Albert Benveniste, Timothy Bourke, Benoît Caillaud, and Marc Pouzet
Hybrid systems exhibit mode-dependent continuous-time dynamics. They are encountered in several phases of Cyber-Physical Systems design: physical system modeling, budgeting time over the computing architecture, safety analyses, and more generally virtual system modeling. These different phases typically involve different kinds of tools, with differing interpretations of the underlying mathematics. By exhibiting a mix of continuous- and discrete-time, hybrid systems raise a number of unexpected challenges for existing modeling and simulation tools. We review these challenges and propose some new perspectives for addressing them. Recalling the theoretical e ort that underpinned the development of synchronous languages---which allowed, for example, the development of a certified compiler for SCADE---we propose redoing the same for hybrid systems modeling tools.
Keywords : Cyber-Physical Systems, Hybrid Systems, physical system modeling, ODE, DAE, nonstandard semantics