State Based Control of Timed Discrete Event Systems using Binary ...
State Based Control of Timed Discrete Event Systems using Binary ...
State Based Control of Timed Discrete Event Systems using Binary ...
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Chapter 2. Supervisory <strong>Control</strong> <strong>of</strong> <strong>Timed</strong> <strong>Discrete</strong> <strong>Event</strong> <strong>Systems</strong> 11Let G be a controlled TDES with Σ partitioned as in the previous section.LetE ⊆ Σ ∗ . We introduce the set <strong>of</strong> all sublanguages <strong>of</strong> E that are controllable with respectto G:C(E) = {K ⊆ E| K is controllable wrt G}Proposition 2.3.1 [29] There exists a unique supremal element in C(E), supC(E), whichcan be described as supC(E) = ⋃ {K| K ∈ C(E)}.Proposition 2.3.2 [29] Let E ⊆ Σ ∗ , and let K=supC(E∩L m (G)). If K ≠ ∅, there existsa marking nonblocking supervisory control (MNSC) V for G such that L m (V/G) = K.Thus K is (if nonempty) the maximally permissive (or minimally restrictive) solution<strong>of</strong> the problem <strong>of</strong> supervising G in such a way that its behavior belongs to E and controlis nonblocking. For more details see [29].
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