Switched max-plus linear-dual inequalities: Application in scheduling of multi-product processing networks

0564906 - MÚ 2023 RIV NL eng C - Conference Paper (international conference)
Zorzenon, D. - Komenda, Jan - Raisch, J.
Switched max-plus linear-dual inequalities: Application in scheduling of multi-product processing networks.
IFAC-PapersOnLine. Volume 55, Issue 28 - Proceedings of 16th IFAC Workshop on Discrete Event Systems WODES 2022. Amsterdam: Elsevier, 2022 - (Komenda, J.; Reveliotis, S.; Masopust, T.; Burget, P.), s. 196-203. ISSN 2405-8963.
[16th IFAC Workshop on Discrete Event Systems WODES 2022. Prague (CZ), 07.09.2022-08.09.2022]
R&D Projects: GA ČR(CZ) GC19-06175J; GA MŠMT(CZ) LTAUSA19098
Institutional support: RVO:67985840
Keywords : P-time event graphs * max-plus algebra * switched max-plus linear systems
OECD category: Automation and control systems
https://doi.org/10.1016/j.ifacol.2022.10.343

P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by max-plus linear-dual inequalities (LDIs), i.e., systems of linear dynamical inequalities in the max-plus algebra and its dual, the min-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operations, each corresponding to an LDI, according to an infinite sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the schedule is fixed and periodic. We show that SLDIs can model single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose an algorithm to compute minimum and maximum cycle times for these processes that improves the time complexity of other existing approaches.
Permanent Link: https://hdl.handle.net/11104/0336480