Section: New Results

Scheduling and Supervisory Control

Participants : Eric Badouel, Benoît Caillaud, Philippe Darondeau.

Model Identification and Synthesis of Discrete-Event Systems

Book chapter [28] focuses on two important and tightly related problems, namely the identification and synthesis of discrete-event systems. Particular attention is devoted to two main formalisms in this area, i.e., finite state automata and Petri nets. The goal of this chapter is to provide a collection of references in this framework, and discuss the main research areas where such problems have been investigated. Due to the extensive literature, only some of the results are discussed in a certain detail, such as the basic ideas related to the theory of regions and the synthesis of labeled Petri nets, while other results are simply mentioned and the reader is addressed to the specific contributions for more details.

Assembling Sessions

Sessions are a central paradigm inWeb services to implement decentralized transactions with multiple participants. Sessions enable the cooperation of workflows while at the same time avoiding the mixing of workflows from distinct transactions. Languages such as BPEL, ORC, AXML that implement Web Services usually realize sessions by attaching unique identifiers to transactions. The expressive power of these languages makes the properties of the implemented services undecidable. In [25] , we propose a new formalism for modelling web services. Our model is session-based, but avoids using session identifiers. The model can be translated to a dialect of Petri nets that allows the verification of important properties of web services.

Towards Distributed Control of Discrete Event Systems

To initiate a discussion on the modeling requirements for distributed control of discrete-event systems, a partially-automated region based methodology is presented in [26] . The methodology is illustrated via a well-known example from distributed computing: the dining philosophers.

Communicating Decentralized Control

Frameworks that incorporate communication into decentralized supervisory control theory address the following problem: find locations in the evolution of the plant behavior where some supervisors send information so that a supervisor that was unable to make the correct control decision prior to receiving external information, is now capable of making the correct control decision. We propose in [19] a solutions to this problem and identify an earliest and a latest placement where such communication results in the synthesis of a correct control solution. In addition to a first and last communication opportunity, there may be a selection of intermediate possibilities where communication would produce the correct control solution. We present a computable procedure to identify a broader range of suitable communication locations.

Residuation of tropical series: rationality issues

In [20] , the decidability of existence, rationality of delay controllers and robust delay controllers are investigated for systems with time weights in the tropical and interval semirings. Depending on the (max,+) or (min,+)-rationality of the series specifying the controlled system and the control objective, cases are identified where the controller series defined by residuation is rational, and when it is positive (i.e., when delay control is feasible). When the control objective is specified by a tolerance, i.e. by two bounding rational series, a nice case is identified in which the controller series is of the same rational type as the system specification series.