Abstract
A behavioral framework for control of (max,+) automata is proposed. It is based on behaviors (formal power series) and a generalized version of the Hadamard product, which is the behavior of a generalized tensor product of the plant and controller (max,+) automata in their linear representations. In the tensor product and the Hadamard product, the uncontrollable events that can neither be disabled nor delayed are distinguished. Supervisory control of (max,+) automata is then studied using residuation theory applied to our generalization of the Hadamard product of formal power series. This yields a notion of controllability of formal power series as well as (max,+)-counterparts of supremal controllable languages. Finally, rationality as an equivalent condition to realizability of the resulting controller series is discussed together with hints on future use of this approach.
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Notes
In particular the definition of parallel composition that is formulated in terms of more general linear description in Prop. 3.1.
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Acknowledgements
This work was supported by the Academy of Sciences of the Czech Republic, Inst. Research Plan No. AV0Z10190503 and by EU.ICT project DISC.
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Komenda, J., Lahaye, S. & Boimond, JL. Supervisory Control of (max,+) Automata: A Behavioral Approach. Discrete Event Dyn Syst 19, 525–549 (2009). https://doi.org/10.1007/s10626-009-0083-6
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DOI: https://doi.org/10.1007/s10626-009-0083-6