Synchronization and Sub-synchronization Problems for Switching Max-Plus Systems: Structural Solvability Conditions

Switching linear systems over the max-plus algebra can be used to model production plants where different choices in resource allocation are possible. In such case, internal and external variables represent the time instants at which internal or external events occur. In particular, output variables represent the time instants at which lots of manufactured goods are released to the market. Here, we consider the problems of system synchronization and sub-synchronization, which consist in forcing the output of a system to equal or to anticipate the output of a given model. Their solution in the max-plus framework provides a viable strategy to control a given production plant in such a way to comply with a desired production time schedule. Using structural methods and introducing novel structural notions, necessary and sufficient solvability conditions are given. Practical methods to construct solutions are illustrated and discussed.