Biblio

Unsafe behavior of cyber-physical systems can have disastrous consequences, motivating the need for formal verification of these kinds of systems. Deductive verification in a proof assistant such as Coq is a promising technique for this verification because it (1) justifies all verification from first principles, (2) is not limited to classes of systems for which full automation is possible, and (3) provides a platform for proving powerful, higher-order modularity theorems that are crucial for scaling verification to complex systems. In this paper, we demonstrate the practicality, utility, and scalability of this approach by developing in Coq sound and powerful rules for modular construction and verification of sampled-data cyber-physical systems. We evaluate these rules by using them to verify a number of non-trivial controllers enforcing safety properties of a quadcopter, e.g. a geo-fence. We show that our controllers are realistic by running them on a real, flying quadcopter.

The safety-critical aspects of cyber-physical systems motivate the need for rigorous analysis of these systems. In the literature this work is often done using idealized models of systems where the analysis can be carried out using high-level reasoning techniques such as Lyapunov functions and model checking. In this paper we present VERIDRONE, a foundational framework for reasoning about cyber-physical systems at all levels from high-level models to C code that implements the system. VERIDRONE is a library within the Coq proof assistant enabling us to build on its foundational implementation, its interactive development environments, and its wealth of libraries capturing interesting theories ranging from real numbers and differential equations to verified compilers and floating point numbers. These features make proof assistants in general, and Coq in particular, a powerful platform for unifying foundational results about safety-critical systems and ensuring interesting properties at all levels of the stack.

The safety-critical aspects of cyber-physical systems motivate the need for rigorous analysis of these systems. In the literature this work is often done using idealized models of systems where the analysis can be carried out using high-level reasoning techniques such as Lyapunov functions and model checking. In this paper we present VERIDRONE, a foundational framework for reasoning about cyber-physical systems at all levels from high-level models to C code that implements the system. VERIDRONE is a library within the Coq proof assistant enabling us to build on its foundational implementation, its interactive development environments, and its wealth of libraries capturing interesting theories ranging from real numbers and differential equations to verified compilers and floating point numbers. These features make proof assistants in general, and Coq in particular, a powerful platform for unifying foundational results about safety-critical systems and ensuring interesting properties at all levels of the stack.