On Correctability Of Classical And Stochastic Discrete Event Systems

Failure diagnosability and correctability of discrete-event systems (DESs) are widely studied. In this paper, we mainly focus on the question about correcting failure events of discrete-event systems under the condition that the controller takes control, for making the system run within accepted states. By the formalization of correctable state, we propose a method to verify correctable states based on the state tree. On the classical presupposition, we propose a corrective method based on cycle of states; on the stochastic presupposition, a corrective formula, by which the controller does optimal correction is proposed. Meanwhile, we extend the topic of correctability and discuss the relation between controllability and correctability, and the relation among failure correctability, diagnosability and prognosability. The main contribution of the thesis is as follows.The thesis deeply investigates the correctability of classical discrete event systems. Firstly, we propose the formalization of correctable state based on state tree, the formalization of correctable language based on correctable state and an algorithm verifying correctable state. Secondly, we discuss the correctability and the corrective quality of discrete event systems with delay under different situations. The corrective methods under different situations are analysed. Thirdly, we provide the construction of corrector based on state cycles, in which the corrector is equipped with the quality of coping with multiple failures, and a constructive algorithm of corrector is presented. Fourthly, a corrective scheme of classical discrete event systems is proposed to make the system correctable, and prevent failures happening again. Fifthly, based on the corrective scheme, we provide a corrective instance and show that the scheme is valid and feasible.In the thesis, we discuss the correctability of stochastic discrete event systems. Firstly, the k-step corrective probability and infinite-step corrective probability are proposed to make the two kinds of probability more consistent with reality. Secondly, we provide a method to calculate infinite-step corrective probability based on linear formulas. Thirdly, we discuss the function of controller in stochastic discrete event systems and propose an optimal corrective scheme based on the correct-formula. Fourthly, a corrective instance of stochastic discrete event systems is provided to illustrate how to construct the k-layer decision tree, how to calculate the infinite-step correct-probability of a state and the optimal failure-correction with the intervention of controller.Finally, we briefly discuss some extended topics of correctability. Firstly, the relation between controllability and correctability is discussed to show that correctability is a special instance of controllability. Secondly, we discuss the relation of failure diagnosis and failure correction. Thirdly, we discuss the relation of failure correction and failure prognosis.