Compensation for infinite number of actuator failures/faults using output feedback control is of both theoretical and practical importance. However, it is challenging and thus still remains open so far in the field of adaptive control. In this paper, we solve this problem by proposing a new tuning function based control scheme. It is demonstrated that all the signals of the closed-loop system are globally bounded and the steady-state tracking error can be reduced as small as desired, regardless of a possibility that there are infinite number of actuator failures. Moreover, when the number of actuator failures becomes finite, our scheme further guarantees that both the tracking error and state estimation errors converge to zero asymptotically. (C) 2017 Published by Elsevier Inc.