A tropical-algebraic method for the control of timed event graphs with partial synchronization

This paper studies a scenario in which the occurrence of one or more events in a discrete event system is subject to external restrictions which may change unexpectedly during run-time. The system is modeled as a timed event graph (TEG) and, in this context, the presence of the aforementioned external restrictions has become known as partial synchronization (PS). This phenomenon arises naturally in several applications, from manufacturing to transportation systems. We develop a formal and systematic method to compute optimal control signals for TEGs in the presence of PS, where the control objective is tracking a given output reference as closely as possible and optimality is understood in the widely-adopted just-in-time sense. The approach is based on the formalism of tropical semirings — in particular, the min-plus algebra and derived semiring of counters. We claim that our method expands modeling and control capabilities with respect to previously existing ones by tackling the case of time-varying PS restrictions, which, to the best of our knowledge, has not been dealt with before in this context.