## Section: Application Domains

### Modeling cyber-physical systems

Hybrid systems modeling plays a particular role in the design of cyber-physical systems, eg. systems mixing physical devices, computing platforms, communication buses and control and diagnosis software. A faithful modeling of the physical environment is a key element in a successful design of a cyber-physical system.

Several types of physical components can be found in a system, for example: mechanical, hydraulic or electrical. Component models should cover several viewpoints. For instance, the three viewpoints of an electronic device would be its electrical, thermal and reliability models. All these viewpoints interact, and it is not possible to analyze any of them in isolation. Let alone these complex cross-viewpoint interactions, modeling physics requires refined mathematics. For instance, it is a misconception to assume that physical laws result in smooth dynamics that can be captured by systems of ordinary differential equations. On the contrary, physics is often nonsmooth, meaning that trajectories may be discontinuous — consider the example of colliding billiard balls. Physical systems are networks of elementary components. The dynamics of each component can often be captured by a simple (differential) equation. However, these (differential) equations are coupled by network equations (Kirchhoff laws, mechanical couplings, ...) resulting from the structure of the system. The end result, is a system mixing differential equations with linear or algebraic constraints: a system of differential algebraic equations (DAE).

The Hycomes team is focusing on the design of hybrid systems modeling languages with DAE and nonsmooth dynamics (Fillipov differential inclusions, or complementarity systems), with applications in the energy industry (power plants, smart grids), and in the railway, automotive and aeronautic industries — see section 3.1 for a deeper insight on the research program.