Supervisory Control Applied to Automata Extended with Variables - Revised

Report, 2008

To get industrial acceptance of supervisory control theory, there is a need to bridge the gap between the signal-based industrial reality and the event-based supervisory control framework. This report tries to shorten this gap by introducing a modeling formalism with automata extended with variables, guard expressions and action functions. The formalism is suitable for modeling plants and specifications in the supervisory control framework. No restrictions are made on the sharing of variables between concurrent automata and don't care updating of shared variables is allowed. This leads to frame problems since unreachable states of subsystems can become reachable in the entire system. To define supervisory control problems in this general setting we introduce the concept of controllable languages with respect to the entire system which is a generalization of the classical definition of controllability. An algorithm that transforms supervisory control problems modeled by automata with shared variables into equivalent ordinary automata supervisory control problems, is presented. This allows the user to model complex behaviors with a compact representation, and at the same time use existing algorithms for synthesis and verification. The proposed approach has been implemented in the supervisory control tool, Supremica.