# A Survey on Dynamic Corrective Control of Asynchronous Sequential Machines
## 5 Fault-Tolerant Control
### Permanent Faults and Intermittent Faults  
Fault tolerance against permanent faults is more difficult than the case of transient faults since their adverse effect lasts indefinitely unless repaired by external operators [72; 73]. Fault-tolerant corrective control against permanent faults has been studied pertaining to two fault aspects: permanent state faults and permanent state transition faults. The former represents a class of faults that degenerate a subset of states, namely, the ASM cannot reach failed states any more after fault occurrences. The latter class indicates that part of the state transitions in the considered ASM is permanently lost by fault. It is clear that both fault types severely reduce the reachability of the machine.  
In [74], the author first addresses a strategy of fault diagnosis and fault-tolerant corrective control against permanent state faults happening to input/output ASMs. Figure 6a shows the notion of permanent state faults introduced in [74]. Here, the state \(X\) is divided into \(p+1\) mutually exclusive subsets  
\[X:=X_{N}\dot{\cup}X_{f_{1}}\dot{\cup}\cdots\dot{\cup}X_{f_{p}},\]  
where \(X_{N}\) is the nominal state set and \(X_{f_{i}}\) is the \(i\)th failure mode with the \(i\)th permanent fault input \(f_{i}\), \(i=1,\ldots,p\). With no fault input, \(\Sigma\) undertakes state transitions between states of \(X_{N}\). When \(f_{i}\) happens, \(\Sigma\) irreversibly falls into the \(i\)th failure mode \(X_{f_{i}}\) and its subsequent behavior is confined within \(X_{f_{i}}\). The author of [74] presents the necessary and sufficient condition and synthesis procedure for a fault-tolerant controller which makes the closed-loop system retain the normal input/output behavior. Another study applies the controller of [74] to materializing a robust Johnson counter employed as the scrub controller in the satellite solid-state data recorder (SSDR) system. The result of [74] is further extended later so that the corrective controller achieves fault tolerance as well as model matching under the occurrence of a maximally allowable number of permanent state faults.  
Figure 6b illustrates the fault-tolerant corrective control system for an input/state ASM \(\Sigma\) subject to permanent state transition faults. In the framework of this configuration, a state feedback fault-tolerant controller is proposed to achieve both model matching and tolerance against permanent state transition faults.  
Intermittent faults [75; 76] lie between transient faults and permanent ones. In general, intermittent faults indicate a kind of faults in which influence on the machine lasts for a finite time after the initial occurrence. Intermittent faults are more general than transient faults since one can regard transient faults as intermittent ones having zero duration of their adverse effects. Compared with transient and permanent faults, studies examining the toleration of intermittent faults are rare in the field of corrective control. A study was reported that provides a preliminary result on the diagnosis and tolerance of intermittent faults in input/state ASMs. On the other hand, ref. [77] analyzes the degraded reachability of switched ASMs caused by intermittent faults and proposes a state-feedback corrective controller that tolerates the influence of any intermittent fault under the single-fault scenario.