Optimization of double-impulse rendezvous using gradient-splitting interval optimization algorithm
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摘要: 研究非固定时间的航天器双脉冲交会轨迹优化问题,设计了基于梯度分割区间优化算法(GIOA)。该算法结合所研究问题的特点,使用每次只选择有限个区间进行操作的区间选择策略、基于梯度优化结果的区间分割策略、基于单调性的区间紧缩策略以及约束条件测试和基于梯度的目标优化估计值更新策略等。梯度优化算法仅用于区间分割和目标优化估计值更新,不但没有影响GIOA对区间优化算法全局性和收敛性的继承,同时加快了包含优化解的小宽度区间的出现,提高了目标优化估计值的更新速度,并由此提高了运算效率。区间选择策略的使用,控制了决策变量区间数量的增长,降低了算法运行的存储需求。算例仿真中,成功求解非固定时间双脉冲交会问题,并展示出算法的优势。Abstract: The optimal problem of time-open double-impulse rendezvous was studied and the gradient-splitting interval optimization algorithm (GIOA) was introduced. Considering the characteristics of the problem, GIOA utilized the interval selection strategy which selected a finite number of subintervals to compute, the interval splitting strategy based on the result of the gradient optimization algorithm, the interval contraction strategy based on monotonicity, the test of constraints and the updating strategy of target estimated value based on gradient, etc. As the gradient-algorithm was only used for the interval splitting strategy and the updating strategy of target estimated value, it had no negative effect on GIOA's inheriting of the global characteristic and convergence of the interval optimization algorithm. Simultaneously it accelerated the appearance of an interval containing the optimal value with small width and the updating rate of target estimated value. Thereby the operation efficiency was improved. By the interval selection strategy, the increase of subinterval numbers has been controlled, and the storage costs have been reduced. In the simulation, GIOA solves the optimal problem of time-open double-impulse rendezvous successfully, and shows the advantages of the algorithm.
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[1] 王华,唐国金.用遗传算法求解双冲量最优交会问题[J].中国空间科学技术,2003,23(1):26-30. WANG H,TANG G J.Solving optimal rendezvous using two impulses based on genetic algorithms[J].Chinese Space Science and Technology,2003,23(1):26-30(in Chinese). [2] 戴光明,李晖.DE算法在空间交会中的应用[J].上海航天,2007,24(3):46-49. DAI G M,LI H.Study on application of differential evolution algorithm in space rendezvous[J].Aerospace Shanghai,2007,24(3):46-49(in Chinese). [3] 梁静静,解永春.基于粒子群算法优化双脉冲绕飞问题[J].空间控制技术与应用,2013,39(5):43-47. LIANG J J,XIE Y C.Double-impulsive fly-around problem based on particle swarm optimization algorithm[J].Aerospace Control and Application,2013,39(5):43-47(in Chinese). [4] 姬晓琴,肖利红,陈文辉.基于T-H方程的多脉冲最优交会方法[J].北京航空航天大学学报,2014,40(7):905-909. JI X Q,XIAO L H,CHEN W H.Optimal multi-impulse rendezvous based on T-H equations[J].Journal of Beijing University of Aeronautics and Astronautics,2014,40(7):905-909(in Chinese). [5] 李晨光,肖业伦.多脉冲C-W交会的优化方法[J].宇航学报,2006,27(2):172-176. LI C G,XIAO Y L.Optimization methods of multi-pulse C-W rendezvous[J].Journal of Astronautics,2006,27(2):172-176(in Chinese). [6] LUO Y Z,TANG G J,LEI Y J.Optimal multi-objective linearized impulsive rendezvous[J].Journal of Guidance,Control,and Dynamics,2007,30(2):383-389. [7] GAO X,LIANG B,QIU Y.A PSO algorithm of multiple impulses guidance and control for GEO space robot[C]//Proceedings of the 13th ICARCV Conference.Piscataway,NJ:IEEE Press,2014:1560-1565. [8] XU L M,LIU H,ZHANG T.Optimal transfer orbit design based on multi-pulse thrust[C]//Proceedings of the 32nd Chinese Control Conference.Piscataway,NJ:IEEE Press,2013:5193-5197. [9] 付磊,安效民,覃曌华,等.基于混合遗传算法的多冲量最优变轨[J].航天控制,2013,31(3):15-19. FU L,AN X M,QIN Z H,et al.The optimal multiple-impulse orbit transfer by using hybrid genetic algorithm[J].Aerospace Control,2013,31(3):15-19(in Chinese). [10] MOORE R E,KEARFOTT R B,CLOUD M J.Introduction to interval analysis[M].2nd ed.Philadelphia:Society for Industrial & Applied Mathematics,2009:7-35. [11] JULIANA S,CHU Q P,MULDER J A.Reentry flight clearance using interval analysis[J].Journal of Guidance,Control,and Dynamics,2008,31(5):1295-1307. [12] DE WEERDT E,CHU Q P,MULDER J A.Global fuel optimization for constrained spacecraft formation rotations[C]//Proceedings of AIAA Guidance,Navigation,and Control Conference. Reston:AIAA,2009:1-21. [13] KAMPEN E V.Global optimization using interval analysis[D].Delft:Technische Universiteit Delft,2010:65-89. [14] 高东迎,岳晓奎.基于区间算法的航天器再入轨迹优化[J].科学技术与工程,2012,20(4):852-856. GAO D Y,YUE X K.Trajectory optimization for reentry vehicle via interval algorithm[J].Science Technology and Engineering,2012,20(4):852-856(in Chinese). [15] CHEN T,KAMPEN E V,YU H,et al.Optimization of time-open constrained Lambert rendezvous using interval analysis[J].Journal of Guidance,Control,and Dynamics,2013,36(1):175-184. [16] CASADO L G,GARCIA I,CSENDES T.A new multisection technique in interval methods for global optimization[J].Computing,2000,65(3):263-269. [17] NATARAY P S V,KOTECHA K.An algorithm for global optimization using the Taylor-Bernstein form as inclusion function[J].Journal of Global Optimization,2002,24(4):417-436. [18] 陈诚.基于区间数学的并行全局寻优算法的研究与系统实现[D].上海:上海大学,2014:25-36. CHEN C.Research and system implementation of parallel global optimal algorithm based on interval mathematics[D].Shanghai:Shanghai University,2014:25-36(in Chinese). [19] RATSCHEK H,ROKNE J.New computer methods for global optimization[M].Chichester:Ellis Horwood Ltd.,1988:85-89. [20] KAMPEN E V,CHU Q P,MULDER J A,et al.Nonlinear aircraft trim using interval analysis[C]//Proceedings of AIAA Guidance,Navigation,and Control Conference and Exhibit.Reston:AIAA,2007,4:4073-4087.
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