Hybrid Systems

In many modern engineering applications -robotics, automation, real-time software, aeronautics, air and ground transportation systems, systems biology, and process control, to name a few -the states of the system undergo a mixture of real-time (continuous) and instantaneous event (discrete) transitions. This mixture can be dictated by the fundamentally non-smooth or discontinuous nature of some physical phenomena (e.g. mechanical impact, network rerouting, and cell differentiation) or intentional by design (integration of discrete logic or digital computers with continuous physical processes). The result of such a coupling of discrete and continuous dynamics is a hybrid system. More specifically, hybrid systems are continuous variable systems with a phased operation, capturing both discrete event (linguistic behavior) and “lower-level” continuous behavior of the system. For this very reason, hybrid systems have recently been at the center of intense research activity in the control theory, computer-aided verification, and artificial intelligence communities.