非线性模型预测控制方法在滑翔弹道控制中的应用研究
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摘要
滑翔增程是目前采用的较为有效的一种弹箭增程技术。制导炮弹要通过无动力滑翔飞行达到“远射程、大落角、高精度”的战术技术指标要求,先要对其滑翔弹道进行优化设计,且制导炮弹滑翔启控点散布大和其飞行过程是一个非线性的、时变的、有约束的和受外界随机干扰影响的控制过程,还要对其飞行控制系统进行良好设计。针对以上制导炮弹滑翔增程技术需求,本文研究了制导炮弹弹道优化,并基于非线性模型预测控制理论设计了其控制系统。本文的主要主要工作和意义有以下几个方面：
1)根据鸭式布局制导炮弹的气动特性和运动特点,建立了其六自由度飞行力学模型。基于“瞬时平衡”假设,对制导炮弹的全弹道刚体运动方程组进行简化,建立了纵向平面内炮弹滑翔飞行的质点运动方程,为研究制导炮弹在纵向平面内的最优滑翔飞行提供了数学模型。
2)基于纵向平面内制导炮弹质心运动模型,结合约束条件与最大射程目标函数,建立了滑翔最大射程弹道优化模型。以直接参数化法和序列二次规划(SQP)方法相结合的优化算法,作为制导炮弹弹道优化的算法。将常规无滑翔最大射程弹道与滑翔最大射程弹道进行比较,得到了滑翔段弹道区别于常规弹道的一些弹道特性。并将考虑了控制余量的滑翔弹道作为滑翔控制跟踪的方案弹道。
3)提出了采用具有解析形式控制律的非线性预测控制(简记为ANMPC)方法来设计制导炮弹滑翔控制器,实现对滑翔方案弹道的跟踪控制。为了设计方便,将控制器分成质心外回路和姿态内回路两个回路进行设计。质心外回路(ANMPC质心控制器)实现对质心位置(高度和侧偏)指令的跟踪,并获得攻角和侧滑角指令。姿态内回路包含ANMPC姿态控制器和ANMPC倾斜稳定控制器,其中ANMPC姿态控制器实现对攻角和侧滑角指令的跟踪控制,获得升降舵偏角和方向舵偏角；而ANMPC倾斜稳定控制器则实现滚转角的稳定,获得副翼偏角。为了分析ANMPC控制器的设计参数,即控制阶数和预测时域,对控制器性能的影响规律,以ANMPC控制器姿态内回路为例进行了仿真分析。在获得设计参数对控制性能的影响规律之后,根据控制器性能要求确定了控制阶数和预测时域,并对ANMPC控制器应用于制导炮弹滑翔控制进行了数值仿真。仿真结果表明ANMPC控制器具有良好的控制效果,实现滑翔增程的目的。
4)研究了基于序列二次规划(SQP)的非线性模型预测控制(SNMPC)在制导炮弹滑翔段控制中的应用,对于可能在制导炮弹滑翔段控制中应用的各种形式的SNMPC方法,包括经典SNMPC、多速率SNMPC和实时SNMPC,进行详细介绍、仿真和分析,目的在于寻找适合于制导炮弹快变动态特性的SNMPC。三种SNMPC的控制效果基本相同,但经典SNMPC控制律求解最慢,多速率和实时SNMPC控制律求解较快。通过对这些SNMPC方法进行分析改进,最终提出了改进型实时SNMPC方法。此改进型实时SNMPC方法在减小在线优化中的待优变量数量的基础上充分利用优化过程中的有用信息实现了控制律的快速求解,因此比较适合运用于设计制导炮弹滑翔控制器。
5)提出了一种新的组合型NMPC(INMPC)方法,此INMPC方法综合了SNMPC方法和ANMPC方法的优点,SNMPC方法能显式地处理有约束的控制问题,ANMPC方法能快速求解控制律。通过SNMPC方法和ANMPC方法的合理组合得到的组合型NMPC方法,克服了SNMPC方法的控制延迟和ANMPC方法没有考虑约束的缺点。因此,INMPC方法更适合于制导炮弹快变动态特性,并能满足其控制的约束条件。设计了制导炮弹INMPC滑翔控制器,通过仿真表明INMPC控制器能满足制导炮弹非线性、多约束和快时变的特点,且INMPC控制器具有一定的鲁棒性。
The gliding flight of projectile is an effective range-extended technology at present. In order to satisfy tactical guideline of 'large range, big terminal angle, high accuracy', the trajectory of the guided projectile with gliding flight is needed to be optimized. Because the gliding control initial point dispersion is larger and the gliding flight process is a nonlinear, time-varying, constrained and effected by random outside disturbances control process, the flight control system is also needed to be designed well. For the requirements of glide range-extended technology, the guided projectile trajectory optimization and nonlinear model predictive control system are designed and researched in the dissertation. The main contents are depicted as follows:
1) According to the aerodynamic and motion characteristics of the canard configuration guided projectile, the six degree of freedom flight dynamic model is established. Based on instantaneous balance assumption, some reductions are applied to the six degree of freedom flight dynamic equations, and the longitudinal particle trajectory equation of the gliding flight projectile is proposed. This longitudinal particle trajectory equation is the numerical model for studying the guided projectile optimal gliding flight.
2) Together with the guided projectile longitudinal particle trajectory equation, constraint conditions and the maximal gliding range objective function, the maximal gliding range trajectory optimizing model is established. The optimal algorithm including direct parametric method and sequential quadratic programming is applied to solve the guided projectile optimal trajectory. The gliding trajectory characteristics are obtained compared with the ordinal trajectory. Taking the gliding trajectory that is cosindering control ability as the concept trajectory for the gliding controller.
3) To design guided projectile gliding controller, a nonlinear model predictive control method with an analytical control law (ANMPC) is proposed. For simplify designing, the guided projectile ANMPC gliding controller is divided into a guidance loop and an attitude control loop. The ANMPC guidance loop converts the mass point altitude and side deflection commands to angel-of-attack and side slip commands. The attitude control loop includes an ANMPC attitude controller and an ANMPC rolling stabilizing controller. The ANMPC attitude controller converts angel-of-attack and side slip commands to elevator and rudder fin deflections, and the ANMPC rolling stabilizing controller converts roll angle command to aileron fin deflection. In order to analyze the design parameters i.e. control order and predictive horizon affecting the ANMPC controller perfonnance, the ANMPC control loop is demonstrated through numerical simulation. And then, the guided projectile ANMPC gliding controller is demonstrated to track the concept gliding trajectory. The simulation results show that the ANMPC gliding controller possesses good control performance and the guided projectile achieves extending range.
4) To design guided projectile gliding controller, another nonlinear model predictive control method basis on sequential quadratic programming (SNMPC) is proposed. There are some kinds of SNMPC methods, including classical SNMPC, multi-rate SNMPC and real-time SNMPC, that may be used to design the gliding controller. In order to finding a kind of SNMPC method which is more appropriate for the guided projectile fast dynamic characteristics, the introductions, simulations and analyses of the SNMPC methods and the comparisons between them are carried our in detail. The control performance of the three kinds SNMPC method is almost the same, but the control law of the classical SNMPC is solved slowly, and the control law of the multi-rate and real-time SNMPC method is solved most fast. And then the classical and real-time SNMPC methods are improved. The improved SNMPC methods decrease the on-line optimal variable numbers and make use of the useful information during the optimization progress, so that they could solve control laws faster. The improved real-time SNMPC is most appropriate for the guided projectile.
5) A new integrated nonlinear model predictive control (INMPC) method is developed. INMPC method, which is obtained by appropriately synthesizing SNMPC and ANMPC methods, combines the advantages of them. SNMPC method could explicitly handle constrained control problems. ANMPC method could provide control law immediately. INMPC method avoids the disadvantages that the control delay of SNMPC method and ANMPC method lack of considering constraints, so that it is adapt to guided projectile fast dynamic characteristics and deals with constraints. An INMPC gliding controller is designed for the guided projectile and numerical simulations are demonstrated. The simulation results indicate that the INMPC gliding controller is able to meet the guided projectile nonlinear, constrained and fast time-varying characteristics, and the INMPC gliding controller possesses robustness.
1)根据鸭式布局制导炮弹的气动特性和运动特点,建立了其六自由度飞行力学模型。基于“瞬时平衡”假设,对制导炮弹的全弹道刚体运动方程组进行简化,建立了纵向平面内炮弹滑翔飞行的质点运动方程,为研究制导炮弹在纵向平面内的最优滑翔飞行提供了数学模型。
2)基于纵向平面内制导炮弹质心运动模型,结合约束条件与最大射程目标函数,建立了滑翔最大射程弹道优化模型。以直接参数化法和序列二次规划(SQP)方法相结合的优化算法,作为制导炮弹弹道优化的算法。将常规无滑翔最大射程弹道与滑翔最大射程弹道进行比较,得到了滑翔段弹道区别于常规弹道的一些弹道特性。并将考虑了控制余量的滑翔弹道作为滑翔控制跟踪的方案弹道。
3)提出了采用具有解析形式控制律的非线性预测控制(简记为ANMPC)方法来设计制导炮弹滑翔控制器,实现对滑翔方案弹道的跟踪控制。为了设计方便,将控制器分成质心外回路和姿态内回路两个回路进行设计。质心外回路(ANMPC质心控制器)实现对质心位置(高度和侧偏)指令的跟踪,并获得攻角和侧滑角指令。姿态内回路包含ANMPC姿态控制器和ANMPC倾斜稳定控制器,其中ANMPC姿态控制器实现对攻角和侧滑角指令的跟踪控制,获得升降舵偏角和方向舵偏角；而ANMPC倾斜稳定控制器则实现滚转角的稳定,获得副翼偏角。为了分析ANMPC控制器的设计参数,即控制阶数和预测时域,对控制器性能的影响规律,以ANMPC控制器姿态内回路为例进行了仿真分析。在获得设计参数对控制性能的影响规律之后,根据控制器性能要求确定了控制阶数和预测时域,并对ANMPC控制器应用于制导炮弹滑翔控制进行了数值仿真。仿真结果表明ANMPC控制器具有良好的控制效果,实现滑翔增程的目的。
4)研究了基于序列二次规划(SQP)的非线性模型预测控制(SNMPC)在制导炮弹滑翔段控制中的应用,对于可能在制导炮弹滑翔段控制中应用的各种形式的SNMPC方法,包括经典SNMPC、多速率SNMPC和实时SNMPC,进行详细介绍、仿真和分析,目的在于寻找适合于制导炮弹快变动态特性的SNMPC。三种SNMPC的控制效果基本相同,但经典SNMPC控制律求解最慢,多速率和实时SNMPC控制律求解较快。通过对这些SNMPC方法进行分析改进,最终提出了改进型实时SNMPC方法。此改进型实时SNMPC方法在减小在线优化中的待优变量数量的基础上充分利用优化过程中的有用信息实现了控制律的快速求解,因此比较适合运用于设计制导炮弹滑翔控制器。
5)提出了一种新的组合型NMPC(INMPC)方法,此INMPC方法综合了SNMPC方法和ANMPC方法的优点,SNMPC方法能显式地处理有约束的控制问题,ANMPC方法能快速求解控制律。通过SNMPC方法和ANMPC方法的合理组合得到的组合型NMPC方法,克服了SNMPC方法的控制延迟和ANMPC方法没有考虑约束的缺点。因此,INMPC方法更适合于制导炮弹快变动态特性,并能满足其控制的约束条件。设计了制导炮弹INMPC滑翔控制器,通过仿真表明INMPC控制器能满足制导炮弹非线性、多约束和快时变的特点,且INMPC控制器具有一定的鲁棒性。
The gliding flight of projectile is an effective range-extended technology at present. In order to satisfy tactical guideline of 'large range, big terminal angle, high accuracy', the trajectory of the guided projectile with gliding flight is needed to be optimized. Because the gliding control initial point dispersion is larger and the gliding flight process is a nonlinear, time-varying, constrained and effected by random outside disturbances control process, the flight control system is also needed to be designed well. For the requirements of glide range-extended technology, the guided projectile trajectory optimization and nonlinear model predictive control system are designed and researched in the dissertation. The main contents are depicted as follows:
1) According to the aerodynamic and motion characteristics of the canard configuration guided projectile, the six degree of freedom flight dynamic model is established. Based on instantaneous balance assumption, some reductions are applied to the six degree of freedom flight dynamic equations, and the longitudinal particle trajectory equation of the gliding flight projectile is proposed. This longitudinal particle trajectory equation is the numerical model for studying the guided projectile optimal gliding flight.
2) Together with the guided projectile longitudinal particle trajectory equation, constraint conditions and the maximal gliding range objective function, the maximal gliding range trajectory optimizing model is established. The optimal algorithm including direct parametric method and sequential quadratic programming is applied to solve the guided projectile optimal trajectory. The gliding trajectory characteristics are obtained compared with the ordinal trajectory. Taking the gliding trajectory that is cosindering control ability as the concept trajectory for the gliding controller.
3) To design guided projectile gliding controller, a nonlinear model predictive control method with an analytical control law (ANMPC) is proposed. For simplify designing, the guided projectile ANMPC gliding controller is divided into a guidance loop and an attitude control loop. The ANMPC guidance loop converts the mass point altitude and side deflection commands to angel-of-attack and side slip commands. The attitude control loop includes an ANMPC attitude controller and an ANMPC rolling stabilizing controller. The ANMPC attitude controller converts angel-of-attack and side slip commands to elevator and rudder fin deflections, and the ANMPC rolling stabilizing controller converts roll angle command to aileron fin deflection. In order to analyze the design parameters i.e. control order and predictive horizon affecting the ANMPC controller perfonnance, the ANMPC control loop is demonstrated through numerical simulation. And then, the guided projectile ANMPC gliding controller is demonstrated to track the concept gliding trajectory. The simulation results show that the ANMPC gliding controller possesses good control performance and the guided projectile achieves extending range.
4) To design guided projectile gliding controller, another nonlinear model predictive control method basis on sequential quadratic programming (SNMPC) is proposed. There are some kinds of SNMPC methods, including classical SNMPC, multi-rate SNMPC and real-time SNMPC, that may be used to design the gliding controller. In order to finding a kind of SNMPC method which is more appropriate for the guided projectile fast dynamic characteristics, the introductions, simulations and analyses of the SNMPC methods and the comparisons between them are carried our in detail. The control performance of the three kinds SNMPC method is almost the same, but the control law of the classical SNMPC is solved slowly, and the control law of the multi-rate and real-time SNMPC method is solved most fast. And then the classical and real-time SNMPC methods are improved. The improved SNMPC methods decrease the on-line optimal variable numbers and make use of the useful information during the optimization progress, so that they could solve control laws faster. The improved real-time SNMPC is most appropriate for the guided projectile.
5) A new integrated nonlinear model predictive control (INMPC) method is developed. INMPC method, which is obtained by appropriately synthesizing SNMPC and ANMPC methods, combines the advantages of them. SNMPC method could explicitly handle constrained control problems. ANMPC method could provide control law immediately. INMPC method avoids the disadvantages that the control delay of SNMPC method and ANMPC method lack of considering constraints, so that it is adapt to guided projectile fast dynamic characteristics and deals with constraints. An INMPC gliding controller is designed for the guided projectile and numerical simulations are demonstrated. The simulation results indicate that the INMPC gliding controller is able to meet the guided projectile nonlinear, constrained and fast time-varying characteristics, and the INMPC gliding controller possesses robustness.
引文
[1]祁载康.制导弹药技术[M].第1版.北京：北京理工大学出版社,2002
[2]王儒策,刘荣忠,苏玳等.灵巧弹药的构造及作用[M].第1版.北京：兵器工业出版社,2001
[3]郭锡福.现代炮弹增程技术[M].第1版.北京：兵器工业出版社,1997
[4]朱如华.增大火炮射程的技术途径[J].现代军事.1995,(7)：24-29
[5]张友安,胡云安.导弹控制和制导的非线性设计方法[M].第1版.北京：国防工业出版社,2003
[6]Devand E, Harcaut J P, Siguerdidjane H. Three-axes missile autopilot design:from linear to nonlinear control strategies [J]. Journal of Guidance, Control, and Dynamics, 2001,24(1):61-74
[7]Steinberg M L. Comparison of intelligent, adaptive, and nonlinear flight control laws [J]. Journal of Guidance, Control, and Dynamics,2001,24(4):693-699
[8]刘智平,周凤岐,周军.战术导弹现代自动驾驶仪设计方法综述[J].航天控制,2006,24(5)：91-96
[9]宋闯,魏毅寅.非线性系统理论在导弹控制中的应用研究进展与展望[J].战术导弹技术,2003,(6)：48-53
[10]卜奎晨,刘莉.末制导炮弹发展趋势及其研究方向[J].系统工程与电子技术,2006,28(11)：1109-1111
[11]牟宇,程振轩,王江.制导炮弹技术现状与发展方向[J].飞航导弹.2008,(7)：33-37
[12]Jepps G. Linearised optimal control and application to a gliding projectile [C]. AIAA Atmospheric Flight Mechanics Conference,1985
[13]Costello M.F. Range extension and accuracy improvement of an advanced projectile using canard control [C]. AIAA Atmospheric Flight Mechanics Conference in Baltimore, Maryland,1995
[14]Fleck V. Increase of range for an artillery projectile by using the lifting force [C].19th International Symposium on Ballistics,1996
[15]丁松滨,王中原.弹丸滑翔弹道的能量法研究[J].兵工学报,2002,23(1)：10-13
[16]丁松滨.滑翔增程炮弹的外弹道理论与应用[D].南京理工大学博士论文,2002
[17]史金光,王中原,易文俊等.滑翔增程弹弹道特性分析[J].兵工学报,2006,27(2)：210-214
[18]史金光,王中原,易文俊.滑翔增程弹方案弹道特性的研究[J].弹道学报,2003,15(1)：51-54
[19]史金光,王中原,许厚谦.滑翔增程弹鸭式舵的气动设计与分析[J].弹道学报,2006,18(4)：33-37
[20]史金光,王中原,曹小兵.滑翔增程弹箭滑控段弹体运动模式对增程效率的影响[J].兵工学报,2007,28(6)：651-655
[21]史金光.炮弹滑翔弹道设计与控制弹道特性研究[D].南京理工大学博士论文,2008
[22]张军娜,王军波.滑翔增程炮弹弹道仿真与优化设计[J].军械工程学院学报,2003,15(2)：42-45
[23]张吉堂,周海清.底排—火箭复合增程弹弹道参数优化研究[J].弹箭与制导学报,1998,16(2)：35-38
[24]I. Michael Ross, Fariba Fahroo. A perspective on methods for trajectory optimization[R]. AIAA/AAS Astrodynamics Specialist Conference and Exhibit 5-8 August 2002, Monterey, California. American Institute of Aeronautics and Astronautles. AIAA-2002-4727
[25]赫孝量,葛照强.最优化与最优控制[M].第1版.西安：西安交通大学出版社,2009
[26]Hitoshi M., Jason C.H. Chuang. Minimum-fuel trajectory along entire flight profile for a hypersonic vehicle with constraint [R]. AIAA-98-4122
[27]周浩,陈万春,殷兴良.高超声速飞行器滑行航迹优化[J].北京航空航天大学学报,2006,32(5)：513-517
[28]周浩,周韬,陈万春,殷兴良.高超声速滑翔飞行器引入段弹道优化[J].宇航学报,2006,27(5)：970-973
[29]雍恩米,唐国金,陈磊.助推—滑翔式导弹中段弹道方案的初步分析[J].国防科技大学学报,2006,28(6)：6-10
[30]李瑜,杨志红,崔乃刚.助推—滑翔导弹弹道优化研究[J].宇航学报,2008,29(1),66-71
[31]Chen Gang, Hu Ying, Wang Ziming, et al. Optimization design on RLV reentry trajectory based on genetic algorithm [J]. Journal of Solid Rocket Technology,2006, 29(4):235-238
[32]Chen Gang, Xu Min, Wang Ziming, et al. RLV reentry trajectory multi-objective optimization design based on NSGA-Ⅱ algorithm [R]. AIAA-2005-6131
[33]陈金明.制导航弹最优滑翔弹道计算方法研究[D].国防科学技术大学硕士论文, 2007
[34]席裕庚.预测控制[M].第1版.北京：国防工业出版社,1993
[35]Morari M., Lee J.H. Model predictive control:past, present and future. Computers and Chemical Engineering,1999, (23):667-682
[36]钱积新,赵均,徐祖华.预测控制[M].第1版.北京：化学工业出版社,2007
[37]Henson M.A. Nonlinear model predictive control:current status and future directions. Computers and Chemical Engineering,1998, (23):187-202
[38]陈红,刘志远,解小华.非线性模型预测控制的现状与问题[J].控制与决策,2001,16(4)：385-391
[39]丁宝苍.预测控制的理论与方法[M].第1版.北京：机械工业出版社,2008
[40]Meadows E S, Rawlings J B. Receding horizon control with an infinite horizon [C]. Proceedings of American Control Conference, San Francisco, California,1993
[41]Keerthi S S, Gilibert E G. Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems:stability and moving horizon approximations [J]. Journal of Optimization Theory and Application,1988,57(2):265-293
[42]Mayne D Q, Michalska H. Receding horizon control of nonlinear systems [J]. IEEE Transactions on Automatic Control,1990,35(7):814-824
[43]Michalska H, Mayne D Q. Robust receding horizon control of constrained nonlinear systems [J]. IEEE Transactions on Automatic Control,1993,38(11):1623-1633
[44]Yang T H, Polak E. Moving horizon control of nonlinear systems with input saturation, disturbances and plant uncertainty [J]. International Journal of Control,1993,58(4): 875-903
[45]De Oliveira S L, Morari M. Robust model predictive control for nonlinear systems [C]. Proceedings of the 33rd IEEE Conference on Decision and control,1994
[46]Chen H, Allgower F. A quasi-infinite horizon nonlinear model predictive scheme with guaranteed stability [J]. Automatica,1998,34(10):1205-1217
[47]Chen W H, Balance D J, O'reilly J. Optimization of attraction domains of nonlinear MPC via LMI methods [C]. Proceedings of American Control Conference,2001
[48]Nicolao G D, Magni L, Scattolini R. On the robustness properties of receding-horizon control with terminal constraints [J]. IEEE Transactions on Automatic Control,1996, 41(3):451-453
[49]Scokaert P O M, Rawlings J B, Meadows E S. Discrete-time stability with perturbations:application to model predictive control [J]. Automatica,1997,33(3): 364-370
[50]Lee J H, Yu Z H. Worst-case formulations of model predictive control for systems with bounded parameters [J]. Automatica,1997,33(5):763-781
[51]Magni L, Nicolao G D, Scattolini R, el at. Robust model predictive control for nonlinear discrete-time systems [J]. International Journal of Robust and Nonlinear Control,2003,13(3-4):229-246
[52]Chu D, Chen T, Marquez H J. Finite horizon robust model predictive control with terminal cost constraints [J]. IEE Process Control Theory Application,2006,153(2): 156-166
[53]Chen W H, Balance D J, O'reilly J. Model predictive control of nonlinear systems: Computational burden and stability [J]. IEE Process Control Theory Application,2000, 147(4):387-393
[54]Cannon M. Efficient nonlinear model predictive control algorithms [J]. Annual Reviews in Control,2004,28(2):229-237
[55]Martinsen F, Biegler L T, Foss B A. Application of optimization algorithms to nonlinear MPC [C].15th Triennial World Congress, Barcelona, Spain
[56]Cannon M, Kouvaritakis B. Efficient constrained model predictive control with asymptotic optimality [C]. Proceedings of the 41st IEEE Conference on Decision and Control, Lasvages, Nevada USA,2002
[57]Lee Y I, Kouvaritakis B, Cannon M. Constrained receding horizon predictive control for nonlinear systems [J]. Automatica,2002,38(12):2093-2102
[58]Tousain R L, Bosgra O H. Efficient dynamic optimization for nonlinear model predictive control-application to a high-density poly-ethylene grade change problem [C]. Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia,2000
[59]Diehl M, Bock H G, Schloder J P, et al. Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations [J]. Journal of Process Control,2002,12(4):577-585
[60]Diehl M, Findeisen R, Allgower F, et al. Stability of nonlinear model predictive control in the presence of errors due to numerical online optimization [C]. Proceedings of the 42nd IEEE Conference on Decision and Control Maui, Hawaii USA,2003
[61]Diehl M, Findeisen R, Allgower F, et al. Nominal stability of real-time iteration scheme for nonlinear model predictive control [J]. IEE Process Control Theory Application, 2005,152(3):296-308
[62]Ohtsuka T, Fujii H A. Real-time optimization algorithm for nonlinear receding-horizon control [J]. Automatica,1997,33(6):1147-1154
[63]Muske K R, Howse J W, Hansen G A. Lagrangian solution methods for nonlinear model predictive control [C]. Proceedings of the American Control Conference Chicago, Illinois,2000
[64]Muske K R. Lagrangian quadratic programming approach for linear model predictive control [C]. Proceedings of the American Control Conference Anchorage, AK,2002
[65]Scokaert P O M, Mayne D Q, Rawlings J B. Suboptimal model predictive control (feasibility implies stability) [J]. IEEE Transactions on Automatic Control,1999, 44(3):648-654
[66]Bacic M, Cannon M, Kouvaritakis B. Invariant sets for feedback linearization based nonlinear predictive control [J]. IEE Process Control Theory Application,2005,152(3): 259-265
[67]Cannon M, Kouvaritakis B. Fast suboptimal predictive control with guaranteed stability [J]. Systems & Control Letters,1998,35(1):19-29
[68]Cannon M, Deshmukh V, Kouvaritakis B. Nonlinear model predictive control with polytypic invariant sets [J]. Automatica,2003,39(8):1487-1494
[69]Zheng A. A computationally efficient nonlinear MPC algorithm [C]. Proceedings of the American Control Conference, Albuquerque, New Mexico,1997
[70]Halldorsson U, Fikart M, Unbehauen H. Multirate nonlinear predictive control [C]. Proceedings of the American Control Conference Anchorage, AK,2002
[71]Halldorsson U, Fikart M, Unbehauen H. Nonlinear predictive control with multirate optimisation step lengths [J]. IEE Process Control Theory Application,2005,152(3): 273-284
[72]Zheng A, Allgower F. Towards a practical nonlinear predictive control algorithm with guaranteed stability for large-scale systems [C]. Proceedings of the American Control Conference, Philadelphia, Pennsylvania,1998
[73]Rossiter J A, Grieder P. Using interpolation to improve efficiency of multiparametric predictive control [J]. Automatica,2005,41(4):637-643
[74]Jung J C, Hess R A. Precise flight-path control using a predictive algorithm [J]. Journal of Guidance, Control, and Dynamics,1991,14(5):936-942
[75]Burchett B, Costello M. Model predictive lateral pulse jet control of an atmospheric rocket [J]. Journal of Guidance. Control, and Dynamics,2002,25(5):860-867
[76]Ollerenshaw D. Costello M. Model predictive control of a direct fire projectile equipped with canards [C]. AIAA Atmospheric Flight Mechanics Conference and Exhibit. San Francisco, California,2005
[77]Slegers N. Model Predictive Control of a Low Speed Munition [C]. AIAA Atmospheric Flight Mechanics Conference and Exhibit, Hilton Head, South Carolina,2007
[78]Miotto D P, LePome R C. Design of a Model Predictive Control Flight Control System for a Reusable Launch Vehicle [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, Texas,2003
[79]Ping L. Nonlinear predictive controllers for continuous systems [J]. Journal of Guidance, Control, and Dynamics,1994,17(3):553-560
[80]Ping L, Pierson B L. Aircraft terrain following based on a nonlinear continuous predictive control approach [J]. Journal of Guidance, Control, and Dynamics,1995, 18(4):817-823
[81]崔枯涛,耿云海,案泽威等.非线性模型预测控制在地形跟踪中的应用[J].航空兵器,1997,4：6-10
[82]崔祜涛,耿云海,崔平远等.非线性预测控制在巡航导弹地形跟踪中的应用[J].飞行力学,1998,16(1)：65-69
[83]崔祜涛,王炳全,耿云海等.非线性预测控制在巡航弹地形跟踪上的应用[J].哈尔滨工业大学学报,1998,30(3)：111-114
[84]贺有智.非线性预测控制在质量矩导弹姿态控制系统设计上的应用[J].战术导弹技术,2005,(1)：47-51
[85]张晓宇,贺有智,王子才.质量矩拦截弹的非线性预测控制器设计[J].弹箭与制导学报,2006,26(2)：885-889
[86]沈冬祥,张晓宇.基于蚁群遗传算法优化的质量矩拦截弹非线性预测控制研究[J].机械与电子,2007,(9)：3-7
[87]Upreti V, Talole S E, Phadke S B. Predictive Estimation and Control based Missile Autopilot Design [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Providence, Rhode Island,2004
[88]Chen W H, Ballance D J, Gawthrop P J. Optimal control of nonlinear systems:a predictive control approach [J]. Automatica,2003,39(4):633-614
[89]Chen W H. Predictive control of general nonlinear systems using approximation [J]. IEE Process Control Theory Application,2004,151(2):137-144
[90]Slegers N, Costello M. Nonlinear Model Predictive Control of a 6 DOF Air Vehicle [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California,2005
[91]方炜,姜长生.基于自适应模糊系统的空天飞行器非线性[J].航空学报,2008,29(4)：988-994
[92]方炜,姜长生.一类基于模糊系统的非线性鲁棒自适应预测控制[J].西安交通大学学报,2008,42(6)：669-673
[93]Mehra R K, Gopinathan M, Sistu P B. Robust Nonlinear Model Predictive Control for Agile Interceptor Missiles [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Boston, MA,1998
[94]Van Soest W R, Chu Q P, Mulder J A. Combined feedback linearization and constrained model predictive control for entry flight [J]. Journal of Guidance, Control, and Dynamics,2006,29(2):427-434
[95]Recasens J J, Chu Q P, Mulder J A. Robust Model Predictive Control of a Feedback Linearized System for a Lifting-body Re-entry Vehicle [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California,2005
[96]Van Soest W R, Chu Q P, Mulder J A, et al. Robust Model Predictive Control of a Feedback Linearized Nonlinear F-16/MATV Aircraft Model [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Keystone, Colorado,2006
[97]方炜,姜长生,朱亮.空天飞行器再入制导的预测控制用[J].航空学报,2006,27(6)：1216-1222
[98]方炜,姜长生.空天飞行器再入过程姿态预测控制律设计[J].系统工程与电子技术,2007,29(8)：1317-1321
[99]Kang Y, Hedrick J K. Design of Nonlinear Model Predictive Controller for a Small Fixed-wing Unmanned Aerial Vehicle [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Keystone, Colorado,2006
[100]雷娟棉,居贤铭,吴甲生.自旋尾翼鸭式布局导弹的滚转特性[J].北京理工大学学报,2004,24(8)：657-659
[101]张晓旻,李怀念,程养民等.自由滚转尾翼飞行器滚转特性分析[J].固体火箭技术,2008,31(4)：307-309
[102]邓帆,陈少松,谭献忠等.不同尾翼鸭式布局远程弹在跨／超声速的气动特性实验研究[J].实验流体力学,2010,24(2)：46-50
[103]张源,许江宁,卞鸿巍.GPS姿态测量系统对惯性导航系统误差修正能力分析[J].情 报指挥控制系统与仿真技术,2005,27(5)：96-100
[104]冯绍军,胡国辉,袁信.低成本IMU/GPS组合导航系统研究[J].南京航空航天大学学报,1998,30(6)：641-645
[105]徐明友.火箭外弹道学[M].第1版.哈尔滨：哈尔滨工业大学出版社,2004
[106]韩子鹏.弹箭外弹道学[M].第1版.北京：北京理工大学出版社,2008
[107]钱杏芳,林瑞雄,赵亚男.导弹飞行力学[M].第1版.北京：北京理工大学出版社,2000
[108]Hans Georg Bock, Karl J. Plitt. A multiple algorithm for direct solution of optimal control problems[C]. Proceeding of the ninth IFAC world congress, Budapest,1984, 242-247
[109]屈菊香.直接多重打靶法在轨迹优化方面的应用[J].飞行力学,1992,10(1)：13-21
[110]胡朝江,陈士橹.改进直接多重打靶算法及其应用[J].飞行力学,2004,22(1)：14-17
[111]张光澄,王文娟,韩会磊等.非线性最优化计算方法[M].第1版.北京：高等教育出版社,2007
[112]陈宝林.最优化理论与算法[M].第2版.北京：清华大学出版社,2005
[113]Brian C. Fabien. Some tools for the direct solution of optimal control problems[J]. Advances in Engineering Software,1998,29(1):45-61
[2]王儒策,刘荣忠,苏玳等.灵巧弹药的构造及作用[M].第1版.北京：兵器工业出版社,2001
[3]郭锡福.现代炮弹增程技术[M].第1版.北京：兵器工业出版社,1997
[4]朱如华.增大火炮射程的技术途径[J].现代军事.1995,(7)：24-29
[5]张友安,胡云安.导弹控制和制导的非线性设计方法[M].第1版.北京：国防工业出版社,2003
[6]Devand E, Harcaut J P, Siguerdidjane H. Three-axes missile autopilot design:from linear to nonlinear control strategies [J]. Journal of Guidance, Control, and Dynamics, 2001,24(1):61-74
[7]Steinberg M L. Comparison of intelligent, adaptive, and nonlinear flight control laws [J]. Journal of Guidance, Control, and Dynamics,2001,24(4):693-699
[8]刘智平,周凤岐,周军.战术导弹现代自动驾驶仪设计方法综述[J].航天控制,2006,24(5)：91-96
[9]宋闯,魏毅寅.非线性系统理论在导弹控制中的应用研究进展与展望[J].战术导弹技术,2003,(6)：48-53
[10]卜奎晨,刘莉.末制导炮弹发展趋势及其研究方向[J].系统工程与电子技术,2006,28(11)：1109-1111
[11]牟宇,程振轩,王江.制导炮弹技术现状与发展方向[J].飞航导弹.2008,(7)：33-37
[12]Jepps G. Linearised optimal control and application to a gliding projectile [C]. AIAA Atmospheric Flight Mechanics Conference,1985
[13]Costello M.F. Range extension and accuracy improvement of an advanced projectile using canard control [C]. AIAA Atmospheric Flight Mechanics Conference in Baltimore, Maryland,1995
[14]Fleck V. Increase of range for an artillery projectile by using the lifting force [C].19th International Symposium on Ballistics,1996
[15]丁松滨,王中原.弹丸滑翔弹道的能量法研究[J].兵工学报,2002,23(1)：10-13
[16]丁松滨.滑翔增程炮弹的外弹道理论与应用[D].南京理工大学博士论文,2002
[17]史金光,王中原,易文俊等.滑翔增程弹弹道特性分析[J].兵工学报,2006,27(2)：210-214
[18]史金光,王中原,易文俊.滑翔增程弹方案弹道特性的研究[J].弹道学报,2003,15(1)：51-54
[19]史金光,王中原,许厚谦.滑翔增程弹鸭式舵的气动设计与分析[J].弹道学报,2006,18(4)：33-37
[20]史金光,王中原,曹小兵.滑翔增程弹箭滑控段弹体运动模式对增程效率的影响[J].兵工学报,2007,28(6)：651-655
[21]史金光.炮弹滑翔弹道设计与控制弹道特性研究[D].南京理工大学博士论文,2008
[22]张军娜,王军波.滑翔增程炮弹弹道仿真与优化设计[J].军械工程学院学报,2003,15(2)：42-45
[23]张吉堂,周海清.底排—火箭复合增程弹弹道参数优化研究[J].弹箭与制导学报,1998,16(2)：35-38
[24]I. Michael Ross, Fariba Fahroo. A perspective on methods for trajectory optimization[R]. AIAA/AAS Astrodynamics Specialist Conference and Exhibit 5-8 August 2002, Monterey, California. American Institute of Aeronautics and Astronautles. AIAA-2002-4727
[25]赫孝量,葛照强.最优化与最优控制[M].第1版.西安：西安交通大学出版社,2009
[26]Hitoshi M., Jason C.H. Chuang. Minimum-fuel trajectory along entire flight profile for a hypersonic vehicle with constraint [R]. AIAA-98-4122
[27]周浩,陈万春,殷兴良.高超声速飞行器滑行航迹优化[J].北京航空航天大学学报,2006,32(5)：513-517
[28]周浩,周韬,陈万春,殷兴良.高超声速滑翔飞行器引入段弹道优化[J].宇航学报,2006,27(5)：970-973
[29]雍恩米,唐国金,陈磊.助推—滑翔式导弹中段弹道方案的初步分析[J].国防科技大学学报,2006,28(6)：6-10
[30]李瑜,杨志红,崔乃刚.助推—滑翔导弹弹道优化研究[J].宇航学报,2008,29(1),66-71
[31]Chen Gang, Hu Ying, Wang Ziming, et al. Optimization design on RLV reentry trajectory based on genetic algorithm [J]. Journal of Solid Rocket Technology,2006, 29(4):235-238
[32]Chen Gang, Xu Min, Wang Ziming, et al. RLV reentry trajectory multi-objective optimization design based on NSGA-Ⅱ algorithm [R]. AIAA-2005-6131
[33]陈金明.制导航弹最优滑翔弹道计算方法研究[D].国防科学技术大学硕士论文, 2007
[34]席裕庚.预测控制[M].第1版.北京：国防工业出版社,1993
[35]Morari M., Lee J.H. Model predictive control:past, present and future. Computers and Chemical Engineering,1999, (23):667-682
[36]钱积新,赵均,徐祖华.预测控制[M].第1版.北京：化学工业出版社,2007
[37]Henson M.A. Nonlinear model predictive control:current status and future directions. Computers and Chemical Engineering,1998, (23):187-202
[38]陈红,刘志远,解小华.非线性模型预测控制的现状与问题[J].控制与决策,2001,16(4)：385-391
[39]丁宝苍.预测控制的理论与方法[M].第1版.北京：机械工业出版社,2008
[40]Meadows E S, Rawlings J B. Receding horizon control with an infinite horizon [C]. Proceedings of American Control Conference, San Francisco, California,1993
[41]Keerthi S S, Gilibert E G. Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems:stability and moving horizon approximations [J]. Journal of Optimization Theory and Application,1988,57(2):265-293
[42]Mayne D Q, Michalska H. Receding horizon control of nonlinear systems [J]. IEEE Transactions on Automatic Control,1990,35(7):814-824
[43]Michalska H, Mayne D Q. Robust receding horizon control of constrained nonlinear systems [J]. IEEE Transactions on Automatic Control,1993,38(11):1623-1633
[44]Yang T H, Polak E. Moving horizon control of nonlinear systems with input saturation, disturbances and plant uncertainty [J]. International Journal of Control,1993,58(4): 875-903
[45]De Oliveira S L, Morari M. Robust model predictive control for nonlinear systems [C]. Proceedings of the 33rd IEEE Conference on Decision and control,1994
[46]Chen H, Allgower F. A quasi-infinite horizon nonlinear model predictive scheme with guaranteed stability [J]. Automatica,1998,34(10):1205-1217
[47]Chen W H, Balance D J, O'reilly J. Optimization of attraction domains of nonlinear MPC via LMI methods [C]. Proceedings of American Control Conference,2001
[48]Nicolao G D, Magni L, Scattolini R. On the robustness properties of receding-horizon control with terminal constraints [J]. IEEE Transactions on Automatic Control,1996, 41(3):451-453
[49]Scokaert P O M, Rawlings J B, Meadows E S. Discrete-time stability with perturbations:application to model predictive control [J]. Automatica,1997,33(3): 364-370
[50]Lee J H, Yu Z H. Worst-case formulations of model predictive control for systems with bounded parameters [J]. Automatica,1997,33(5):763-781
[51]Magni L, Nicolao G D, Scattolini R, el at. Robust model predictive control for nonlinear discrete-time systems [J]. International Journal of Robust and Nonlinear Control,2003,13(3-4):229-246
[52]Chu D, Chen T, Marquez H J. Finite horizon robust model predictive control with terminal cost constraints [J]. IEE Process Control Theory Application,2006,153(2): 156-166
[53]Chen W H, Balance D J, O'reilly J. Model predictive control of nonlinear systems: Computational burden and stability [J]. IEE Process Control Theory Application,2000, 147(4):387-393
[54]Cannon M. Efficient nonlinear model predictive control algorithms [J]. Annual Reviews in Control,2004,28(2):229-237
[55]Martinsen F, Biegler L T, Foss B A. Application of optimization algorithms to nonlinear MPC [C].15th Triennial World Congress, Barcelona, Spain
[56]Cannon M, Kouvaritakis B. Efficient constrained model predictive control with asymptotic optimality [C]. Proceedings of the 41st IEEE Conference on Decision and Control, Lasvages, Nevada USA,2002
[57]Lee Y I, Kouvaritakis B, Cannon M. Constrained receding horizon predictive control for nonlinear systems [J]. Automatica,2002,38(12):2093-2102
[58]Tousain R L, Bosgra O H. Efficient dynamic optimization for nonlinear model predictive control-application to a high-density poly-ethylene grade change problem [C]. Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia,2000
[59]Diehl M, Bock H G, Schloder J P, et al. Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations [J]. Journal of Process Control,2002,12(4):577-585
[60]Diehl M, Findeisen R, Allgower F, et al. Stability of nonlinear model predictive control in the presence of errors due to numerical online optimization [C]. Proceedings of the 42nd IEEE Conference on Decision and Control Maui, Hawaii USA,2003
[61]Diehl M, Findeisen R, Allgower F, et al. Nominal stability of real-time iteration scheme for nonlinear model predictive control [J]. IEE Process Control Theory Application, 2005,152(3):296-308
[62]Ohtsuka T, Fujii H A. Real-time optimization algorithm for nonlinear receding-horizon control [J]. Automatica,1997,33(6):1147-1154
[63]Muske K R, Howse J W, Hansen G A. Lagrangian solution methods for nonlinear model predictive control [C]. Proceedings of the American Control Conference Chicago, Illinois,2000
[64]Muske K R. Lagrangian quadratic programming approach for linear model predictive control [C]. Proceedings of the American Control Conference Anchorage, AK,2002
[65]Scokaert P O M, Mayne D Q, Rawlings J B. Suboptimal model predictive control (feasibility implies stability) [J]. IEEE Transactions on Automatic Control,1999, 44(3):648-654
[66]Bacic M, Cannon M, Kouvaritakis B. Invariant sets for feedback linearization based nonlinear predictive control [J]. IEE Process Control Theory Application,2005,152(3): 259-265
[67]Cannon M, Kouvaritakis B. Fast suboptimal predictive control with guaranteed stability [J]. Systems & Control Letters,1998,35(1):19-29
[68]Cannon M, Deshmukh V, Kouvaritakis B. Nonlinear model predictive control with polytypic invariant sets [J]. Automatica,2003,39(8):1487-1494
[69]Zheng A. A computationally efficient nonlinear MPC algorithm [C]. Proceedings of the American Control Conference, Albuquerque, New Mexico,1997
[70]Halldorsson U, Fikart M, Unbehauen H. Multirate nonlinear predictive control [C]. Proceedings of the American Control Conference Anchorage, AK,2002
[71]Halldorsson U, Fikart M, Unbehauen H. Nonlinear predictive control with multirate optimisation step lengths [J]. IEE Process Control Theory Application,2005,152(3): 273-284
[72]Zheng A, Allgower F. Towards a practical nonlinear predictive control algorithm with guaranteed stability for large-scale systems [C]. Proceedings of the American Control Conference, Philadelphia, Pennsylvania,1998
[73]Rossiter J A, Grieder P. Using interpolation to improve efficiency of multiparametric predictive control [J]. Automatica,2005,41(4):637-643
[74]Jung J C, Hess R A. Precise flight-path control using a predictive algorithm [J]. Journal of Guidance, Control, and Dynamics,1991,14(5):936-942
[75]Burchett B, Costello M. Model predictive lateral pulse jet control of an atmospheric rocket [J]. Journal of Guidance. Control, and Dynamics,2002,25(5):860-867
[76]Ollerenshaw D. Costello M. Model predictive control of a direct fire projectile equipped with canards [C]. AIAA Atmospheric Flight Mechanics Conference and Exhibit. San Francisco, California,2005
[77]Slegers N. Model Predictive Control of a Low Speed Munition [C]. AIAA Atmospheric Flight Mechanics Conference and Exhibit, Hilton Head, South Carolina,2007
[78]Miotto D P, LePome R C. Design of a Model Predictive Control Flight Control System for a Reusable Launch Vehicle [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, Texas,2003
[79]Ping L. Nonlinear predictive controllers for continuous systems [J]. Journal of Guidance, Control, and Dynamics,1994,17(3):553-560
[80]Ping L, Pierson B L. Aircraft terrain following based on a nonlinear continuous predictive control approach [J]. Journal of Guidance, Control, and Dynamics,1995, 18(4):817-823
[81]崔枯涛,耿云海,案泽威等.非线性模型预测控制在地形跟踪中的应用[J].航空兵器,1997,4：6-10
[82]崔祜涛,耿云海,崔平远等.非线性预测控制在巡航导弹地形跟踪中的应用[J].飞行力学,1998,16(1)：65-69
[83]崔祜涛,王炳全,耿云海等.非线性预测控制在巡航弹地形跟踪上的应用[J].哈尔滨工业大学学报,1998,30(3)：111-114
[84]贺有智.非线性预测控制在质量矩导弹姿态控制系统设计上的应用[J].战术导弹技术,2005,(1)：47-51
[85]张晓宇,贺有智,王子才.质量矩拦截弹的非线性预测控制器设计[J].弹箭与制导学报,2006,26(2)：885-889
[86]沈冬祥,张晓宇.基于蚁群遗传算法优化的质量矩拦截弹非线性预测控制研究[J].机械与电子,2007,(9)：3-7
[87]Upreti V, Talole S E, Phadke S B. Predictive Estimation and Control based Missile Autopilot Design [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Providence, Rhode Island,2004
[88]Chen W H, Ballance D J, Gawthrop P J. Optimal control of nonlinear systems:a predictive control approach [J]. Automatica,2003,39(4):633-614
[89]Chen W H. Predictive control of general nonlinear systems using approximation [J]. IEE Process Control Theory Application,2004,151(2):137-144
[90]Slegers N, Costello M. Nonlinear Model Predictive Control of a 6 DOF Air Vehicle [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California,2005
[91]方炜,姜长生.基于自适应模糊系统的空天飞行器非线性[J].航空学报,2008,29(4)：988-994
[92]方炜,姜长生.一类基于模糊系统的非线性鲁棒自适应预测控制[J].西安交通大学学报,2008,42(6)：669-673
[93]Mehra R K, Gopinathan M, Sistu P B. Robust Nonlinear Model Predictive Control for Agile Interceptor Missiles [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Boston, MA,1998
[94]Van Soest W R, Chu Q P, Mulder J A. Combined feedback linearization and constrained model predictive control for entry flight [J]. Journal of Guidance, Control, and Dynamics,2006,29(2):427-434
[95]Recasens J J, Chu Q P, Mulder J A. Robust Model Predictive Control of a Feedback Linearized System for a Lifting-body Re-entry Vehicle [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California,2005
[96]Van Soest W R, Chu Q P, Mulder J A, et al. Robust Model Predictive Control of a Feedback Linearized Nonlinear F-16/MATV Aircraft Model [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Keystone, Colorado,2006
[97]方炜,姜长生,朱亮.空天飞行器再入制导的预测控制用[J].航空学报,2006,27(6)：1216-1222
[98]方炜,姜长生.空天飞行器再入过程姿态预测控制律设计[J].系统工程与电子技术,2007,29(8)：1317-1321
[99]Kang Y, Hedrick J K. Design of Nonlinear Model Predictive Controller for a Small Fixed-wing Unmanned Aerial Vehicle [C]. AIAA Guidance, Navigation, and Control Conference and Exhibit, Keystone, Colorado,2006
[100]雷娟棉,居贤铭,吴甲生.自旋尾翼鸭式布局导弹的滚转特性[J].北京理工大学学报,2004,24(8)：657-659
[101]张晓旻,李怀念,程养民等.自由滚转尾翼飞行器滚转特性分析[J].固体火箭技术,2008,31(4)：307-309
[102]邓帆,陈少松,谭献忠等.不同尾翼鸭式布局远程弹在跨／超声速的气动特性实验研究[J].实验流体力学,2010,24(2)：46-50
[103]张源,许江宁,卞鸿巍.GPS姿态测量系统对惯性导航系统误差修正能力分析[J].情 报指挥控制系统与仿真技术,2005,27(5)：96-100
[104]冯绍军,胡国辉,袁信.低成本IMU/GPS组合导航系统研究[J].南京航空航天大学学报,1998,30(6)：641-645
[105]徐明友.火箭外弹道学[M].第1版.哈尔滨：哈尔滨工业大学出版社,2004
[106]韩子鹏.弹箭外弹道学[M].第1版.北京：北京理工大学出版社,2008
[107]钱杏芳,林瑞雄,赵亚男.导弹飞行力学[M].第1版.北京：北京理工大学出版社,2000
[108]Hans Georg Bock, Karl J. Plitt. A multiple algorithm for direct solution of optimal control problems[C]. Proceeding of the ninth IFAC world congress, Budapest,1984, 242-247
[109]屈菊香.直接多重打靶法在轨迹优化方面的应用[J].飞行力学,1992,10(1)：13-21
[110]胡朝江,陈士橹.改进直接多重打靶算法及其应用[J].飞行力学,2004,22(1)：14-17
[111]张光澄,王文娟,韩会磊等.非线性最优化计算方法[M].第1版.北京：高等教育出版社,2007
[112]陈宝林.最优化理论与算法[M].第2版.北京：清华大学出版社,2005
[113]Brian C. Fabien. Some tools for the direct solution of optimal control problems[J]. Advances in Engineering Software,1998,29(1):45-61