Input-to-state stability of model-based spacecraft formation control systems with communication constraints

This paper investigates the formation keeping problem for multiple spacecraft in the framework of networked control systems (NCSs). A continuous-time representation of the NCS is considered for the tracking control of relative translational motion between two spacecraft in a leader–follower formation in the presence of communication constraints and system uncertainties. Model-based control schemes are presented, which employ state feedback (when the relative position and velocity vectors are directly measurable) and output feedback (when velocity measurements are not available), respectively, to guarantee input-to-state stability (ISS) of the system. The stability conditions on network transfer intervals are derived as simple eigenvalue tests of a well-structured test matrix. The results are then extended to include network communication delay. Numerical simulations are presented to demonstrate the effectiveness of the control scheme ensuring high formation keeping precision and robustness to nonlinearities and system uncertainties. The proposed controllers are robust not only to structured uncertainties such as system parameter perturbations but also to unstructured uncertainties such as external disturbances and measurement noises.