Time-optimal deployment of a tethered subsatellite based on differential inclusion

This paper presents the nonlinear time-optimal control for the three-dimensional deployment process of a tethered subsatellite model, which also takes tether elasticity and the mission-related state-control constraints into consideration. Instead of the commonly used state-space model, a second-order differential inclusion formulation is exploited in this study to achieve a significant reduction of the number of system variables. The optimal control is solved by discretizing the optimal control problem based on a direct algorithm, and numerically solving the resulting large-scale optimization problem via a nonlinear programming solver. The case studies in the paper well demonstrate the performance of the proposed strategy.