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首页> 外文期刊>Journal of aerospace engineering >Hybrid QPSO and SQP Algorithm with Homotopy Method for Optimal Control of Rapid Cooperative Rendezvous
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Hybrid QPSO and SQP Algorithm with Homotopy Method for Optimal Control of Rapid Cooperative Rendezvous

机译：同伦方法的混合QPSO和SQP算法在快速协作交会中的最优控制

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The fuel-optimal rapid cooperative rendezvous problem between two spacecraft under finite thrust, based on the indirect method, was investigated and converted into a two-point boundary value problem (TPBVP) in this study by using Pontryagin's maximum principle. First, normalization processing of initial costate variables with unknown scopes was carried out to restrict them on a unit hypersphere. The quantum particle swarm optimization (QPSO) algorithm was used to preliminarily search for the initial costate variables of the high-dimensional energy-optimal problem, and then the results obtained were further corrected by the sequence quadratic programming (SQP) algorithm. The preceding combinatorial optimization algorithm with normalization technique considerably increases the probability of finding the approximate initial values of the globally optimal solution. Based on these modified initial costates, the smooth energy-optimal results were transitioned to the desirable nonsmooth fuel-optimal results by the homotopy method. Through the combination of the preceding effective techniques, the following difficulties were successfully overcome: (1) The optimal control was a strongly nonlinear problem under continuous high thrust; (2) in a cooperative rendezvous, the terminal rendezvous orbit was unknown and the parameter variables were doubled, leading to high-dimensional control equations; and (3) the narrow convergence domain of the shooting function made the shooting process extremely sensitive to the initial guess of the costates. The simulation results demonstrate not only the feasibility of the indirect method in solving fuel-optimal cooperative rendezvous, but also the superiority over another orbit transfer optimization method, the hybrid method. (c) 2019 American Society of Civil Engineers.
机译：基于庞特里亚金的最大原理，基于间接方法，研究了两个航天器在有限推力作用下的燃料最优快速协同会合问题，并将其转换为两点边值问题（TPBVP）。首先，对具有未知范围的初始costate变量进行归一化处理，以将其限制在单位超球面上。使用量子粒子群优化算法（QPSO）初步搜索高维能量最优问题的初始代价变量，然后用序列二次规划（SQP）算法对所得结果进行进一步校正。先前使用归一化技术的组合优化算法大大增加了找到全局最优解的近似初始值的可能性。基于这些修改过的初始costates，通过同伦方法将平滑的能量最优结果转换为理想的非平滑燃料最优结果。通过将上述有效技术相结合，成功克服了以下困难：（1）最优控制是在连续高推力作用下的强非线性问题； （2）在一个合作交会点，最终交会轨道是未知的，并且参数变量增加了一倍，从而产生了高维控制方程； （3）射击功能的狭窄收敛域使射击过程对肋骨的最初猜测极为敏感。仿真结果不仅证明了间接方法在解决燃料最优协同集合方面的可行性，而且还证明了其优于另一种轨道转移优化方法-混合方法的优越性。 （c）2019美国土木工程师学会。

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