Formal Verification of Stability Properties of Cyber-physical Systems

We increasingly rely on computers to interact with the physical world for us. At the large end, software underlies the control systems of commercial aircraft and power plants, and at the small end it controls medical devices and hobbyist UAVs. The failure of any of these systems can have severe consequences which are often measured in the loss of human lives. Formal verification has proven a promising approach to achieving very strong guarantees in more classic areas of computer science. In this work we present an overview of our experiences formalizing stability properties of cyber-physical systems (CPSs) using the Coq proof assistant. In particular, we describe and contrast two approaches for proving the stability of the linear, one-dimensional proportional controller (P-controller) depicted in Figure 1. This system runs in a loop where the controller sets the velocity (v) of the system and then the position (x) evolves continuously according to the differential equation ẋ = v for at most ∆ time while v remains constant. The goal of the controller is to move the system to x = 0.