The Laser Interferometer Space Antenna ( LISA ) mission is a planned gravitational wave detector consisting of three spacecraft in heliocentric orbit . Laser interferometry is used to measure distance fluctuations between test masses aboard each spacecraft to the picometer level over a 5 million kilometer separation . Laser frequency fluctuations must be suppressed in order to meet the measurement requirements . Arm - locking , a technique that uses the constellation of spacecraft as a frequency reference , is a proposed method for stabilizing the laser frequency . We consider the problem of arm - locking using classical optimal control theory and find that our designs satisfy the LISA requirements .