This paper presents a control theoretic approach to realizing fault tolerance in asynchronous sequential circuits. The considered asynchronous circuit is assumed to work in space environment and is subject to faults caused by total ionizing dose (TID) effects. In our setting, TID effects cause permanent changes in state transition characteristics of the asynchronous circuit. Under a certain condition of reachability redundancy, it is possible to design a corrective controller so that the closed-loop system can maintain the normal behavior despite occurrences of TID faults. As a case study, the proposed control scheme is applied to an asynchronous arbiter implemented in FPGA.