New representations for (max,+) automata with applications to performance evaluation and control of discrete event systems

A large class of timed discrete event systems can be modeled by means of (max,+) automata, that is automata with weights in the so-called (max,+) algebra. In this contribution, specific recursive equations over (max,+) and (min,+) algebras are shown to be suitable for describing extremal behaviors of (max,+) automata. Several pertinent performance indicators can be easily derived or approximated from these representations with a low computation complexity. It is also shown how to define inputs which model exogenous influences on their dynamic evolution, and a new approach for the control of (max,+) automata is proposed.