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Corrective control of asynchronous sequential machines is to design a feedback controller so that the behaviour of the closed-loop asynchronous machine matches that of a prescribed model. This study proposes a control scheme for asynchronous machines with uncontrollable external inputs, over which the controlling agent has no influence. The existence condition for an appropriate controller and its design procedure are analytically presented. It is shown that an asynchronous machine must have additional reachability to achieve control objectives against transitions caused by uncontrollable inputs. In particular, the authors apply the proposed control scheme to implementing single-event-upset error counters used by error detection and correction circuits. The authors' result demonstrates that corrective control can be employed in real digital systems.