The Relative Degree of Controllability of Solar Sails in Artificial Lagrangian Orbits

The problem of orbital controllability of solar sails in artificial Lagrangian orbits (ALOs) has received little attention from academics in the field of control. As a result, an important property for missions involving ALOs has not yet been investigated; namely, the degree of controllability (DOC). This thesis examines the relative degree of orbital controllability of solar sails in artificial Lagrangian orbits using the singular values of the controllability Gramian. The relative degree of controllability is determined by comparing the condition number of the controllability Gramian corresponding to individual ALOs. The finite time controllability Gramian is computed for the unstable system, and the magnitude of the individual singular values are used to determine the relative potential for control. Regions of potential for control are revealed for the Earth-Sun system; particularly near the Earth. No conclusions are made regarding absolute controllability, nor is an exact measure of controllability computed for arbitrary ALOs.