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

International audienceIt 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 presenting resource sharing phenomena, it is useful to extend the usual set of 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. In this paper, we provide the solution to the problem, and discuss the implementation of procedures for computing the Hadamard product and affine operations. Such procedures have been recently implemented on top of the C++ library ETVO. Tests are conducted to evaluate their performance in solving optimal-control problems on TEGs with resource sharing and output-reference updat