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

0582950 - MÚ 2025 RIV DE eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GC19-06175J
Institutional support: RVO:67985840
Keywords : max-plus algebra * Petri nets * scheduling * switched systems
OECD category: Automation and control systems
Impact factor: 2, year: 2022
Method of publishing: 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.
Permanent Link: https://hdl.handle.net/11104/0350992