基于配点法的轨道在线优化方法研究

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.

Research of on-line orbit optimization based on direct collocation method

In order to settle the on-line orbit optimization problem,a method based on a direct collocation method is put forward.Firstly,a trajectory optimization control model is established.Secondly,the trajectory optimization model is dispersed into a discrete model by using the direct collocation method.Then,we change the optimization problem into a nonlinear programming problem.Finally,we solve the nonlinear programming problem by using the Lagrange multiplier method.The simulation results demonstrate that direct collocation method combined with the Lagrange multiplier method is not sensitive to the initial conditions we choose.The results also show that an accurate trajectry optimization result can be got by using this method in a short period.Therefore,direct collocation method is a viable one for us to settle the on-line optimization problem.