HybridsystemsTheorie

HybridsystemsTheorie, literally “Hybrid Systems Theory,” describes the interdisciplinary study of systems that combine continuous dynamics with discrete events. It formalises how components such as physical processes, digital controllers, and network protocols interact within a single framework. The theory provides formal models, analytical tools and simulation techniques for verifying safety, stability and performance properties of these integrated systems. Classic models include hybrid automata, timed automata, and piecewise‑differentiable systems. Flow‑switch graphs capture continuous flows interrupted by instantaneous transitions, while differential inclusions express uncertainties in continuous dynamics.

The body of research is rooted in control theory and computer science. Early contributions in the 1970s by scholars such as Jean‑Pierre Laumond and Stephen LaValle introduced hybrid automata for robotics. In the 1990s, the verification community developed tools like SpaceEx and HyTech, which apply reachability analysis to hybrid models. More recent work focuses on uncertainty quantification, learning‑based control, and cyber‑physical systems security.

Practically, Hybrid Systems Theory underpins the design of automotive control units, avionics, power‑grid management, and industrial process control. It also informs the certification of autonomous vehicles and smart‑grid microgrids. The field continues to evolve with the integration of machine‑learning components, demanding new hybrid modelling paradigms that can capture data‑driven dynamics alongside traditional physical laws.