。另外，考虑到控制算法中对执行机构安装误差的补偿项使得控制输入指令不易求取，提出了一种基于优化思想的控制输入计算方法，保证推力输入指令的在线实时解算。随后针对系统中可能出现的“振颤”现象进行了分析，并改进了控制算法，给出了严格的稳定性分析。数值仿真验证了所设计的有限时间控制律的有效性。
同样针对空间近距离操作任务，考虑到实际中执行机构幅值受限，研究了含有控制饱和的航天器姿轨联合控制问题，并进一步研究了含有控制饱和的有限时间姿轨联合控制问题。首先，基于抗饱和控制思想，结合自适应Backstepping技术，提出了具有抗饱和能力的鲁棒姿轨联合控制律，通过在虚拟控制中引入一个辅助信号，并对其动力学的巧妙设计，有效补偿了控制饱和误差带来的系统性能损失。随后，为兼顾抗饱和能力及有限时间控制律的强机动性和高控制精度，将已设计的鲁棒有限时间控制律和抗饱和控制律结合，基于切换思想，提出了抗饱和鲁棒有限时间姿轨联合控制律，并基于切换系统理论给出了闭环系统的稳定性分析。仿真结果表明，初期运行的抗饱和控制律能够有效处理执行机构饱和问题，当系统退饱和且满足给定的切换条件时，控制律切换至有限时间控制律，能够保证航天器相对位姿以较小的方法误差快速收敛于期望状态，较好地吸取了两者的优势。
针对空间相对轨道机动任务，提出了基于滤波Backstepping技术的鲁棒姿轨联合控制律，解决了欠驱动情形下的航天器姿轨联合控制问题。由于这类任务中，单台轨控发动机的固连安装导致轨控推力矢量与星体姿态角呈非线性耦合关系，使得现有的非线性控制技术很难直接使用，这成为该类任务的姿轨联合控制问题的一个设计难点。本文基于三角函数性质，提出了一种向量分解技术，巧妙地处理了这种非线性级联关系，使得Backstepping思想得以成功应用。由于系统阶次较高，在利用Backstepping技术进行控制律设计时，每一步设计均引入一阶滤波器以避免“级数膨胀”现象。随后，从理论上给出了严格的闭环稳定性分析，其中，利用奇异扰动理论证明了标称情形下闭环系统的指数稳定性，并利用Lyapunov理论证明了一般情形下闭环系统的最终一致有界性。最后，通过对月面软着陆最终着陆段的仿真验证了所提出控制律的有效性。
最后，研究了一类特殊的空间相对轨道机动任务——近圆轨道目标交会的姿轨联合控制问题。需要指出的是，利用本文所提出的向量分解技术可以将该控制问题转化为对一类推广的半严反馈系统的输出镇定问题，该系统具有低阶子系统呈线性形式、高阶子系统呈半严反馈形式且整体系统呈现级联形式的结构特点。因此，首先针对这类非线性系统，根据其结构特点，提出了一种基于H∞技术的鲁棒自适应Backstepping控制方法，解决了这类推广的半严反馈系统的鲁棒自适应控制问题，所设计的控制律不仅能够保证闭环系统的稳定性，而且能够按给定水平实现对系统不确定性的抑制。随后，利用所提出的控制算法针对近圆轨道目标交会任务构造了航天器鲁棒姿轨联合控制律，以保证轨控发动机推力受限情形下，主动航天器与目标之间的相对轨道沿着参考轨迹运行，完成最终交会，并能以给定水平抑制系统中的各种不确定性。最后，通过空间拦截任务的仿真验证了所提出控制律的有效性和优越性。
The attitude and orbit control of spacecraft is the key technology in space missions.With the development of worldwide space activities, especially for the proximity mis-sions such as on-orbit maintenance, formation flying, astroid soft landing and space in-terception, the position and the attitude of spacecraft are often required to simultaneouslyachieve the desired states with high maneuverability and control accuracy. To this extent,traditional separated position and attitude control strategy is hard to meet the increas-ing requirements of these future space missions. In contrast, integrated translation androtation control scheme fully takes into consideration the mutual couplings between thetranslation dynamics and the rotation dynamics, and can simultaneously control the posi-tion and attitude motion, which is able to essentially improve the system performance andguarantee high control accuracy and maneuverability. The present dissertation focuses onthe integrated translation and rotation modeling and control of spacecraft in space prox-imity operations and space orbit maneuver, both of which are based on spacecraft relativemotion in proximity. The main researches are listed as follows.
Two kinds of coupled relative attitude and orbit dynamics of spacecraft are formulat-ed for two type proximity missions mentioned above. The mutual couplings between theorbital dynamics and the attitude dynamics are analyzed. During the modeling, accordingto the requirements of both missions, two actuator configurations are given to providecontrol force and control torque. Due to the diferent actuator layout, the coupled dy-namics for proximity operations performs a full-actuated system, while the one for orbitmaneuver missions possesses an under-actuated system.
Considering space proximity operations, in order to make full use of full-actuatedsystem such that the system maneuverability and control precision can be improved, westudy the robust integrated translation and rotation finite-time control problem of a s-pacecraft. To do so, by designing a class of well-behaviored trajectory with finite-timeconvergence, the finite-time control problem is equivalently transformed into a trajectorytracking problem, and thus a robust finite-time control law is developed via adaptive back-stepping technique. In addition, an approach for computing the thrust input is addressedsince it cannot be evaluated explicitly and directly from the developed control law. Fur-thermore, the control scheme is modified to eliminate potential chattering phenomenonand the stability analysis is given as well. The following numerical simulation shows that the position and the attitude of spacecraft are able to converge to their desired values ina pre-determined time, despite of unknown mass properties, thruster misalignment andexternal disturbances, which demonstrates the efectiveness of the proposed control law.
In the sequel, based on the same mission, since the actuator outputs are limited inapplications, the integrated translation and rotation control problem of a rigid spacecraftwith control saturation is considered, and further, the integrated finite-time control prob-lem with control saturation is studied. To solve the first problem, based on anti-windupphilosophy and adaptive backstepping method, an anti-windup robust integrated transla-tion and rotation control law is proposed, where an auxiliary signal is introduced into thevirtual control to compensate for the influence caused by control saturation. Then, in or-der to obtain the high control accuracy and maneuverability from the designed finite-timecontroller and simultaneously deal with control saturation, based on switched control phi-losophy, the proposed finite-time controller and the anti-windup controller are synthesizedand thus the robust integrated translation and rotation anti-windup finite-time control lawis developed, which solves the second problem. The closed-loop stability is guaranteed byusing switched system theory. It can be demonstrated from numerical simulations that,the anti-windup controller takes efect initially to deal with input constraints, and oncethe control saturation no longer happens and the given switch condition is satisfied, thefinite-time controller takes over the system such that the relative position and the attitudeof spacecraft are able to accurately converge to the desired values in a fast response.
After that, we focus on the integrated translation and rotation control for relativeorbit maneuver, whose dynamics possesses an under-actuated system. In these missions,a single orbital thruster is often fixed on the spacecraft body and thus the orbital thrustvector for orbit control performs nonlinear with respect to the attitude angles, which be-comes the chief difculty of the control problem. To deal with this nonlinear cascadedrelationship, based on transformations of trigonometric functions, a vector decompositionis proposed such that the backstepping philosophy is applicable. It follows that the fil-tered backstepping technique is used to construct the robust integrated control law, wherea first-order filter is introduced in each design step to facilitate the derivation of the vir-tual controls. Then, the rigorous closed-loop stability analysis is given by using singularperturbation theory and Lyapunov theory. Numerical simulation of a lunar soft landingscenario shows the efectiveness of the proposed control law.
Finally, we study the spacecraft rendezvous mission with a target in near-circularorbit, which is a special-type relative orbit maneuver mission. For this mission, by us- ing the proposed vector decomposition, the integrated translation and rotation controlissue can be equivalently transformed into the output stabilization of a class of extend-ed semi-strict feedback systems, whose structure holds the features that1) the low-orderdynamics perform linear systems,2) the high-order dynamics take the semi-strict feed-back form, and3) the whole system possesses the cascaded structure. Thus, accordingto these features, a H∞-based robust adaptive backstepping control law is proposed suchthat the robust adaptive control problem of this type nonlinear system can be solved. Theproposed control scheme is able to not only guarantee the ultimate uniform boundednessbut also attenuate the system uncertainties with a given level. Based on the proposed con-trol scheme, a robust integrated translation and rotation control law is constructed suchthat the spacecraft is able to rendezvous with target along the reference trajectory andsimultaneously attenuate various system uncertainties. The following numerical simula-tion of a space interception scenario is given to illustrate the efectiveness of the designedintegrated controller.
引文
[1]杨乐平,朱彦伟,黄涣.航天器相对运动轨迹规划与控制[M].第一版.北京:国防工业出版社,2010:1–82.
[2]袁建平,和兴锁，等.航天器轨道机动动力学[M].第一版.北京:中国宇航出版社,2010:462–499.
[3] Terui F. Position and Attitude Control of a Spacecraft by Sliding Mode Con-trol[C]//Proceedings of the1998American Control Conference. Philadelphia, US-A: IEEE Press,1998:217–221.
[4] Stansbery D T, Cloutier J R. Position and Attitude Control of a Spacecraft Us-ing the State-Dependent Riccati Equation Technique[C]//Proceedings of the2000American Control Conference. Chicago, USA: IEEE Press,2000:1867–1871.
[5] Xin M, Balakrishnan S N, Stansbery D T. Spacecraft Position and Attitude Con-trol with theta-D Technique[C]//Proceedings of AIAA Guidance, Navigation andControl Conference. Reno, USA: AIAA Press, AIAA Paper No.2004-540,2004.
[6] Xin M, Pan H. Nonlinear Optimal Control of Spacecraft Approaching a TumblingTarget[C]//Proceedings of the2009American Control Conference. St Louis, USA:IEEE Press,2009:4818–4823.
[7]荆武兴,杨涤,吴瑶华，等.引力引起的空间站轨道与姿态耦合动力学方程的建立与计算[J].哈尔滨工业大学学报,1991,6(3):53–59.
[8] Naasz B J, Berry M M, Kim H Y, et al. Integrated Orbit and Attitude Control for aNanosatellite with Power Constraints[C]//Proceedings of AAS/AIAA Space FlightMechanics Conference. Ponce, Puerto Rico: AAS Press, AAS Paper No.AAS-03-100,2003:9–25.
[9] Fragopoulos D, Innocenti M. Autonomous spacecraft6-DOF relative motion con-trol using quaternions and H-infinity methods[C]//Proceedings of AIAA Guidance,Navigation and Control Conference. San Diego, USA: AIAA Press, AIAA PaperNo.1996-3725,1996.
[10] Wang P K C, Hadaegh F Y, Lau K. Synchronized Formation Rotation and AttitudeControl of Multiple Free-Flying Spacecraft[J]. Journal of Guidance, Control andDynamics,1999,22(1):28–35.
[11] Yamanaka K. Simultaneous Translation and Rotation Control Law for Forma-tion Flying Satellites[C]//Proceedings of AIAA Guidance, Navigation and ControlConference. Denver, USA: AIAA Press, AIAA Paper No.2000-4440,2000.
[12]彭冬亮,荆武兴,徐世杰.停靠阶段轨道姿态耦合动力学与控制研究[J].飞行力学,2002,20(1):33–37.
[13] Welsh S J, Subbarao K. Adaptive Synchronization and Control of Free FlyingRobots for Capture of Dynamic Free-Floating Spacecrafts[C]//Proceedings of A-IAA/AAS Astrodynamics Specialist Conference and Exhibit. Rhode Island, USA:AIAA Press,2004.
[14] Kristiansen R, Grotli E I, Nicklasson P J, et al. A Model of Relative Positionand Attitude in a Leader-Follower Spacecraft Formation[C]//Proceedings of the46th Scandinavian Conference on Simulation and Modeling. Trondheim, Norway:
[s.n.],2005.
[15] Xin M, Balakrishnan S N, Pernicka H J. Position and Attitude Control ofDeep-Space Spacecraft Formation Flying Via Virtual Structure and theta-D Tech-nique[C]//Proceedings of AIAA Guidance, Navigation and Control Conference.San Francisco, USA: AIAA Press, AIAA Paper No.2005-6090,2005.
[16] Xu Y, Tatsch A, Fitz-Coy N G. Chattering Free Sliding Mode Control for a6-DOF Formation Flying Mission[C]//Proceedings of AIAA Guidance, Navigationand Control Conference. San Francisco, USA: AIAA Press, AIAA Paper No.2005-5711,2005.
[17] Krogstad T R, Gravdahl J T.6-DOF Mutual Synchronization of Formation FlyingSpacecraft[C]//Proceedings of the45th IEEE Conference on Decision and Control.San Diego, USA: IEEE Press,2006:5706–5711.
[18] Kristiansen R, Grotli E I, Nicklasson P J, et al. A Model of Relative Translation andRotation in Leader-Follower Spacecraft Formations[J]. Modeling, Identificationand Control,2007,28(1):3–13.
[19] Kristiansen R, Nicklasson P J, Gravdahl J T. Spacecraft Coordination Control in6DOF: Integrator Backstepping vs Passivity-Based Control[J]. Automatica,2008,44:2896–2901.
[20] Shan J. Six-Degree-of-Freedom Synchronised Adaptive Learning Control forSpacecraft Formation Flying[J]. IET Control Theory and Applications,2008,2(10):930–949.
[21] Subbarao K, Welsh S. Nonlinear Control of Motion Synchronization for Satel-lite Proximity Operations[J]. Journal of Guidance, Control and Dynamics,2008,31(5):1284–1294.
[22]张艳召,袁建平,罗建军.小卫星临近作业轨道和姿态联合控制[J].中国空间科学技术,2008,5:13–19.
[23] Chung S J, Ahsun U, Slotine J J E. Application of Synchronization to FormationFlying Spacecraft: Lagrangian Approach[J]. Journal of Guidance, Control andDynamics,2009,32(2):512–526.
[24] Shan J. Synchronized Attitude and Translational Motion Control for SpacecraftFormation Flying[J]. Proceedings of the Institution of Mechanical Engineers PartG-Journal of Aerospace Engineering,2009,223:749–768.
[25] Xin M, Pan H. Integrated Control of Position, Attitude, and Flexible Motionfor Satellite Proximity Operations[C]//Proceedings of AIAA Guidance, Navigationand Control Conference. Chicago, USA: AIAA Press, AIAA Paper No.2009-5670,2009.
[26]朱彦伟.航天器近距离相对运动轨迹与控制研究[D].长沙:国防科学技术大学,2009:116–122.
[27]朱彦伟,杨乐平.航天器快速绕飞任务的六自由度滑模控制研究[J].宇航学报,2009,30(4):1482–1488.
[28]朱彦伟,杨乐平.空间机器人抓捕任务的六自由度同步控制逼近策略[J].国防科技大学学报,2009,31(6):43–49.
[29] Segal S, Gurfil P. Efect of Kinematic Rotation-Translation Coupling on Relative S-pacecraft Translational Dynamics[J]. Journal of Guidance, Control and Dynamics,2009,32(3):1045–1050.
[30] Xin M, Pan H. Integrated Nonlinear Optimal Control of Spacecraft in ProximityOperations[J]. International Journal of Control,2010,83(2):347–363.
[31]高有涛,陆宇平,徐波.非合作目标编队飞行耦合动力学建模与六自由度控制[J].南京航空航天大学学报,2010,42(2):159–165.
[32]刘智勇,何英姿.相对位置和姿态动力学耦合航天器的自抗扰控制器设计[J].航天控制,2010,28(2):17–22.
[33]吴云华,曹喜滨,张世杰，等.编队卫星相对轨道与姿态一体化耦合控制[J].南京航空航天大学学报,2010,42(1):13–20.
[34] Wu Y H, Cao X B, Xing Y J, et al. Relative Motion Coupled Control for FormationFlying Spacecraft Via Convex Optimization[J]. Aerospace Science and Technolo-gy,2010,14:415–428.
[35] Xing Y, Cao X, Zhang S, et al. Relative Position and Attitude Estimation forSatellite Formation with Coupled Translational and Rotational Dynamics[J]. ActaAstronautica,2010,67:455–467.
[36] Curti F, Romano M, Bevilacqua R. Lyapunov-Based Thrusters’ Selection for S-pacecraft Control: Analysis and Experimentation[J]. Journal of Guidance, Controland Dynamics,2010,33(4):1143–1160.
[37]铁钰嘉,岳晓奎,曹静.基于航天器姿轨耦合模型的非线性前馈控制[J].中国空间科学技术,2010,12(6):11–30.
[38] Min H, Wang S, Sun F, et al. Distributed Six Degree-of-Freedom Spacecraft For-mation Control with Possible Switching Topology[J]. IET Control Theory andApplications,2011,5(9):1120–1130.
[39] Ji L, Liu K, Xiang J. On All-Propulsion Design of Integrated Orbit and AttitudeControl for Inner-Formation Gravity Field Measurement Satellite[J]. Science Chi-na,2011,54(12):3233–3242.
[40]吉莉,刘昆,项军华.内编队重力场测量卫星微推力器姿轨一体化控制研究[J].国防科技大学学报,2011,33(6):89–94.
[41] Lv Y, Hu Q, Ma G, et al.6-DOF Synchronized Control for Spacecraft FormationFlying with Input Constraint and Parameter Uncertainties[J]. ISA Transactions,2011,50:573–580.
[42]卢伟,耿云海,陈雪芹，等.在轨服务航天器对目标的相对位姿耦合控制[J].航空学报,2011,32(5):857–865.
[43]朱志斌,李果,何英姿，等.基于Theta-D次优控制器设计的相对姿轨耦合控制[J].现代防御技术,2011,39(2):73–78.
[44]朱志斌,李果,何英姿，等.基于滚动优化的模块航天器姿轨协同控制[J].中国空间科学技术,2011,2:1–8.
[45]吉莉,刘昆,项军华.内编队重力场测量卫星全推力姿轨一体化控制研究[J].中国科学：技术科学,2012,42(2):220–229.
[46]朱志斌,李果,何英姿，等.基于滚动优化和微分Theta-D方法的快速绕飞航天器姿轨协同控制[J].宇航学报,2012,33(2):167–174.
[47] Pan H, Kapila V. Adaptive Nonlinear Control for Spacecraft Formation Flying withCoupled Translation and Attitude Dynamics[C]//Proceedings of the40th IEEEConference on Decision and Control. Orlando, USA: IEEE Press,2001:2057–2062.
[48] Wong H, Pan H, Kapila V. Output Feedback Control for Spacecraft Formation Fly-ing with Coupled Translation and Attitude Dynamics[C]//Proceedings of the2005American Control Conference. Portland, USA: IEEE Press,2005:2419–2426.
[49] Wong H. Formation Design and Nonlinear Control of Spacecraft Formation Fly-ing[D]. New York: Polytechnic University,2006:47–79.
[50]李化义,张迎春,强文义，等.相对位置和相对姿态耦合的编队控制[J].上海航天,2008,1:11–15.
[51]杨佳,朱站霞,张艳召.绕飞监测小卫星姿轨联合自适应控制研究[J].飞行力学,2008,26(5):59–62.
[52]张洪珠.基于对偶四元数的航天器姿轨一体化动力学建模与控制[D].哈尔滨:哈尔滨工业大学,2010:1–12.
[53] Murray R M, Li Z, Sastry S S. A Mathematical Introduction to Robotic Manipula-tion[M].1st. Florida: CRC Press,2000:30–110.
[54]斯利格(著),杨向东(译).机器人学的几何基础[M].第一版.北京:清华大学出版社,2008:23–105.
[55] Wu Y, Hu X, Hu D, et al. Strapdown Inertial Navigation System Algorithms Basedon Dual Quaternions[J]. IEEE Transactions on Aerospace and Electronic Systems,2005,41(1):110–132.
[56]武元新.对偶四元数导航算法与非线性高斯滤波研究[D].长沙:国防科学技术大学,2005:18–53.
[57] Han D P, Wei Q, Li Z X. A Dual-quaternion Method for Control of Spatial RigidBody[C]//Proceedings of IEEE International Conference on Networking, Sensingand Control. Sanya, China: IEEE Press,2008:1–6.
[58] Han D P, Wei Q, Li Z X. Kinematic Control of Free Rigid Bodies Using D-ual Quaternions[J]. International Journal of Automation and Computing,2008,5(3):319–324.
[59]韩大鹏.基于四元数代数和李群框架的任务空间控制方法研究[D].长沙:国防科学技术大学,2008:18–53.
[60] Wang X, Yu C. Feedback Linearization Regulator with Coupled Attitude andTranslation Dynamics Based on Unit Dual Quaternion[C]//2010IEEE Internation-al Symposium on Intelligent Control Part of2010IEEE Multi-Conference on Sys-tems and Control. Yokohama, Japan: IEEE Press,2008:2380–2384.
[61] Brodsky V, Shoham M. Dual Numbers Representation of Rigid Body Dynamics[J].Mechanism and Machine Theory,1999,34:693–718.
[62] Wang J, Liang H, Sun Z. Relative Coupled Dynamics and Control using DualNumber[C]//Proceedings of3rd International Symposium on Systems and Controlin Aeronautics and Astronautics. Harbin, China: IEEE Press,2010.
[63]王剑颖,梁海潮,孙兆伟.基于对偶数的相对耦合动力学与控制[J].宇航学报,2010,31(7):1711–1717.
[64] Wang J, Sun Z.6-DOF Robust Adaptive Terminal Sliding Mode Control for S-pacecraft Formation Flying[J]. Acta Astronautica,2012,73:76–87.
[65] Wang J, Liang H, Sun Z, et al. Relative Motion Coupled Control Based on DualQuaternion[J]. Aerospace Science and Technology,2012.
[66] Ploen S R, Hadaegh F Y, Sharf D P. Rigid Body Equations of Motion for Mod-eling and Control of Spacecraft Formations-Part1: Absolute Equations of Mo-tion[C]//Proceedings of the2004American Control Conference. Boston, USA:IEEE Press,2004:2646–3653.
[67] Gaulocher S. Modeling The Coupled Translational and Rotational Relative Dy-namics for Formation Flying Control[C]//Proceedings AIAA Guidance, Naviga-tion and Control Conference. San Francisco, USA: AIAA Press, AIAA PaperNo.2005-6091,2005.
[68] Gaulocher S, Chretien J, Pittet C. Six-axis Control Design and Controller Switch-ing for Spacecraft Formation Flying[C]//Proceedings AIAA Guidance, Navigationand Control Conference. Keystone, USA: AIAA Press, AIAA Paper No.2006-6583,2006.
[69] Sinclair A J, Hurtado J E, Junkins J L. Investigations on the Use of the Cayley Formfor Feedback Controller Design[C]//Proceedings AIAA Guidance, Navigation andControl Conference. Rhode Island, USA: AIAA Press, AIAA Paper No.2004-4761,2004.
[70] Sinclair A J, Hurtado J E, Junkins J L. Application of the Cayley Form to Gen-eral Spacecraft Motion[J]. Journal of Guidance, Control and Dynamics,2006,29(2):368–373.
[71] Pena R S, Alonso R, Anigstein P A. Robust Optimal Solution to the Attitude/ForceControl Problem[J]. IEEE Transactions on Aerospace and Electronic Systems,2000,36(3):784–792.
[72] Servidia P A, Pena R S. Thruster Design for Position/Attitude Control of S-pacecraft[J]. IEEE Transactions on Aerospace and Electronic Systems,2002,38(4):1172–1180.
[73]唐生勇,张世杰,张育林，等.姿轨一体化控制航天器推力器构型设计[J].航天控制,2010,28(3):20–28.
[74] Miele A, Weeks M W, Ciarcia M. Optimal Trajectories for Spacecraft Ren-dezvous[J]. Journal of Optimization Theory and Application,2007,132:353–376.
[75] Miele A, Ciarcia M, Weeks M W. Guidance Trajectories for Spacecraft Ren-dezvous[J]. Journal of Optimization Theory and Application,2007,132:377–400.
[76] Sharma R, Sengupta P, Vadali S R. Near-Optimal Feedback Rendezvous in Ellip-tic Orbits Accounting for Nonlinear Diferential Gravity[J]. Journal of Guidance,Control and Dynamics,2007,30(6):1803–1813.
[77] Gao H, Yang X, Shi P. Multi-Objective Robust H∞Control of Spacecraft Ren-dezvous[J]. IEEE Transactions on Control Systems Technology,2009,17(4):794–802.
[78] Miele A, Ciarcia M, Weeks M W. Rendezvous Guidance Trajectories via Multiple-Subarc Sequential Gradient-Restoration Algorithm[J]. Journal of Aerospace Engi-neering,2009,22(2):160–172.
[79] Ramanan R V, Lal M. Analysis of Optimal Strategies for Soft Landing on theMoon form Lunar Parking Orbits[J]. Journal of Earth Systems and Science,2005,114(6):807–813.
[80] Liu X L, Duan G R, Teo K L. Optimal Soft Landing Control for Moon Lander[J].Automatica,2008,44:1097–1103.
[81] Lim H, Bang H. Adaptive Control for Satellite Formation Flying under ThrustMisalignment[J]. Acta Astronautica,2009,65:112–122.
[82] Slotine J E, Li W. Applied Nonlinear Control[M]. Englewood Clifs: Prentice Hall,1991.
[83]李鹏,陈兴林,宋申民，等.交会对接最后逼近段姿轨耦合控制[J].智能系统学报,2010,5(6):530–533.
[84] Khalil H K. Nonlinear Systems[M].3rd. Upper Saddle River: Prentice Hall,2002.
[85] Astrom K J, Wittenmark B. Adaptive Control[M].2nd. New York: Addison-Wesley Publishing Company Inc.,1995.
[86] Byrnes J, Isidori A. New Results and Examples in Nonlinear Feedback Stabiliza-tion[J]. Systems and Control Letters,1989,12(5):437–442.
[87] Krstic M, Kanellakopoulos I, Kokotovic P. Nonlinear and Adaptive Control De-sign[M]. New York: Wiley,1995.
[88] Kanellakopoulos I, Kokotovic P, Morse A S. Systematic Design of Adaptive Con-trollers for Feedback Linearizable Systems[J]. IEEE Transactions on AutomaticControl,1991,31:1241–1253.
[89] Jiang Z P. A Combined Backstepping and Small-Gain Approach to Adaptive Out-put Feedback Control[J]. Automatica,1999,35:1131–1139.
[90] Lin W, Qian C J. Adaptive Regulation of Cascade Systems with NonlinearParametrization[J]. International Journal of Robust and Nonlinear Control,2002,12:1093–1108.
[91] Polycarpou M M, Ioannou P A. A Robust Adaptive Nonlinear Control Design[J].Automatica,1996,32(3):423–427.
[92] Jiang Z P, Mareels I M Y. A Small-Gain Control Method for Nonlinear CascadedSystems with Dynamic Uncertainties[J]. IEEE Transactions on Automatic Control,1997,42:292–308.
[93] Marino R, Tomei P. Robust Adaptive State-Feedback Tracking for Nonlinear Sys-tems[J]. IEEE Transactions on Automatic Control,1998,43(1):84–89.
[94] Jiang Z P. Decentralized Disturbance Attenuating Output-Feedback Trackers forLarge-Scale Nonlinear Systems[J]. Automatica,2002,38:1407–1415.
[95] Lin W, Qian C J, Huang X. Disturbance Attenuation of a Class of Non-linearSystems Via Output Feedback[J]. International Journal of Robust and NonlinearControl,2003,13:1359–1369.
[96] Xian B, Dawson D M, de Queiroz M S, et al. A Continuous Asymptotic TrackingControl Strategy for Uncertain Multi-input Nonlinear Systems[J]. IEEE Transac-tions on Automatic Control,2004,49(7):1206–1211.
[97] Karagiannis D, Jiang Z P, Ortega R, et al. Output-Feedback Stabilization of aClass of Uncertain Non-Minimum-Phase Nonlinear Systems[J]. Automatica,2005,41:1069–1615.
[98] Cai Z, de Querioz M S, Dawson D M. Robust Adaptive Asymptotic Tracking ofNonlinear Systems With Additive Disturbance[J]. IEEE Transactions on Automat-ic Control,2006,51(3):524–529.
[99] Chen B, Liu X, Liu K, et al. Direct Adaptive Fuzzy Control of Nonlinear Strict-Feedback Systems[J]. Automatica,2009,45:1530–1535.
[100] Chang Y, Cheng C C. Block Backstepping Control of Multi-Input Nonlinear Sys-tems with Mismatched Perturbations for Asymptotic Stability[J]. InternationalJournal of Control,2010,83(10):2028–2039.
[101] Jiang Z P, Praly L. Design of Robust Adaptive Controllers for Nonlinear Systemswith Dynamic Uncertainties[J]. Automatica,1998,34(7):825–840.
[102] Yao B, Tomizuka M. Adaptive Robust Control of Nonlinear Systems in a Semi-Strict Feedback Form[J]. Automatica,1997,33(5):893–900.
[103] Yao B, Tomizuka M. Adaptive Robust Control of MIMO Nonlinear Systems inSemi-Strict Feedback Form[J]. Automatica,2001,37(9):1305–1321.
[104] Liu X, Su H, Yao B, et al. Adaptive Robust Control of Nonlinear Systems withDynamic Uncertainties[J]. International Journal of Adaptive Control and SignalProcessing,2009,23:353–377.
[105] Lu L, Yao B. Adaptive Robust Control of a Class of Nonlinear Systems in Semi-Strict Feedback Form with Non-Uniformly Detectable Unmeasured Internal S-tates[J]. International Journal of Adaptive Control and Signal Processing,2010,24:961–981.
[106] Koshkouei A J, Zinober A S I, Burnham K J. Adaptive Sliding Mode BacksteppingControl of Nonlinear Systems with Unmatched Uncertainty[J]. Asian Journal ofControl,2004,6(4):447–453.
[107] Ngo K B, Mahony R, Z P J. Integrator Backstepping using Barrier Functions forSystems with Multiple State Constraints[C]//Proceedings of44th IEEE Conferenceon Decision and Control. Seville, Spain: IEEE Press,2005:8306–8312.
[108] Tee K P, Ge S S. Control of Nonlinear Systems with Full state Constraint Using ABarrier Lyapunov Function[C]//Proceedings of44th IEEE Conference on Decisionand Control. Shanghai, China: IEEE Press,2009:8618–8623.
[109] Ren B, Ge S S, Tee K P, et al. Adaptive Control for Parametric Output Feed-back Systems with Output Constraint[C]//Proceedings of44th IEEE Conferenceon Decision and Control. Shanghai, China: IEEE Press,2009:6650–6655.
[110] Tee K P, Ge S S, Li H, et al. Control of Nonlinear Systems with Time-varying Out-put Constraints[C]//Proceedings of2009IEEE International Conference on Controland Automation. Christchurch, New Zealand: IEEE Press,2009:524–529.
[111] Tee K P, Ge S S, Tay E H. Barrier Lyapunov Functions for the Control of Output-Constrained Nonlinear Systems[J]. Automatica,2009,45:918–927.
[112] Chen M, Ge S S, Ren B. Adaptive Tracking Control of Uncertain MIMO NonlinearSystems with Input Constraints[J]. Automatica,2011,47(3):452–465.
[113] Farrell J A, Polycarpou M, Sharma M. Adaptive Backstepping with Magnitude,Rate and Bandwidth Constraints: Aircraft Longitude Control[C]//Proceedings of2003American Control Conference. Denver, USA: IEEE Press,2003:3898–3904.
[114] Polycarpou M, Farrell J A, Sharma M. On-Line Approximation Control of Uncer-tain Nonlinear Systems: Issues with Control Input Saturation[C]//Proceedings of2003American Control Conference. Denver, USA: IEEE Press,2003:543–548.
[115] Farrell J A, Sharma M, Polycarpou M. Backstepping-Based Flight Control withAdaptive Function Approximation[J]. Journal of Guidance, Control and Dynamics,2005,28(6):1089–1102.
[116] Bateman A, Hull J, Lin Z. A Backstepping-Based Low-and-High Gain Design forMarine Vehicles[J]. International Journal of Robust and Nonlinear Control,2009,19:480–493.
[117] Yan F, Wang J. Non-Equilibrium Transient Trajectory Shaping Control via Mul-tiple Barrier Function for a Class of Nonlinear Systems[C]//Proceedings of2010American Control Conference. Baltimore, USA: IEEE Press,2010:1695–1700.
[118] Huang X, Lin W, Yang B. Finite-Time Stabilization in the Large for Uncer-tain Nonlinear Systems[C]//Proceedings of2004American Control Conference.Boston, USA: IEEE Press,2004:1073–1078.
[119] Huang X, Lin W, Yang B. Global Finite-Time Stabilization of a Class of UncertainNonlinear Systems[J]. Automatica,2005,41:881–888.
[120] Hong Y, Jiang Z P. Finite-Time Stabilization of Nonlinear Systems With Parametricand Dynamic Uncertainties[J]. IEEE Transactions on Automatic Control,2006,51(12):1950–1956.
[121] Pan Z, Basar T. Adaptive Controller Design for Tracking and Disturbance Atten-uation in Parametric Strict-Feedback Nonlinear Systems[J]. IEEE Transactions onAutomatic Control,1998,43(8):1066–1083.
[122] Yang Y, Zhou C. Adaptive Fuzzy H∞Stabilization for Strict-Feedback CanonicalNonlinear Systems Via Backstepping and Small-Gain Approach[J]. IEEE Trans-actions on Fuzzy Systems,2005,13(1):104–114.
[123] Niu Y, Lam J, Wang X, et al. Adaptive H∞Control Using Backstepping Designand Neural Network[J]. ASME Journal of Dynamic Systems, Measurement andControl,2005,127:478–485.
[124] Zhang X, Lin Y, Mao J. A Robust Adaptive Dynamic Surface Control for a Class ofNonlinear Systems with Unknown Prandtl-Ishilinskii Hysteresis[J]. InternationalJournal of Robust and Nonlinear Control,2011,21:1541–1561.
[125] Swaroop D, Gerdes J C, Yip P P, et al. Dynamic Surface Control of NonlinearSystems[C]//Proceedings of1997American Control Conference. New Mexico,USA: IEEE Press,1997:3028–3034.
[126] Swaroop D, Hedrick J K, Yip P P, et al. Dynamic Surface Control for aClass of Nonlinear Systems[J]. IEEE Transactions on Automatic Control,2000,45(10):1893–1899.
[127] Song B, Howell A, Hedrick K. Dynamic Surface Control Design for a Classof Nonlinear Systems[C]//Proceedings of40th IEEE Conference on Decision andControl. Florida, USA: IEEE Press,2001:2797–2802.
[128] Yoo S J, Park J B, Choi Y H. Adaptive Dynamic Surface Control for DisturbanceAttenuation of Nonlinear Systems[J]. International Journal of Control, Automationand Systems,2009,7(6):882–887.
[129] Tong S C, Li Y M, Feng G, et al. Observer-based Adaptive Fuzzy BacksteppingDynamic Surface Control for a Class of MIMO Nonlinear Systems[J]. IEEE Trans-actions on Systems, Man and Cybernetics–Part B: Cybernetics,2011,41(4):1124–1131.
[130] Yang Z, Nagai T, Kanae S, et al. Dynamic Surface Control Approach to AdaptiveRobust Control of Nonlinear Systems in Semi-Strict Feedback Form[J]. Interna-tional Journal of Systems Science,2007,38(9):709–724.
[131] Zhang G, Chen J, Li Z. Adaptive Robust Control for Servo Mechanism with Partial-ly Unknown States Via Dynamic Surface Control Approach[J]. IEEE Transactionson Control Systems Technology,2010,18(3):723–731.
[132] Chen J, Li Z, Gan M. Adaptive Robust Dynamic Surface Control with CompositeAdaptation Laws[J]. International Journal of Adaptive Control and Signal Process-ing,2010,24:1036–1050.
[133] Farrell J A, Polycarpou M, Sharma M, et al. Command Filtered Backstepping[J].IEEE Transactions on Automatic Control,2009,54(6):1391–1395.
[134] Dong W, Farrell J A, Polycarpou M, et al. Command Filtered Adaptive Backstep-ping[J]. IEEE Transactions on Control Systems Technology,2012,20(3):566–580.
[135] Yu Y, Zhong Y. Robust Backstepping Output Tracking Control for SISO UncertainNonlinear Systems with Unknown Virtual Control Coefcients[J]. InternationalJournal of Control,2010,83(6):1182–1192.
[136] Yu Y, Zhong Y. Semiglobal Robust Backstepping Output Tracking for Strict-Feedback Form Systems with Nonlinear Uncertainty[J]. International Journal ofControl, Automation and Systems,2011,9(2):366–375.
[137] Hughes P C. Spacecraft Attitude Dynamics[M]. New York: John Wiley&Sons,1986:10–20.
[138] Sidi M J. Spacecraft Dynamics and Control[M]. New York: Cambridge UniversityPress,1997.
[139]刘暾,赵钧.空间飞行器动力学[M].第一版.哈尔滨:哈尔滨工业大学出版社,2003.
[140] Benson D. A Gauss Pseudospectral Transcription for Optimal Control[D]. Boston:Massachusetts Institute of Technology,2005.
[141] Benson D A, Thorvaldsen G T, Rao A V. Direct Trajectory Optimization andCostate Estimation via an Orthogonal Collocation Method[C]//Proceedings of A-IAA Guidance, Navigation and Control Conference. Keystone, USA: AIAA Press,AIAA Paper No.2006-6358,2005.
[142] Huntington G T, Rao A V. Optimal Reconfiguration of Spacecraft FormationsUsing the Gauss Pseudospectral Method[J]. Journal of Guidance, Control andDynamics,2008,31:689–698.
[143] Dai R, Cochran J E. Three-Dimensional Trajectory Optimization in ConstrainedAirspace[J]. Journal of Aircraft,2009,46:627–634.
[144] Bhat S P, Berstein D S. Continuous Finite-Time Stabilization of the Translationaland Rotational Double Integrators[J]. IEEE Transactions on Automatic Control,1998,43(5):678–682.
[145] Yu X H, Man Z H. Multi-Input Uncertain Linear Systems with Terminal Sliding-Mode Control[J]. Automatica,1998,34(3):389–392.
[146] Park K B, Tsuji T. Terminal Sliding Mode Control of Second-Order Nonlinear Un-certain Systems[J]. International Journal of Robust and Nonlinear Control,1999,9:769–780.
[147] Bhat S P, Berstein D S. Finite-Time Stability of Continuous Autonomous System-s[J]. SIAM Journal of Control and Optimization,2000,38(3):751–766.
[148] Hong Y G. Finite-Time Stabilization and Stabilizability of a Class of ControllableSystems[J]. Systems and Control Letters,2002,46(4):231–236.
[149] Man Z, Mike O, Yu X. A Robust Adaptive Terminal Sliding Mode Control forRigid Robotic Manipulators[J]. Systems and Control Letters,2002,46(4):231–236.
[150] Yu X, Yu X, Shirinzadeh B, et al. Continuous Finite-Time Control for RoboticManipulators with Terminal Sliding Mode[J]. Automatica,2005,41:1957–1964.
[151] Su Y. Global Continuous Finite-Time Tracking of Robot Manipulators[J]. Interna-tional Journal of Robust Nonlinear Control,2009,19:1871–1885.
[152] Zhao D, Li S, Gao F. Finite Time Position Synchronised Control for Parallel Ma-nipulators using Fast Terminal Sliding Mode[J]. International Journal of SystemsScience,2009,40(8):829–843.
[153] Zhao D, Li S, Gao F. A New Terminal Sliding Mode Control for Robotic Manipu-lators[J]. International Journal of Control,2010,82(10):1804–1813.
[154] Zhao D, Li S, Gao F. Robust Finite-Time Control Approach for Robotic Manipu-lators[J]. IET Control Theory and Applications,2010,4(1):1–15.
[155] Ding S, Li S. Stabilization of the Attitude of a Rigid Spacecraft with ExternalDisturbances using Finite-Time Control Techniques[J]. Aerospace Science andTechnology,2009,13:256–265.
[156] Jin E, Sun Z. Robust Controllers Design with Finite Time Convergence for Rigid S-pacecraft Attitude Tracking Control[J]. Aerospace Science and Technology,2008,12:324–330.
[157] Liu H, Li J. Terminal Sliding Mode Control for Spacecraft Formation Flying[J].IEEE Transactions on Aerospace and Electronics Systems,2009,45(3):835–846.
[158] Zhou D, Sun S, Teo K L. Guidance Laws with Finite Time Convergence[J]. Journalof Guidance, Control, and Dynamics,2009,32(6):1838–1846.
[159] Wen J T, Delgado K K. The Attitude Control Problem[J]. IEEE Transactions onAutomatic Control,1991,36(10):1148–1162.
[160]周彬.饱和与时滞控制系统设计的单参量Lyapunov方程方法[D].哈尔滨:哈尔滨工业大学,2010:1–11.
[161] Branicky M S. Multiple Lyapunov Functions and Other Analysis Tools forSwitched and Hybrid Systems[J]. IEEE Transactions on Automatic Control,1998,43(4):475–482.
[162] Lu J, Brown L J. A Multiple Lyapunov Functions Approach for Stability ofSwitched Systems[C]//Proceedings of2010American Control Conference. Bal-timore, USA: IEEE Press,2010:3253–3256.
[163]段广仁.线性系统理论[M].第二版.哈尔滨:哈尔滨工业大学出版社,1997.
[164] Fukao T, Yamawaki A, Adachi N. Nonlinear and H∞Control of Active SuspensionSystems with Hydraulic Actuators[C]//Proceedings of38th IEEE Conference onDecision and Control. Arizona, USA: IEEE Press,1999:5125–5128.
[165] Ma M M, Chen H. Disturbance Attenuation Control of Active Suspension withNonlinear Actuator Dynamics[J]. IET Control Theory and Applications,2011,5(1):112–122.
[166] Yeh F K, Cheng K Y, Fu L C. Variable Structure-Based Nonlinear Missile Guid-ance/Autopilot Design with Highly Maneuverable Actuators[J]. IEEE Transactionson Control Systems Technology,2004,12(6):944–949.
[167] Yeh F K. Design of Nonlinear Terminal Guidance/Autopilot Controller for Missileswith Pulse Type Input Devices[J]. Asian Journal of Control,2010,12(3):399–412.
[168] Khargonekar P P, Peterson I R, Zhou K. Robust Stabilization of Uncertain LinearSystems: Quadratic Stabilizability and H∞Control IEEE Transactions on Auto-matic Control,1990,35(3):356–361.
[169] Boyd S, Ghaoui L E, Feron E, et al. Linear Matrix Inequalities in Systems andControl Theory[M]. Philadelphia: SIAM,1994.
[170] Hu T, Lin Z, Chen B M. Analysis and Design for Discrete-Time Linear SystemsSubject to Actuator Saturation[J]. Systems and Control Letters,2002,45:97–112.