# State-Bust Feedback Control for Fault Recovery of Input/State Asynchronous Sequential Machines
###### Abstract  
Static corrective controllers are more efficient than dynamic ones since they consist of only logic elements, whereas their existence conditions are more restrictive. In this paper, we present a static corrective control scheme for fault diagnosis and fault tolerant control of input/state asynchronous sequential machines (ASMs) vulnerable to transient faults. The design flexibility of static controllers is enlarged by virtue of using a diagnoser and state bursts. Necessary and sufficient conditions for the existence of a diagnoser and static fault tolerant controller are presented, and the process of controller synthesis is addressed based on the derived condition. Illustrative examples on practical ASMs are provided to show the applicability of the proposed scheme. asynchronous sequential machines (ASMs); static corrective control; fault tolerant control; diagnoser; state bursts +
Footnote †: journal: Applied Sciences  
11 August 2021  
15 October 2021  
Footnote †: journal: Applied Sciences  
11 August 2021  
With this additional argument, the static controller is given greater easiness in generating the control input. The reachability condition required for the proposed controller is the same as that for dynamic ones. To facilitate the design of a diagnoser and controller, we utilize the state burst, or the fast sequence of transient states traversed by the machine during transitions. As a similar subject to the present study, the diagnosability of discrete event systems (DESs) is much investigated in supervisory control of DESs [16; 17; 18; 19; 20]. The proposed diagnoser differs from these results in that while the diagnosers in supervisory control receive traces of inputs (events), the proposed diagnoser utilizes stable bursts traversed by the ASM. Moreover, the diagnosers in supervisory control cannot be applied to corrective control since they do not discriminate between stable and transient states, nor do they comply with fundamental mode operations. Here, transient faults are referred to as short-lived violation of the system's normal behavior, each fault showing no correlation with one another. Typical examples of transient faults include radiation particles, surging voltage, etc. Though not considered in this paper, there are other types of faults--permanent faults and intermittent ones. If the adverse effect of a fault persists indefinitely, it is classified as a permanent fault. Occurrences of permanent faults are mainly attributed to a physical defect or an inadequacy in the design of the system. On the other hand, an intermittent fault is a malfunction of a device or system that occurs at intervals. It may be caused by unstable or marginally stable hardware or inadequacy in the design, for example, by loose wires [21]. The outcome of transient faults caused by the adversarial input bears a strong resemblance to intelligent attacks in cyber-physical systems, where attackers may change the enablement of actuators commanded by a supervisor or sensor readings of the controlled system [22; 23; 24]. However, the adversarial input addressed in this study does not come from an intelligent entity; it is regarded as a randomly generated outer disturbance, e.g., single event upset (SEU) faults in radiation environments [14; 15], or intrinsic faults occurring to the actuator [25; 26; 27]. Still, the considered fault situation is severe since the transient fault may occur at arbitrary moments. Fault diagnosis and fault tolerant control is an area of active research not only in event-driven systems, but also in continuous-time dynamic systems. Notable among the recent results is [28] that addresses adverse effects on time delay between fault occurrence and fault accommodation in T-S fuzzy systems. Further, references [29; 30] present active fault tolerant control for overcoming un-modeled actuator faults while considering time delay attributed to fault diagnosis.