Switched max-plus linear-dual inequalities: cycle time analysis and applications

0582950 - MÚ 2025 RIV DE eng J - Článek v odborném periodiku
Zorzenon, D. - Komenda, Jan - Raisch, J.
Switched max-plus linear-dual inequalities: cycle time analysis and applications.
Discrete Event Dynamic Systems-Theory and Applications. Roč. 34, č. 1 (2024), s. 199-250. ISSN 0924-6703. E-ISSN 1573-7594
Grant CEP: GA ČR(CZ) GC19-06175J
Institucionální podpora: RVO:67985840
Klíčová slova: max-plus algebra * Petri nets * scheduling * switched systems
Obor OECD: Automation and control systems
Impakt faktor: 2, rok: 2022
Způsob publikování: Open access
https://doi.org/10.1007/s10626-023-00389-5

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 primal and dual operations of the max-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operation, each corresponding to a set of LDIs, according to a sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the considered schedule is fixed and either periodic or intermittently periodic. We show that SLDIs can model a wide range of applications including 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 algorithms to compute: i. minimum and maximum cycle times for these processes, improving the time complexity of other existing approaches, ii. a complete trajectory of the robot including start-up and shut-down transients.
Trvalý link: https://hdl.handle.net/11104/0350992