11th International Conference on Analysis and Optimization by Guy Cohen, Jean-Pierre Quadrat

By Guy Cohen, Jean-Pierre Quadrat

The convention, coorganized via INRIA and Ecole des Mines de Paris, specializes in Discrete occasion platforms (DES) and is aimed toward engineers, scientists and mathematicians operating within the fields of automated regulate, Operations learn and facts who're attracted to the modelling, research and optimization of DES. numerous tools akin to Automata concept, Petri nets, and so forth. are proposed to explain and examine such structures. comparability of those varied mathematical methods and the worldwide war of words of theoretical ways with purposes in production, telecommunications, parallel computing, transportation, and so forth. are the objectives of the convention.

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Additional resources for 11th International Conference on Analysis and Optimization of Systems: Discrete Event Systems : Sophia-Antipolis, June 15-16-17, 1994

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The way we enhance all the control options is by allowing the control decision at each observation instant to be a nondeterministic one. There are two constraints involved in allowing the control actions to take place within a nondeterministic range of choices : (i) the control action should not generate strings outside the given legal language ; (ii) every string generated should allow completion to a task termination string, that is, supervisory control should be non-blocking. The latter constraint has a special significance since, unlike the deterministic theory, supervision is nondeterministic and deadlock is more natural unless precautions are taken.

Xt-1 C Xi and Xl E X j for some i ¢ j. M with respect to Xi and Xj. Any trajectory can be decomposed into a sequence of sub-trajectories, say tl t2 • .. tm such that each segment tl is either an internal or a direct trajectory. For the mapping 0 : X x Con(A4) ~ Tr(Ad), O((x, or)) = x o x l x 2 . . Xp ~ Tra(A//), where tr = UoUlU2... Up-1 ~ Con(A/l) and xo = x, xi = ~(xi-1, ui-1), 1 < i < p, i) we c a n define the block control events U[ = 0 -1 (Tra(Jr)i) and U/ = 0 -1 (Tra(Jr) . These sets shall play the role of high level control inputs in the partition machine defined below.

The automaton TA, modelling the requirement that all cars on Avenue A eventually get through the intersection. get through. ) We now describe the formal context in which we seek to prove that X performs the tasks defined by T1 and T2. The "behavior" of X is defined in terms of its (nonterminating) executions. Each behavior of X is by definition an (infinite) sequence x = (z0, x ~ , . . ) where each xi = XAi * zB~ * xCi, for tokens XAi , XBi , Xci output from A, B and C respectively. Thus, for example, we may have x0 = (A: cars_waiting) * (S: cars_waiting) • (C: go_A).

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