ÐIn this paper, we describe the incremental specification of a power transformer station controller using a controller synthesis methodology. We specify the main requirements as simple properties, named control objectives, that the controlled plant has to satisfy. Then, using algebraic techniques, the controller is automatically derived from this set of control objectives. In our case, the plant is specified at a high level, using the data-flow synchronous SIGNAL language, and then by its logical abstraction, named polynomial dynamical system. The control objectives are specified as invariance, reachability, ... properties, as well as partial order relations to be checked by the plant. The control objectives equations are synthesized using algebraic transformations. Index TermsÐDiscrete event systems, polynomial dynamical system, supervisory control problem, optimal control, SIGNAL, SIGALI, power plant.

We present a methodology for the veri cation of reactive systems, and its application to a case study. Systems are speci ed using the synchronous data ow language Signal. As this language is based on an equational approach (i.e. Signal programs are constraint equations between signals), it is natural to translate its Boolean part into a system of polynomial equations over three values denoting true, false and absent. Using operations in algebraic geometry on the polynomials, it is possible to check properties concerning the system, such as liveness, invariance, reachability and attractivity. We apply this method to the veri cation of the automatic circuit breaking control system of an electric power transformer station. This system handles the reaction to electrical defects on high voltage lines.

International audienceWe present a formal specification and verification of the automatic circuit-breaking behavior of an electric power transformer station, using the synchronous approach to reactive real-time systems implemented by the data-flow language Signal. Synchronous languages have a mathematical model that supports the various phases of the development of a control system: specification, verification, simulation, code generation, and implementation. The complex hierarchical, state-based and preemptive behavior of the power station controller is specified in Signalgti, an extension of Signal with notions of time intervals and preemptive tasks. To validate the specification, a graphical simulator is generated using Signal's execution environment, and the required behaviour is proven to be satisfied, using its proof method

AbstractÐIn this paper, we describe the incremental specification of a power transformer station controller using a controller synthesis methodology. We specify the main requirements as simple properties, named control objectives, that the controlled plant has to satisfy. Then, using algebraic techniques, the controller is automatically derived from this set of control objectives. In our case, the plant is specified at a high level, using the data-flow synchronous SIGNAL language, and then by its logical abstraction, named polynomial dynamical system. The control objectives are specified as invariance, reachability, ... properties, as well as partial order relations to be checked by the plant. The control objectives equations are synthesized using algebraic transformations.

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