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1、硕士学位论文序列二次规划(SQP)算法及其在航天器追逃中的应用THE SEQUENTIAL QUADRATIC PROGRAM-MING (SQP) ALGORITHM AND APPLYING TOPURSUIT-EVASION OF THE SPACECRAFT罗 建2012 年 7 月国内图书分类号：V412.4+1 学校代码：10213国际图书分类号：533 密级： 公开工学硕士学位论文序列二次规划(SQP)算法及其在航天器追逃中的应用硕 士 研 究 生：罗 建导 师：张秋华 教授申 请 学 位：工学硕士学 科：固体力学所 在 单 位：航天学院答 辩 日 期：2012 年 7 月授 予
2、 学 位 单 位：哈尔滨工业大学Classified Index: V412.4+1U.D.C: 533Dissertation for the Master Degree in EngineeringTHE SEQUENTIAL QUADRATIC PROGRAM-MING (SQP) ALGORITHM AND APPLYING TOPURSUIT-EVASION OF THE SPACECRAFTCandidate：Supervisor：Academic Degree Applied for：Speciality：Affiliation：Date of Defence：Luo JianP
3、rof. Zhang QiuhuaMaster of EngineeringSolid MechanicsSchool of AstronauticsJuly, 2012Degree-Conferring-Institution： Harbin Institute of Technology哈尔滨工业大学工学硕士学位论文摘 要两航天器追逃问题可以描述成一个零和微分对策模型，是一个典型的双边最优控制问题。本文假设两个航天器都被赋予相当的机动能力，且都在连续恒定小推力的作用下飞行；当追踪航天器在某一瞬时达到逃逸航天器的瞬时位置时，追逃过程结束；在追逃过程中，追踪航天器的目的是以最快的时间追上逃逸航
4、天器，相反逃逸航天器则是想将追踪的时间无限期延长。本文主要研究的内容是在三维模型下的两航天器追逃策略问题，基于绝对坐标系下，建立两航天器的动力学模型，应用鞍点平衡法解决零和微分对策问题，该方法首先是从最优解存在的必要条件入手，结合边界条件和横截条件进行分析，推导出双边最优控制问题最优解存在的必要条件，然后将双边最优控制问题转化为单边最优控制问题，最后采用数值算法对单边最优控制问题进行求解。本文采用序列二次规划(SQP)算法对单边最优控制问题进行求解，在应用序列二次规划(SQP)算法方法进行求解时，需要一个初始的猜测解，这个猜测解由遗传算法(GA)估算出来。这种方法可以认为是一种预处理技术，并对
5、这类问题十分有效，但目前来看，对于反复寻找这种初值解的尝试是一项具有挑战性的工作。本文研究得出以下结论： (1) 双边最优控制问题可以等价的转化为单边最优控制问题，应用序列二次规划和遗传算法相互结合的数值算法对于解决两航天器追逃对策问题十分有效，并且 GA-SQP 算法具有很好的稳定性，能够成功找到两航天器的最优飞行轨迹和最佳飞行策略； (2) 两航天器之间的初值距离是影响对策时间的一个重要因素。两航天器具有相同的初始高度和初始速度时，对策时间的长短与两航天器之间的初始距离成正比关系;初始速度的大小和方向也是决定对策时间的一个重要因素，在两航天器具有不同的初始高度和初始速度时，对策时间的长短与
6、距离成反比关系。关键词：微分对策；航天器；追逃；遗传算法；序列二次规划算法-I-哈尔滨工业大学工学硕士学位论文AbstractThe problem of pursuit-evasion about two spacecraft is formulated an evasivespacecraft by a pursuing spacecraft as a zero-sum differential game, which is atwo-sided optimization problem. Each spacecraft is given a modest capability toman
7、euver, a low, constant, thrust-to-mass ratio is assumed for both spacecraft. Thegame has been terminated if the pursuing spacecraft reaches the instantaneousposition of the evading spacecraft. In the pursuit-evasion process, the objective ofthe pursuer is to minimize the time for interception, where
8、as the evader tries to delayit indefinitely.The contents of this paper studies is the three-dimensional orbital pursuit-evasion strategy,Based on the absolute coordinate system, establishment of two spacecraft dynamic model,andthen deduced from the bilateral optimal control problem. Saddle-point equ
9、ilibrium solutionsare using direct numerical method that uses the analytical necessary conditions,boundary conditions and transversality conditons to find the optimal control for theproblem, and then constitute a two-sided optimization problem, transform into asingle-objective optimal control proble
10、m, finally using the numerical method to solve thesingle-objective optimal control problem and the sequential quadratic programmingalgorithm (SQP) is adopted to solve this problem. When using the SQP algorithm aninitial guess of the solution is required, and this is provided by generating anapproxim
11、ate solution using genetic algorithms. The evolutionary algorithm isemployed as a preprocessing technique and is very useful in this context and can beseen an pre-processing, and trial-and-error selection of first-attempt values for thevariables involved is very challenging for the problem at hand.T
12、he conclusion of this contents have two point. First, transforming thetwo-sided optimization problem into a single-objective optimal control problem ，and then using the sequential quadratic programming algorithm combining genetic- II -哈尔滨工业大学工学硕士学位论文algorithms is very effective and has good stabilit
13、y to find the optimal flight path of the twospacecraft and the best flight strategy. Second, assignment distance between the two spacecraftis an important factor in countermeasures time. The initial distance is proportional to the lengthof the response time between the two spacecraft, when two space
14、craft have the same initialheight and initial velocity; When the two spacecraft have different initial height and initialvelocity, the length of the response time is inversely proportional to the distance, the velocitymagnitude and direction is also an important factor. When they have different initial heightinitial velocity,Countermeasures for the duration of the inversely proportional relation withdistance.Keywords: differential game; spacecraft; pursuit; genetic algorithm; sequentialquadratic programming algorithm- III -哈尔滨工业大学工学硕士学位论文目录摘 要. IAbstract. II第 1 章 绪论 . 11.1 课题背景 .
