Control Lyapunov Function Based Finite-Horizon Optimal Control for Repointing of a Spacecraft

Abstract

This paper addresses the problem of optimally repointing the optical axis of a spacecraft to align with the target direction. A new metric defining the repointing error is proposed where the corresponding kinematic equations provide a simple and convenient form for control design. The proposed control integrates a Control Lyapunov Function (CLF) approach with a sliding mode controller which simultaneously guarantees the optimality and robustness of the closed-loop system. Firstly, a CLF based control scheme is used to ensure that the state optimally converges to the sliding surface. Then a fixed-time non-singular terminal sliding mode controller is employed to provide robust convergence to the origin along the sliding surface. The convergence time is finite for any initial states and is thus useful for applications with critical time constraints. The region of attraction and convergence time is analyzed. Finally, numerical investigations are conducted to verify the effectiveness and superiority of the proposed algorithm with respect to the classical CLF method.