The James Webb Space Telescope (JWST) Optical Simulation Testbed (JOST) is a tabletop experiment designed to study wavefront sensing and control for a segmented space telescope, including both commissioning and maintenance activities. JOST is complementary to existing testbeds for JWST (e.g. the Ball Aerospace Testbed Telescope TBT) given its compact scale and flexibility, ease of use, and colocation at the JWST Science and Operations Center. The design of JOST reproduces the physics of JWST’s three-mirror anastigmat (TMA) using three custom aspheric lenses. It provides similar quality image as JWST (80% Strehl ratio) over a field equivalent to a NIRCam module, but at 633 nm. An Iris AO segmented mirror stands for the segmented primary mirror of JWST. Actuators allow us to control (1) the 18 segments of the segmented mirror in piston, tip, tilt and (2) the second lens, which stands for the secondary mirror, in tip, tilt and x, y, z positions. We present the full linear control alignment infrastructure developed for JOST, with an emphasis on multi-field wavefront sensing and control. Our implementation of the Wavefront Sensing (WFS) algorithms using phase diversity is experimentally tested. The wavefront control (WFC) algorithms, which rely on a linear model for optical aberrations induced by small misalignments of the three lenses, are tested and validated on simulations.