Direct adaptive control with bounded tracking errors

Direct model reference adaptive control procedures were developed to control linear plants which satisfy a positivity condition. Using a combination of proportional and integral adaptive gains these procedures achieved asymptotically perfect model output tracking with a large class of time-variable input commands. However, if perfect output tracking is not possible due to output measuring disturbances or due to the internal structure of the plant, the adaptive control system may diverge. Such divergence is now shown to be eliminated if the pure integration in the adaptive gains is replaced with a first order pole.