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

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 nondeterministic situations, and suggest unambiguous control policies. Each of these policies can then be analysed. In each case, we get general timed PNs, which are not TEGs, and spectral theory in the min-max algebra yield the periodicity of the system. An optimal control strategy may then be selected.