Asynchronous Sequential Machines Research Articles

Fault tolerant control of asynchronous sequential machines with transient faults in non-fundamental mode

This paper addresses fault tolerant corrective control of asynchronous sequential machines (ASMs) against transient faults causing unauthorized state transitions. While the prior work considers only those kinds of faults that comply with fundamental mode operations, the constraint is relaxed in this study. Hence the transient faults may occur not only in fundamental mode, or when the machine stays at a stable state, but also in non-fundamental mode, or when the machine passes through transient states. The condition for overcoming transient faults occurring in non-fundamental mode turns out to be stricter than the case of fundamental mode. A novel scheme of corrective control is presented to make the closed-loop system immune against any fault occurrence in non-fundamental mode. An illustrative example is provided to demonstrate the synthesis procedure of the proposed corrective controller.

A Matrix Approach for the Static Correction Problem of Asynchronous Sequential Machines

This paper investigates the static correction problem of asynchronous sequential machines (ASMs) via semi-tensor product (STP) of matrices. For an input/state ASM, the static correction problem is to find a static state feedback controller to solve model matching. This controller contains no memory units and consists of only some logic gates. First, by STP method, two algebraic forms are derived to describe the dynamics of an input/state ASM and the function of a static state feedback controller, respectively. Then, as two special cases, the static state feedback controllers for no mismatch and only one mismatch are given. Based on these two cases and analyzing reachability of an ASM, a static state feedback controller design for model matching is presented. Moreover, the number of working points this controller contains is the least. Finally, the proposed method is applied to a simple home security system.

Robust corrective control of asynchronous sequential machines with control input and feedback faults

Fault tolerance for asynchronous sequential machines (ASMs) is studied in the framework of corrective control theory. The considered ASM is subjected to adversarial inputs entering the closed-loop system through control input and state feedback channels. If the adversarial input occurs at the control input channel, the machine undergoes unauthorized state transitions. If the adversarial input occurs at the feedback channel, it distorts the state feedback value that is transmitted to the controller. We present a scheme of fault diagnosis on each fault event and the existence condition and design procedure for a corrective controller that invalidates any fault occurrence in an asynchronous mechanism. An illustrative example is provided to validate the proposed fault diagnosis and fault tolerant control methodology.

Model matching and fault‐tolerant control of switched asynchronous sequential machines with transient faults

Switched asynchronous sequential machines (ASMs) are endowed with inherent fault-tolerance capability. This study presents model matching and fault-tolerant control of switched ASMs based on corrective control theory. The objective is to design a corrective controller that matches the stable-state behaviour of the closed-loop system to that of a reference model while overcoming all transient faults infiltrating into the machine. In particular, the proposed control scheme can invalidate not only transient faults causing unauthorised state transitions in single submachine, but also those ones invoking unwanted switching operations between submachines. The existence condition and design procedure for a fault-tolerant corrective controller is addressed in the framework of corrective control. For experimental verification, the proposed scheme is applied to the read-only memory controller for on-board computers implemented on a field programmable gate array system.

Corrective control of parallel interconnected asynchronous sequential machines with output feedback

The problem of controlling two parallel interconnected asynchronous sequential machines (ASMs) by a single corrective controller is studied. The objective is to realise immediate recovery against transient faults that cause unauthorised state transitions to each ASM. Since only output feedback is available to the controller, the correction procedure must be able to accommodate state uncertainty underlying the composite machine. A computationally efficient scheme of controller synthesis is presented in the framework of corrective control theory. To validate the practicality of the scheme, the authors apply the proposed controller to a faulty asynchronous FPGA system in parallel connection. Experimental results confirm the instantaneous fault recovery of the closed-loop system.

Fault tolerant control for a class of interconnected asynchronous sequential machines

This paper considers fault tolerant control for parallel interconnected asynchronous sequential machines (ASMs) governed by a single corrective controller with output feedback. The control objective is to diagnose unauthorized state transitions and to recover the normal input/output behavior of the closed-loop system in an asynchronous mechanism. The existence condition and design algorithm for a fault tolerant controller is addressed in the framework of corrective control. The proposed scheme is efficient in that it does not require complete modeling of parallel composition nor output bursts in the feedback channel. An illustrative example is provided to demonstrate the procedure of controller synthesis.

Exact fault recovery for asynchronous sequential machines with output bursts

This paper presents an enhanced fault tolerant control strategy for a class of input/output asynchronous sequential machines (ASMs) in which output feedback takes the form of bursts. We design a corrective controller that counteracts any unauthorized state transition occurring to the ASM. As the controlled machine is steered on a feedback path, uncertainty about the goal state is reduced by the information that output bursts provide. Hence the use of output bursts in the correction procedure allows the controller to conduct more refined fault recovery than the case of accessing unit output characters as feedback. We present the existence condition and design procedure for a controller that achieves exact fault recovery, and provide an illustrative example to demonstrate the procedure of controller synthesis.

Robust Controllability of Switched Asynchronous Sequential Machines

This paper investigates robust controllability of switched asynchronous sequential machines (ASMs) with permanent faults. A switched ASM can change its mode through a number of submachines in an asynchronous mechanism. The main objective is to develop a condition for the corrective control scheme that makes the closed-loop system robust against permanent faults while matching its stable-state behavior to that of a reference model. The reachability degradation of the switched ASM caused by faults is described in terms of a matrix expression. In the proposed methodology, each submachine serves as a structural redundancy of the switched ASM allowing robust corrective control of the closed-loop system.

Model matching of switched asynchronous sequential machines via matrix approach

ABSTRACTThis paper investigates model matching problem of switched asynchronous sequential machines (ASMs) via semi-tensor product (STP) of matrices. A switched ASM is composed of several input/state ASMs and it cut-overs between submachines in asynchronous mechanism. By using STP method, a switched ASM is depicted as a discrete-time equation form. Under this framework, stable transition matrix and admissible model-input-state transition matrix are defined. Then, two important problems, reachability and optimal control input design of switched ASMs, are discussed by these two new matrices, respectively. Finally, a necessary and sufficient condition for the existence of a controller for model matching is obtained and a practical example on asynchronous error accumulators is provided to show the feasibility of the proposed method.

Fault recovery for cascaded asynchronous sequential machines

In this study, the authors investigate the fault-tolerant control problem of a cascaded asynchronous sequential machine (ASM) in which two ASMs subject to adversarial inputs constitute a cascade composition. The main objective is to develop a corrective controller that can diagnose and tolerate any unauthorised state transition occurring in the cascaded machine. In particular, the authors address fault-tolerant control for two control configurations, one with a state feedback and the other with an output feedback. The existence condition for a controller is found to be different with respect to each feedback availability. The authors apply the proposed control scheme to robust operations of memory scrubbing modules in space-borne computers implemented on field-programmable gate array systems. Experimental results show the practicability of the proposed methodology.

Conditions for Fault Recovery of Interconnected Asynchronous Sequential Machines with State Feedback

Conditions for Fault Recovery of Interconnected Asynchronous Sequential Machines with State Feedback

Calculating skeleton matrix of asynchronous sequential machines based on the semi‐tensor product of matrices

In this study, the problem of calculating the skeleton matrix for asynchronous sequential machine (ASMs) is addressed in the framework of the semi-tensor product (STP) of matrices. By applying the STP of matrices and Boolean algebra, a new algebraic expression of ASMs is deduced. By utilising the algebraic expression, the skeleton matrix of ASMs can be easily derived, then the notion of generalised skeleton matrix is further defined for the ASMs with infinite cycles or critical races, and an algorithm of calculating the generalised skeleton matrix is also proposed. For the model matching problem of input/output ASMs, a novel approach is proposed to calculate reachability indictor and generalised fused skeleton matrix. Two examples are presented to illustrate the effectiveness of the proposed results.

Matrix approach to model matching of composite asynchronous sequential machines

Composite asynchronous sequential machines (ASMs) are studied by a matrix-based approach in this study. A composite ASM consists of several input/state asynchronous machines in a cascading fashion. By using the semi-tensor product method, the algebraic expression of composite ASMs is presented, based on which reachability of composite ASMs is investigated. Then, a necessary and sufficient condition for the existence of a controller for model matching is obtained and an algorithm to design the corresponding controller is established. Finally, an example is proposed to illustrate the effectiveness of the obtained results.

Fault tolerance in switched ASMs with intermittent faults

This study presents new results of fault recovery in switched asynchronous sequential machines (ASMs). The proposed strategy incorporates switching operations and corrective control to tolerate intermittent faults for which any recovery procedure is infeasible for finite time after initial fault occurrence. Each submachine constituting the switched ASM serves as a temporary substitution for the faulty submachine. The reachability of the switched ASM is analysed and a methodology is proposed to determine the existence condition for a corrective controller that achieves fault recovery in an asynchronous mechanism. Using the proposed scheme, the authors implement a fault-tolerant read-only memory controller for on-board computers on field-programmable gate array systems and validate its applicability through a case study.

Model matching of input/output asynchronous sequential machines based on the semi-tensor product of matrices

This paper investigates the model matching problem of input/output asynchronous sequential machines (ASMs) based on the semi-tensor product (STP) of matrices. The controller of the model matching problem is separated to an observer B and a control unit F. When the controller C=(F,B) of the model matching problem exists, the control process is considered with the minimal state set of the controller. Three algorithms which only involve matrix operations are proposed to assign values to the structure matrices of the observer B and the control unit F. In the framework of the STP of matrices, a new algebraic expression for the dynamics of the separated closed-loop system is established and we can easily verify the results of the model matching problem. In this paper, the model matching process is considered with matrix multiplication which is easy to operate. An illustrative example is presented to show the theoretical results and the effectiveness of the proposed algorithms.

Fault-Tolerant Corrective Control With Bounded Delays

Corrective control theory ensures the robust operation of asynchronous sequential machines subject to transient faults. This note is concerned with the problem of fault-tolerant corrective control when the reachability of the asynchronous machines fails to satisfy the existence condition for a corrective controller. We show that with limited reachability, the closed-loop system may recover the normal input/state specification within a bounded delay. Delay-bound controllability and the maximum allowable delay for a given asynchronous machine are analyzed in the framework of corrective control. An algorithm for controller design is presented and demonstrated in an example.

Fault Diagnosis for Composite Asynchronous Sequential Machines with Cascade Composition

Fault Diagnosis for Composite Asynchronous Sequential Machines with Cascade Composition

Static feedback control of switched asynchronous sequential machines

This paper presents model matching of switched asynchronous sequential machines (ASMs) using static feedback control. Comprised of a number of submachines, the switched ASM changes its present mode according to the switching signal generated by the controller. Not only the state transitions in each submachine but also the switching operations over different submachines are carried out in an asynchronous mechanism. The control goal is to make the stable-state behavior of the closed-loop system exhibit the same input/state characteristics as a given reference model. In particular, we focus on designing a static controller, which consists of only logic gates with no memory elements, in order to minimize the controller size. The study of a synthetic example is provided to illustrate the existence condition for a feedback controller and its construction algorithm.

Conditions for Model Matching of Switched Asynchronous Sequential Machines with Output Feedback

Conditions for Model Matching of Switched Asynchronous Sequential Machines with Output Feedback

Static corrective control for asynchronous sequential machines and its application to on‐board computers

Corrective controllers can modify the stable-state behaviour of asynchronous sequential machines in a desirable way. This study addresses a static corrective control scheme formulated as a static feedback law. As no internal states are needed, the use of static corrective controllers greatly reduces the implementation cost. The existence condition for static corrective controllers is found to be more restrictive than that of dynamic controllers. Based on the existence condition, the output of the static corrective controller is assigned so as to match the closed-loop system to a reference model. The proposed static controller is applied to the model matching problem of on-board computer error counters implemented on field-programmable gate array systems.