Augmented MPSP solution to optimal impulsive control for orbital spacecraft

This paper proposes an augmented impulsive model predictive static programming (MPSP) method for orbital control of spacecraft with impulsive inputs. As is well known, the most salient challenge of the underlying problem is how to rapidly determine both the optimal impulse times and inputs that satisfy the terminal conditions. To this end, the variational linearization approach is introduced to address the impulse dynamic of orbital spacecraft. Then, a successive quadratic approximation technique is proposed to handle the minimum-fuel performance index with the summation form of the L2-norm of impulse inputs. Moreover, an alternate-time iteration strategy is proposed to ensure the convergence of the solution through a two-step augmentation. The proposed scheme not only extends the MPSP framework to deal with the minimum-fuel optimal control problem of orbital spacecraft, but also significantly improves the convergence while retaining its computational efficiency. Numerical results verified the performance of the proposed scheme, and compared with conventional approaches, the proposed algorithm demonstrated improved performance in terms of total impulse cost with augmented efficiency.