无需初值猜测的间接法小推力轨道设计

Low-thrust Trajectory Optimization Using Indirect Shooting Method without Initial Costate Guess

在间接法求解小推力轨道计算中,通过先选取合适的性能指标,并对小推力最优控制问题转化为两点边值问题的方程在开普勒轨道附近线性展开,有效增强了协态变量初值收敛性,使得该方法无需对协态变量初值进行反复的随机猜测,迭代过程也不需要人工干预,提高了轨道搜索应用中的计算效率.之后再对性能指标进行迭代优化,可获得逼近于Bang-bang控制的控制方案.

Based on the optimal control theory,the optimal control problem of the lowthrust trajectory is transformed into a sequence of nonlinear two-point bound-value problem （TPBVP）.In the process of solving the TPVBP,the initial constates need repeated random guesses and iterative computations.In order to enhance the convergence of the iteration, we select an appropriate performance index,and then linearize the equations of the TPBVP around the Keplerian orbits.For multi-revolution transfers,we use the multi-splicing Keplerian arcs instead of the multi-revolution Lambert trajectory to ensure the effectiveness of the linearization.The method is totally automatic with multiple iterations.With this method,we can get the results within 3 ~ 5 iterations,and the random guess of the initial constates is unnecessary.Then by iterative optimization of the performance index,we can get a better control strategy.