Journal
DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS
Volume 19, Issue 4, Pages 525-549Publisher
SPRINGER
DOI: 10.1007/s10626-009-0083-6
Keywords
(max, plus )-automata; Supervisory control; Hadamard product; Supremal controllable formal power series
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Funding
- Academy of Sciences of the Czech Republic, Inst. [AV0Z10190503]
- EU.ICT
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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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