IBEX

Thanks to advances in computational power and miniaturisation, software is increasingly embedded in infrastructures and industrial processes to boost efficiency, safety, and production. In this context it is now qualified as cyber-physical to emphasise its tight interaction with physical processes (such as velocity, movement, and temperature), and to sign a shift from usual software engineering practices to a more multifaceted view that combines computer science, control theory, and analysis. There has been important progress in the development of mathematical foundations for cyber-physical systems. Existing results typically take the form of a hybrid process algebra, which add the notion of a differential equation to an existing, well-established process algebra. However, the fact that computational processes are intermixed with physical ones raises challenging aspects that severely hinder these results as foundations for an engineering discipline of cyber-physical software. Specifically, the latter bring an inherent layer of uncertainty, due to noise in sensors and actuators. Moreover, they require notions of behavioural distance for realistically comparing two systems in an algebraic, rigorous way. The goal of this project is thus to develop the mathematical foundations of cyber-physical programming by taking into account the quantitative aspects discussed above: uncertainty and behavioural distance.