#### Title

SUPERVISORY CONTROL AND FAILURE DIAGNOSIS OF DISCRETE EVENT SYSTEMS: A TEMPORAL LOGIC APPROACH

#### Year of Publication

2002

#### Document Type

Dissertation

#### College

Engineering

#### Department

Electrical Engineering

#### First Advisor

Ratnesh Kumar

#### Abstract

Discrete event systems (DESs) are systems which involve quantities that take a discrete set of values, called states, and which evolve according to the occurrence of certain discrete qualitative changes, called events. Examples of DESs include many man-made systems such as computer and communication networks, robotics and manufacturing systems, computer programs, and automated trac systems. Supervisory control and failure diagnosis are two important problems in the study of DESs. This dissertation presents a temporal logic approach to the control and failure diagnosis of DESs. For the control of DESs, full branching time temporal logic-CTL* is used to express control specifications. Control problem of DES in the temporal logic setting is formulated; and the controllability of DES is defined. By encoding the system with a CTL formula, the control problem of CTL* is reduced to the decision problem of CTL*. It is further shown that the control problem of CTL* (resp., CTL{computation tree logic) is complete for deterministic double (resp., single) exponential time. A sound and complete supervisor synthesis algorithm for the control of CTL* is provided. Special cases of the control of computation tree logic (CTL) and linear-time temporal logic (LTL) are also studied; and for which algorithms of better complexity are provided. For the failure diagnosis of DESs, LTL is used to express fault specifications. Failure diagnosis problem of DES in the temporal logic setting is formulated; and the diagnosability of DES is defined. The problem of testing the diagnosability is reduced to that of model checking. An algorithm for the test of diagnosability and the synthesis of a diagnoser is obtained. The algorithm has a polynomial complexity in the number of system states and the number of fault specifications. For the diagnosis of repeated failures in DESs, different notions of repeated failure diagnosability, K-diagnosability, [1,K]-diagnosability, and [1,1]-diagnosability, are introduced. Polynomial algorithms for checking these various notions of repeated failure diagnosability are given, and a procedure of polynomial complexity for the on-line diagnosis of repeated failures is also presented.

#### Recommended Citation

Jiang, Shengbing, "SUPERVISORY CONTROL AND FAILURE DIAGNOSIS OF DISCRETE EVENT SYSTEMS: A TEMPORAL LOGIC APPROACH" (2002). *University of Kentucky Doctoral Dissertations*. 338.

https://uknowledge.uky.edu/gradschool_diss/338