Implementation of procedures for optimal control of timed event graphs with resource sharing

Abstract

It is a well-known fact that the dynamics of timed event graphs (TEGs), a subclass of timed Petri nets able to model delay and synchronization phenomena, admits linear representation in dioids of formal power series. In order to model and control systems of TEGs with resource sharing phenomena, it is useful to extend the standard set of dioid operations between series by including the Hadamard product, its residual, and its dual residual. Until now, however, the characterization of the largest set of series for which the dual residual of the Hadamard product is defined was still incomplete. Rather than being a mere theoretical dilemma, this open problem delayed the development of reliable algorithms for optimal control of the considered class of systems. In this paper, we provide the solution to the problem, and discuss the implementation of procedures for computing the Hadamard product and related operations. Tests are conducted to evaluate their performance in solving optimal control problems for systems of TEGs with resource sharing and output-reference update