A State Class Based Controller Synthesis Approach for Time Petri Nets.

We propose a new algorithm for reachability controller synthesis with time Petri nets (TPN). We consider an unusual semantics of time Petri nets in which the firing date of a transition is chosen in its static firing interval when it becomes enabled. This semantics is motivated i) by a practical concern: it aims at approaching the implementation of the controller on a real-time target; ii) by a theoretical concern: it ensures that in the classical state class graph [ 6 ], every state in each state class is an actual reachable state from the TPN, which is not the case with the usual interval-based semantics. We define a new kind of two-player timed game over the state class graph and we show how to efficiently and symbolically compute the winning states using state classes. The approach is implemented in the tool Roméo [ 23 ]. We illustrate it on various examples including a case-study from [ 2 ].