Interval Analysis in Dioid: Application to Robust Open-Loop Control for Timed Event Graphs

This paper deals with robust open-loop control synthesis for timed event graphs, where the number of initial tokens and time delays are only known to belong to intervals. We discuss here the existence and the computation of a greatest interval of control included in the robust control set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each control is computed in order to guarantee that the controlled system behavior is greater than the lower bound of a desired output reference set and is lower than the upper bound of this set. The synthesis presented here is mainly based on dioid, interval analysis and residuation theory.