The Ramadge-Wonham framework for control of discrete event systems is augmented with timing features by use of Ostroff's semantics for timed transition models. It is shown that the RW concept of controllability and the existence of maximally permissive supervisory controls can be suitably generalized. The enhanced setting admits subsystem composition and the concept of forcible event as an event that preempts the tick of a global clock. An example of a simple manufacturing cell illustrates how the new framework can be used to solve synthesis problems which may include logic-based, temporal and quantitative optimality specifications. >

Supervisory control of timed discrete-event systems

The framework given by P.J. Ramadge and W.M. Wonham (SIAM J. Control Optim., Vol. 25, no.1, p.206-30, 1987) for control of discrete event systems is augmented with timing features by use of Ostroff's semantics for timed transition models (1989, 1990). It is shown that the corresponding concept of controllability, and the existence of minimally restrictive supervisory controls can be suitably generalized. The enhanced setting admits subsystem composition, and the concept of forcible event as an event that preempts the tick of a global clock. An example of a simple manufacturing cell illustrates how the new framework can be used to solve synthesis problems which may include logic-based, temporal and quantitative optimality specifications. >

The supervisory control of timed discrete-event systems

The aim of this thesis is to explore new ways to achieve complexity reduction in discrete event systems (DES). We present three different ways of reducing complexity. First, we present a symbolic supervisory control design method for composite systems such that the complete state space never needs to be computed. Instead of a supervisor implemented by a static lookup table, we provide a function that can be efficiently and dynamically computed at each state to determine the control action. This symbolic function can be suitably modified to ensure that the system under control is free of deadlocks. Secondly, we present a heuristic algorithm to reduce the size of a (static) supervisor. Our symbolic supervision scheme is not able to guarantee non-blocking behaviour in the system under control. So to ensure non-blockingness it may be necessary to use a lookup table. Finding the smallest lookup table for a given control task is an NP-hard problem. We propose a greedy supervisor reduction algorithm based on the concept of control covers. This algorithm seems to work quite well in a large number of cases. Finally, we present a compact model of timed discrete event systems (TDES). We use local timers at each state of the TDES to model the passage of time. This model is quite robust to changes in time scale and is closed under control.

Complexity reduction in discrete event systems

It is well known that the optimal nonblocking supervisory control problem of timed discrete event systems is NP-hard, subject in particular to state space explosion that is exponential in the number of system components In this thesis, we propose to manage complexity by organizing the system as a Timed State Tree Structure (TSTS) TSTS are an adaptation of STS to timed Supervisory Control Theory (SCT) Based on TSTS we present an e±cient recursive symbolic algorithm that can perform nonblocking supervisory control design for systems of state size 10^12 and higherFailure diagnosis is the process of detecting and identifying deviations of a system from its normal behavior using the information available through sensors A method for fault diagnosis of the TSTS model is proposed A state based diagnoser is constructed for each timed holon of TSTS Fault diagnosis is accomplished using the state estimates provided by the timed holon diagnosers The diagnosers may communicate among each other in order to update their state estimates At any given time, only a subset of the diagnosers are operational, and as a result, instead of the entire model of the system, only the models of the timed holons associated with the operational diagnosers are usedIt is shown that the computational complexity of constructing and storing the transition systems required for diagnosis in the proposed approach is polynomial in the number of system components, whereas in the original monolithic approach the computational complexity is exponential

Timed State Tree Structures: Supervisory Control and Fault Diagnosis

The paper presents an extension to OBDDs with timing information, called timed binary decision diagrams (TBDDs). TBDDs are also canonical and allow the symbolic manipulation of Boolean functions with timing information. A TBDD software package is implemented based on the existing CMU BDD package. Experimental results demonstrate the efficiency of the TBDDs in representing circuits with both functional and timing information.

Timed binary decision diagrams

This paper shows how Real-Time can be introduced into the algebraic description of finite automata, to provide a tool for modelling discrete-event-systems

P. Moller

Papers

Introducing Real Time in the Algebraic Theory of Finite Automata