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## On the rational use of Petri nets, automata and the max algebra for the optimal control of DEDS.

Wagneur, E.;
Demongodin, I.
In:
*Proc. 8th Int. Workshop on Petri Net and Performance Models (PNPM'99), 8-10 October 1999, Zaragoza, Spain*, pages 179-186.
1999.

Abstract:
We show here how the discrete Petri nets, languages and automata; and
max-algebra approaches to DEDS yield complementary results. Using a simple
discrete event dynamic system, we show how this complementarity may be
used for the optimal control of a DEDS: the conditions ensuring liveness
of the Petri net model yield admissible control strategies; the automaton
of the system then exhibits non-deterministic situations, and suggest
unambiguous control policies. Each of these policies can then be analyzed.
In each case, we get general timed PN's, which are not TEG's, and spectral
theory in the min-max algebra yield the periodicity of the system. An
optimal control strategy may then be selected.

Keywords:
Petri nets, discrete event systems, finite automaton, max-algebra,
supervisory control.

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