Optimization of bounded low-thrust rendezvous with terminal constraints by interval analysis

A new indirect resolution method of an optimal control problem is proposed in this paper. And the optimization of the spacecraft low-thrust rendezvous with the fuel-minimum index to a safe region under the collision avoidance constraints is investigated. The objective is to minimize the fuel consumption in a power-limited low-thrust system, which leads to a bounded continuous control. The number of thrust arcs is unknown and the terminal positions in the rendezvous' safe region are unfixed for this optimization problem. The indirect resolution method of the optimal control employs deterministic interval analysis and gradient-based method to obtain the initial guess of the co-state variables. The interval analysis is used to sufficiently split, contract and clip the initial search space. And the gradient-based method is to determine the initial guess for each remained sub-space. Aiming at a low-thrust control system with the upper bound of acceleration of 5e−4 m/s2, numerical results are given to validate the proposed optimization method.