Distributed Model Predictive Control of timed continuous Petri nets

In this paper we focus on distributed control of timed continuous Petri nets (TCPN). We assume that subsystems are connected by places modeling buffers. The problem we handle here is to drive all the subsystems to their desired final states, which is similar to the classical set-point control problem in general continuous-state systems. We first propose a centralized MPC controller, in which asymptotic stability is guaranteed by means of adding constraints to force the state trajectory to be inside an interior convex subset of the reachability space. Then, we apply this controller to a distributed setting, and for this aim we use a particular strategy to maintain the positiveness of the markings of buffer places. We prove that, by using the proposed algorithm, the desired final states of all subsystems can be reached in finite time (even if at different time instants). In our method, no high level coordinator is needed and only limited communication occurs among neighboring subsystems.