Process tracking by equivalent states in modal supervisory control

This paper proposes an extension of the process tracking in modal supervisory control that takes into account the models of the controlled processes which are not trimmed. Indeed, in Supervisory Control Theory (SCT), when a process is not controllable to respect the specifications, the controlled process is computed by the algorithm of the supremal controllable sublanguage. However, the final step of the algorithm of the supremal controllable sublanguage computes the trim of the model. This is coherent to remove states that are neither accessible nor co-accessible because the process is a unique model. Nevertheless, in the case where the design is done with many models, like in modal approach, some inaccessible states in a mode can be accessible from another one. The proposed framework identifies the accessible states, called equivalent states, by other models. This identification uses the name of states to determine their equivalents among models of modes. The aim is to improve switching modes, not only by using languages, but also the name of states in the automata.