Uncertainty and Reconfigurability in Hilbertean Formal Methods

摘要

Hilbertian Formal Methods is a recently introduced paradigm for embedded systems operating in harsh physical environments. This paradigm has been more developed for the deterministic case. However, it is very rare that a physical environment follows precisely a deterministic rule and then it is more realistic to consider stochastic models. A major problem in dealing with stochastic differential equations, the ubiquitous mathematical for phenomena arising from biology, medicine, meteorology and other domains, is that they can be solved only for very particular classes (linear and quasi linear). The Hilbertian Formal Methods are designed for situations when the solutions are not known (like for non-linear stochastic equations), but enough mathematical information about them can be derived helping in solving problems like stability, controllability, convergence, system design and verification. In this paper, we present an integrated formal model for embedded systems operating in uncertain and nonlinear environments that can reconfigure their communication structure. This is achieved by introducing the observability logic, which is a formal notation for the observations of environment evolutions. This logic is integrated with a probabilistic version of the Pi-calculus that makes possible the real time communication of the measurements of the continuous evolutions, concurrency and reconfiguration of the embedded system. For example, these characteristics are necessary for mobile robot brigades, storm surge barrier systems, sensor networks or cardiac stimulators.