Optimization of double-impulse rendezvous using gradient-splitting interval optimization algorithm

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.