Optimal Sliding Mode Attitude Synchronization Control for Autonomous Docking to an Out-of-Control Target

In order to solve the attitude synchronization control problem for an on-orbit servicing spacecraft autonomous docking to an out-of-control target in the presence of unknown bounded disturbances, system uncertainties and measurement noise, an optimal sliding mode control law is presented in this paper. By using the optimal control method, the first sliding surface was obtained, which is an optimal sliding surface. Then, the second sliding surface was obtained by the integrating the signum function of the first sliding surface, which was used to autonomously compensate the disturbances and model uncertainties. Furthermore, an optimal sliding mode control law was designed by the sliding mode control method. The relative attitude variables will converge to the origin in the sense of optimality with a predetermined quadratic cost function after the system reaching the first sliding surface. Simulation results verified the effectiveness of the designed optimal sliding mode control law, and the robustness to the unknown bounded disturbances, system uncertainties and measurement noise were also demonstrated.