Optimization of linear max-plus systems with application to timing analysis
Optimization of linear max-plus systems with application to timing analysis
The equation A ⊗ x = B ⊗ y over (max, +)
Theoretical Computer Science
Just in Time Control of Constrained (max,+)-Linear Systems
Discrete Event Dynamic Systems
Eigenvectors of interval matrices over max-plus algebra
Discrete Applied Mathematics
Discrete Event Dynamic Systems
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In this paper, we propose a (max,+)-based method for the supervision of discrete event systems subject to tight time constraints. Systems under consideration are those modeled as timed event graphs and represented with linear (max,+) state equations. The supervision is addressed by looking for solutions of constrained state equations associated with timed event graph models. These constrained state equations are derived by reducing duration constraints to elementary constraints whose contributions are injected in the system's state equations. An example for supervisor synthesis is given for an industrial manufacturing plant subject to a strict temporal constraint, the thermal treatment of rubber parts for the automotive industries. Supervisors are calculated and classified according to their performance, considering their impact on the production throughput.