Supervisory control of heap models using synchronous composition

Heaps models are powerful models for concurrent timed discrete event systems. They admit linear description using dioid algebras. Inspired by supervisory control of logical discrete event systems we introduce parallel composition of heap models, called synchronous product, to formally describe the action of supervisor (represented by another heap model) on the system. This additional explicit concurrency for naturally concurrent heap models is useful for studying supervisory control in the algebraic framework of dioid algebras. Timing aspects of supervisory control, i.e. optimal timing of the controller, is studied based on residuation theory.