Linear systems over the max-plus algebra can model discrete event systems where synchronization, without competition, is involved. The lack of competition can be partly circumvented by considering multiple linear models, each representing a possible choice in resource allocation, and a switching mechanism, thus obtaining a switching linear max-plus system. We propose a formulation of the model matching problem for systems of such kind. The aim is to force a given plant to match exactly the output of a given model. A sufficient condition for the solvability of the problem is obtained by extending the geometric approach to switching systems over the max-plus algebra.
The Model Matching Problem for Switching Max-Plus Systems: a Geometric Approach / Animobono, D.; Scaradozzi, D.; Zattoni, E.; Perdon, A. M.; Conte, G.. - 55:(2022), pp. 7-12. (Intervento presentato al convegno 1st IFAC Workshop on Control of Complex Systems, COSY 2022 - Proceedings tenutosi a ita nel 2022) [10.1016/j.ifacol.2023.01.040].