A (Max, plus ) Algebra Approach for Linear Time-varying Constrained Systems

The class of discrete event systems (DES) which involve only synchronization phenomena can be represented by linear state equations in particular algebraic structures. The (max, +) algebra is a dioid over which, these systems can have a linear state representation with special sum and product operations. The study of the DES over this (max, +) algebra is usually made through the corresponding timed event graph (TEG). In this paper, we extend the study over this dioid to DES that are subject to time-varying constraints. We enrich the existing TEG formalism to characterize these systems and propose a modeling and control policy. An example of a supply chain system illustrates this study.