Control laws for an adaptive optics system for the Palomar Mountain Hale Telescope are described. These are derived using a linear matrix model of the optics, which gives the Hartman-sensor centroids and the science camera wavefront as functions of deformable mirror (DM) commands and atmospheric phase. The matrices defining this system can be directly measured from the optics, some at finer spatial resolution than the wavefront sensor can resolve. A minimum-wavefront compensator feeds back both the wavefront sensor centroids and previous DM commands, using the atmospheric covariance to smooth the response at the finer spatial scale. The DM command feedback provides direct observability of waffle, piston and other modes unobservable in the wavefront sensor. Compensator gains can be updated using Kalman filtering techniques to track the evolution of the atmospheric covariance matrix.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.