Peyman Gohari

On the complexity of supervisory control design in the RW framework

The time complexity of supervisory control design for a general class of problems is studied. It is shown to be very unlikely that a polynomial-time algorithm can be found when either (1) the plant is composed of m components running concurrently or (2) the set of legal behaviors is given by the intersection of n legal specifications. That is to say, in general, there is no way to avoid constructing a state space which has size exponential in m+n. It is suggested that, rather than discouraging future work in the field, this result should point researchers to more fruitful directions, namely, studying special cases of the problem, where certain structural properties possessed by the plant or specification lend themselves to more efficient algorithms for designing supervisory controls. As no background on the subject of computational complexity is assumed, we have tried to explain all the borrowed material in basic terms, so that this paper may serve as a tutorial for a system engineer not familiar with the subject.

Decentralized Supervisory Control of Discrete-Event Systems Over Communication Networks

In this paper, we investigate the problem of designing embedded decentralized discrete-event controllers over communication networks. It is assumed that there is a path between every pair of processes in the network. The control objective is specified by a prefix-closed language that is controllable and observable, but not coobservable. The paper is focused on communication among processes necessary to meet the control objective. As such, process models are left unspecified; it is only required that disabling any of the controllable events do not block communication among processes. Our findings support the idea that in the presence of ideal communication channels, the protocol design for noncoobservable specifications can be reduced to the synthesis of communicating decentralized supervisors, and we propose solutions for a restricted class of problems. The paper is concluded with a positive result for the case where channels are unreliable.

On observer design for a class of impulsive switched systems

In this work, the problem of state observation for a class of impulsive switched systems is addressed. Corresponding to each subsystem, an identity Luenberger observer is employed and a switching observer is constructed accordingly. The asymptotic stability property of the proposed switching observer is discussed and LMI-based algorithms are given which provide sufficient conditions for asymptotic stability of the switching observer for switching signals with an average dwell time greater than a specific value. Since switched systems without impulse are a special case of impulsive switched systems, the results of this work can be used to design observers for switched systems without impulse as well. Numerical examples are given to show the effectiveness of the proposed algorithms.

Formalizing real-time scheduling using priority-based supervisory control of discrete-event systems

In this note, we formalize real-time task scheduling by applying an extension of supervisory control theory (SCT) of discrete-event systems to real-time models. The set of all possible timed traces of the system is specified by a discrete timed automaton where each transition is associated with an event occurrence or the passage of one unit of time. We introduce priorities to SCT, and apply them to the setting of discrete timed automata in order to develop a formal and unified framework for task scheduling on a single CPU.

Implementing supervisory control maps with PLC

The supervisory control theory of discrete-event systems (DES) can be used to construct a supervisor for any event-driven system in which the state space is discrete. To implement supervisors we propose to use programmable logic controllers (PLCs), which are widely used in industrial applications. In our work, we develop a new conversion algorithm which directly transforms a supervisor represented by a finite automaton to a ladder logic diagram (LLD). To demonstrate the correctness of our proposed approach, we design supervisors for a boiler control system using supervisory control theory of Ramadge and Wonham, convert DES supervisors to PLC controllers using our conversion technique, and verify using a PLC simulation software that the converted LLD can be executed by the PLC and that the original behavior of the DES supervisors under PLC implementation can be achieved.

Implementation of supervisory control using extended finite-state machines

This article aims at bridging the gap between traditional designs to discrete-event control problems and supervisory control theory of Ramadge and Wonham. We propose to implement supervisory control by extending the plants finite state machine with Boolean variables, guard formulas and updating functions. Boolean variables are used to encode the supervisors states, event observation is captured by a set of Boolean functions that update the value of variables, and control is introduced by guarding events with Boolean formulas. The framework developed in this work is fundamental in our ongoing research on communication between supervisors in a distributed discrete-event system.

Supervisory control of discrete-event systems with output : Application to hybrid systems

In this paper, the problem of supervisory control of discrete-event systems (DES) with output is presented and discussed at length. In such systems a causal output function is employed to assign each sequence of inputs with a corresponding sequence of outputs. When the specification of the desired behavior is given by a formal language over the output alphabet, necessary and sufficient conditions are derived for the existence of nonblocking input as well as nonblocking output supervisory control. The idea of sibling is introduced to solve the problem of nondeterminism in discrete-event abstractions of hybrid systems, giving rise to the development of a theory for nonblocking supervisory control of hybrid systems. Our results enable one to apply classical supervisory control theory to design supervisors for DES approximations of hybrid systems, and to import many interesting concepts from classical theory such as modular and hierarchical control.

A framework for modeling communication among decentralized supervisors for discrete-event systems

Following the authors work on extended finite-state machines (EFSMs), we propose a framework to study communication among decentralized supervisors for a (distributed) discrete-event system (DES). Equipped with agent-wise labeling maps (ALMs), this framework serves to explore the information structure of the system naturally while enjoying an abstract viewpoint to rigorously express the desired properties. After its development in the centralized case, we extend the framework to the case of decentralized supervisors and prove the existence and efficient computation of ALMs. Examples illustrate the applicability of the approach.

Multiprocessor scheduling in supervisory control of discrete-event systems framework

We present a framework for designing schedulers for hard real-time systems upon uniform multiprocessors based on Supervisory Control Theory (SCT) for timed discrete-event systems (TDES). The contribution of this work lies in the development of a formal constructive method for controlling the preemptive and migrative execution of real-time tasks on a set of uniform processors. This approach allows a unified view of scheduling theory based on the timing analysis of models of real-time applications, i.e., the complications of checking schedulability and determining a scheduling algorithm are considered as dual problems: a solution to the former implies a solution to the latter and vice versa.

Efficient implementation of fairness in discrete-event systems using queues

Fair synthesis of supervisory control for discrete-event systems is discussed. It is argued that a least restrictive supervisor does not in general exist unless a bound is placed on the number of transitions before which a desired event is required to happen. It is shown how such bounded fairness can be implemented using first-input-first-output (FIFO) queues. Although the language generated by a queue is not the largest among bounded fair restrictions of a behavior, nonoptimality can be exploited in hierarchical implementation of queues by grouping a subset of subsystems as a team and designing two modular queues: one to implement fairness locally among the team members, and the other to implement fairness globally between the team and other subsystems.