A bang-bang control law is presented for use in three axis gas jet attitude control systems where precise pointing is required within stringent mass and power limitations. A switching boundary similar to the time optimal one for a double integrator adapts to a disturbance acceleration estimate, a fixed magnitude offset from the phase plane origin being changed in sign whenever the boundary is crossed. The latter feature facilitates optimal acquisition of the ideal limit cycle of preset amplitude, the number of thruster operations being automatically minimized to prolong valve life. In order to render performance largely independent of the iteration period of the microprocessor or digital computer assumed for implementation, at least two successive switching times of the desired control function are predicted, being signed to include the sense of control to be applied. The control law is able to function in the presence of disturbance torques ranging in magnitude from a small fraction of the available control torque to values actually approaching the control torque. The control law is intended to be complemented by a state estimator providing estimates of the disturbance acceleration, body rate and pointing error.