Scalable Verification of Cyber-Physical Systems

Abstract

In this thesis, several challenges in the verification of cyber-physical systems are considered. First, verification methods are generally not scalable, i.e. they suffer when performed on high-dimensional systems and require sometimes unreasonable computational time. Verification of hybrid systems, in addition, involves the computation of complex operations. Next, nonlinear systems are harder to reason as opposed to linear systems. Also, there is a pressing need to reason about safety in a limited time or even instantly. Thus, the following solutions are presented to address scalability and performance issues in verification. To begin with, we leverage the structure of systems when safety properties are defined only in low dimensions. In particular, an algorithm is proposed to exploit decomposition in the reachability analysis of linear hybrid systems. It allows to verify systems with up to thousands of state variables without additional approximation error for linear hybrid systems with a low number of constraints. Next, a data-driven framework to handle nonlinear, even black-box, systems is provided. It is based on Koopman operator and Fourier Features, well-known approximation techniques which, in some cases, could exactly represent the original system. Then, two options are offered to handle nonlinear initial sets created by such linearization: (i) utilize interval arithmetics along with refinement steps and calls to the SMT solver and (ii) combine polynomial zonotopes with efficient set operations to obtain a tight approximation for nonlinear reachable sets. This enables an extremely fast verification in comparison with state-of-the-art tools for nonlinear systems as it shown on several nonlinear system benchmarks. Finally, we developed an algorithm which verifies the system on-the-fly. It generates reachable regions by simulations, which are enclosed by barrier certificates to provide formal guarantees. These barrier certificates are produced by neural networks and verified by SMT solvers. Although the algorithm is currently restricted by scalability of FOSSIL, it already demonstrate promising results in verification both for nonlinear models and in online settings.