Symbolic-Numeric Reachability Analysis of Closed-Loop Control Software

We study the problem of falsifying reachability properties of real-time control software acting in a closed-loop with a given model of the plant dynamics. Our approach employs numerical techniques to simulate a plant model, which may be highly nonlinear and hybrid, in combination with symbolic simulation of the controller software. The state-space and input-space of the plant are systematically searched using a plant abstraction that is implicitly defined by ``quantization'' of the plant state, but never explicitly constructed. Simultaneously, the controller behaviors are explored using a symbolic execution of the control software. On-the-fly exploration of the overall closed-loop abstraction results in abstract counterexamples, which are used to refine the plant abstraction iteratively until a concrete violation is found. Empirical evaluation of our approach shows its promise in treating controller software that has precise, formal semantics, using an exact method such as symbolic execution, while using numerical simulations to produce abstractions of the underlying plant model that is often an approximation of the actual plant. We also discuss a preliminary comparison of our approach with techniques that are primarily simulation-based.