Continuous flow systems and control methodology using Hybrid Petri nets

In this paper, we consider the control synthesis of a particular class of systems called continuous flow systems, such as transport systems, manufacturing systems, communication systems, biological systems... etc. These systems are positive systems where continuous and discrete event dynamics interact. They are then considered as hybrid systems. Numerous tools and techniques exist in the literature for modeling and analyzing such systems. As positiveness is a hard constraint, an appropriate tool integrating naturally this constraint is strongly needed. Hybrid Petri Nets (HPNs) are an elegant modeling tool of positive systems, while Hybrid Automata (HA) are a powerful tool giving formally the reachable dynamic space. Combining these two tools aim to a sound approach for control synthesis of continuous flow systems. We start by considering the process to control and compute its behavior, or its reachable state space using specialized software like PHAVer. Algebraic inequalities define this reachable state space. The constrained behavior is obtained by restricting this state space into a smaller desired space. This reduction is expressed in term of linear constraints only over the continuous variables; while the control is given by the discrete transitions (occurrence dates of controllable events). The control synthesis methodology is based on the control of a hybrid system modeled by a D-elementary HPN. The control consists in modifying the guard of the controllable transitions so that the reachable controlled state space is maximally permissive.