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针对传统轨道优化方法无法应用于轨道在线优化的问题,提出了三阶辛普森配点法结合乘子法求解轨道在线优化问题的方法。首先建立变轨的最优化模型;然后,用三阶辛普森配点法将该最优控制问题转化为受约束的非线性规划问题;最后,采用增广拉格朗日乘子法对转化得来的受约束的非线性规划问题进行求解。仿真结果表明,所提出的方法可以得到高精度的轨道优化结果,并且对状态量和控制量的初值选取不敏感,且仿真具有实时性,计算速度快,可以达到在线进行轨道优化的要求。
Aiming at the problem that the traditional orbit optimization method can not be applied to on-line optimization of orbits, a method of solving the orbit on-line optimization problem by using the third-order Simpson collocation method combined with multiplier method is proposed. First, the optimization model of orbit change is established. Then, the optimal control problem is transformed into a constrained nonlinear programming problem by the third-order Simpson collocation method. Finally, the augmented Lagrange multiplier method Constrained nonlinear programming problem. The simulation results show that the proposed method can obtain high-precision orbit optimization results and is insensitive to the initial values of state variables and control variables. Moreover, the simulation has real-time performance and fast calculation speed, which can meet the requirements of on-line orbit optimization.