This thesis investigates the design of an autonomous controller for the spacecraft of the LISA constellation, developed in collaboration with Thales Alenia Space. LISA relies on interferometric measurements between satellites and requires the onboard test masses, housed within each spacecraft, to follow a trajectory as close as possible to free-fall along the nominal orbit while controlling the spacecraft to remain centered around them. Ensuring this “near-free evolution” while respecting actuation limits and operating in the presence of disturbances and measurement noise, makes the control of the test-mass relative position and velocity a particularly demanding problem. The work first evaluates whether a linear-control strategy can achieve the required performance for a system that is inherently nonlinear.