V. Chandra

A polynomial algorithm for testing diagnosability of discrete-event systems

Failure diagnosis in large and complex systems is a critical task. In the realm of discrete-event systems, Sampath et al. (1995) proposed a language based failure diagnosis approach. They introduced the diagnosability for discrete-event systems and gave a method for testing the diagnosability by first constructing a diagnoser for the system. The complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types. We give an algorithm for testing diagnosability that does not construct a diagnoser for the system, and its complexity is of fourth order in the number of states of the system and linear in the number of the failure types.

Automated control synthesis for an assembly line using discrete event system control theory

The design of logic controllers for event-driven systems continue to rely largely on intuitive methods rather than on formal techniques. This approach results in a control code that requires extensive verification, is hard to maintain and modify, and may even fail at times. Supervisory control theory (SCT) provides a formal approach to logic control synthesis. In order to demonstrate the usefulness of the supervisory control theory in manufacturing systems, an educational test-bed that simulates an automated car assembly line has been built using LEGO/spl reg/ blocks. Finite state machines (FSMs) are used for modeling operations of the assembly line, and for the specifications that accomplish the task of successfully completing the assembly repeatedly. Using the technique of SCT, we derive a supervisor that enforces the specifications while offering the maximum flexibility of assembly. Subsequently a controller is extracted from the maximally permissive supervisor for the purpose of implementing the control by selecting, when possible, at most one controllable event from among the ones allowed by the supervisor. Testing to check the correctness of the control code is reduced, since the controller is guaranteed to enforce the specifications.

Modeling Discrete Event Systems With Faults Using a Rules-based Modeling Formalism

Obtaining accurate models of systems which are prone to failures and breakdowns is a difficult task. In this paper we present a methodology which makes the task of modeling failure prone discrete event systems (DESs) considerably less cumbersome, less error prone, and more user-friendly. The task of obtaining commonly used automata models for DESs is non-trivial for most practical systems, owing to the fact that the number of states in the commonly used automata models is exponential in the number of signals and faults. In contrast a model of a discrete event system, in the rules based modeling formalism proposed by the co-authors of this paper, is of size polynomial in the number of signals and faults. In order to model failures, we augment the signals set of the rules based formalism to include binary valued fault signals, the values representing either a non-faulty or a faulty state of a certain failure type. Addition of new fault signals requires introduction of new rules for the added fault signal events, and also modification of the existing rules for non-fault events. The rules based modeling formalism is further extended to model real-time systems, and we apply it to model delay-faults of the system as well. The model of a failure prone DES in the rules based can automatically be converted into an equivalent (timed)-automaton model for a failure analysis in the automaton model framework.

A discrete event systems modeling formalism based on event occurrence rules and precedences

The analysis (verification, diagnosis, control, etc.) of discrete event systems requires a correct model of the system and of its specifications. In this paper, we present a new modeling formalism for generating valid models of complex systems. The class of systems this applies to is one which consists of signals that take binary values. The technique presented here makes the task of modeling considerably less cumbersome and less error-prone and is user-friendly. Another advantage of using this modeling formalism is that the size of the system model is polynomial in the number of signals, whereas the number of states in the automata models is exponential in the number of signals. We present automated techniques for deriving an automaton-based model from the model in the proposed formalism. We illustrate the modeling formalism using examples drawn from manufacturing systems and process control.

Decentralized Control of Discrete Event Systems Using Prioritized Composition With Exclusion

A necessary and sufficient condition for decentralized control of discrete event systems via prioritized composition with exclusion (PCX) is provided. PCX was extended from prioritized synchronous composition (PSC) in order to model various Boolean modes of decision fusion by allowing the exclusivity of participation in system interactions . A notion of PCX-coobservability is introduced that captures the nature of PCX-based decision fusion, and a testing algorithm with polynomial complexity in the states of plant and specification is presented. The result is extended for multiple supervisors with multiple exclusivity sets based on an extended PCX definition.

A Event Occurrence Rules based Compact Modeling Formalism for a Class of Discrete Event Systems

The analysis, failure diagnosis and control of discrete event systems (DESs) requires an accurate model of the system. In this paper we present a methodology which makes the task of modeling DESs considerably less cumbersome, less error prone, and more user-friendly than it usually is. In doing so we simplify the modeling formalism of [4, 5], proposed for obtaining valid models of complex discrete event systems, by eliminating ‘precedence relations’, and capturing them as part of the ‘event occurrence rules’. Under the new modeling formalism the size of the system model is polynomial in the number of signals; whereas the number of states in the commonly used automata models is exponential in the number of signals. We present automated techniques for deriving an automaton model from the model in the proposed formalism. We illustrate the modeling formalism using examples drawn from manufacturing and process control systems.

Prioritized Composition With Exclusion and Generation for the Interaction and Control of Discrete Event Systems

Interaction of multiple discrete event systems (DESs) represented as automata are carried out using composition operations. These operations on automata enforce concurrency, wherein an event exists in the composed automaton if it exists in the participating states of the interacting automata possessing the event in their event set. Heymann generalized this by introducing event priorities, wherein an event exists in the composed automaton if it exists in the participating state of the interacting automata having priority over the event. For two interacting automata P and Q, while prioritized composition can model the P, Q, AND, and OR boolean interactions, it cannot model boolean interactions which require exclusivity of participation, namely, “exclusive P”, “exclusive Q”, “exclusive P or exclusive Q”, “exclusive P and exclusive Q”. In order to also model these additional interactions we propose a generalization of prioritized composition by introducing an exclusivity set besides the existing priority sets. The resulting composition is called prioritized composition with exclusion. We also introduce prioritized composition with exclusion and generation that allows for all sixteen boolean modes of interaction possible when two automata interact. This is done by the further introduction of a nor-generative set. This event set together with the two priority sets and an exclusivity set makes it possible to model eight additional boolean interactions which do not require either of the interacting automata to participate for the event to be enabled in the composed automaton. The applicability of these interactions to decentralized supervisory decision fusion and in composing the rules based model of systems has been illustrated.

A new modeling formalism and automata model generator for a class of discrete event systems

The control of discrete event systems (DES) requires a correct model of the system and of its control specifications. In this paper we present a new modeling formalism for generating valid models of complex systems. The class of systems this applies to, is one which consists of signals that take binary values. The technique presented here makes task of modeling considerably less cumbersome, less error prone, and is user-friendly. Another advantage of using this modeling formalism is that the size of the system model is polynomial in the number of signals; whereas the number of states in the automata models is exponential in the number of signals. We present automated techniques for deriving a state machine based model from the model in the proposed formalism. Such a state machine model can then be used for the purpose of automated supervisor synthesis for which a vast body of tools already exists, based upon the Ramadge & Wonham (1987) supervisory control theory (SCT). We illustrate the modeling formalism using examples drawn from manufacturing systems and process control.

Modeling discrete event systems with faults using a rules based modeling formalism

In this paper we present a methodology which makes the task of modeling failure prone discrete event systems (DESs) considerably less cumbersome, less error prone, and more user-friendly. In order to model failures, we augment the signals set of the rules based formalism proposed by the co-authors of this paper, to include binary valued fault signals, the values representing either a non-faulty or a faulty state of a certain failure type. The rules based modeling formalism is further extended to model real-time systems, and we apply it to model delay-faults of the system as well. The model of a failure prone DES in the rules based can automatically be converted into an equivalent (timed)-automaton model for the analysis in an automaton model framework.

A computer implementable algorithm for the synthesis of an optimal controller for acyclic discrete event processes

An optimal control theory for designing a controller, that selects unique control actions is developed for controlling discrete event systems (DESs). Prior work on supervisor synthesis problems studied the design of supervisors for satisfying qualitative specifications within the framework of the DESs. In this paper we define and investigate the synthesis of an optimal controller in the sense that, regardless the state of the plant, the worst cost of all surviving paths from that state to the set of frontier marked states is minimized. Our work differs from prior works on optimal control of DESs in that the controller selects a unique controllable event to be executed per state, rather than a set of admissible controllable events. An efficient algorithm is provided to solve this problem under complete observation.