Enforcing safety of cyberphysical systems using flatness and abstraction

Abstract

The diffusion of cyberphysical systems acting in human-populated environments brings to the fore the problem of implementing provably safe control laws, to avoid potentially dangerous collisions between moving parts of the system, and with nearby obstacles, without compromising the system's functionality. The limiting factor in most implementations is the model's complexity, and a common workaround includes the reduction of the physical model, based on differential equations, to a finite symbolic model. Following this strategy, we are investigating ways to exploit the specific structure of many mechanical systems (the differentially flat systems) to achieve this simplification. Our objective is to construct a supervisor enforcing a given set of safety rules, while imposing as little constraints as possible on the system's functionality. In this paper, we outline our approach, and present an example -- a collision avoidance algorithm for a fleet of vehicles converging to an intersection. Our approach improves on previous results by providing a deterministic symbolic model for a class of system, regardless of their stability properties, and by addressing explicitly the problem of safety enforcing.