Proving Abstractions of Dynamical Systems through Numerical Simulations

A key question that arises in rigorous analysis of cyberphysical systems under attack involves establishing whether or not the attacked system deviates significantly from the ideal allowed behavior. This is the problem of deciding whether or not the ideal system is an abstraction of the attacked system. A quantitative variation of this question can capture how much the attacked system deviates from the ideal. Thus, algorithms for deciding abstraction relations can help measure the effect of attacks on cyberphysical systems and to develop attack detection strategies. In this paper, we present a decision procedure for proving that one nonlinear dynamical system is a quantitative abstraction of another. Directly computing the reach sets of these nonlinear systems are undecidable in general and reach set over-approximations do not give a direct way for proving abstraction. Our procedure uses (possibly inaccurate) numerical simulations and a model annotation to compute tight approximations of the observable behaviors of the system and then uses these approximations to decide on abstraction. We show that the procedure is sound and that it is guaranteed to terminate under reasonable robustness assumptions

Cyber-Physical System Checkpointing and Recovery

Transitioning to more open architectures has been making Cyber-Physical Systems (CPS) vulnerable to malicious attacks that are beyond the conventional cyber attacks. This paper studies attack-resilience enhancement for a system under emerging attacks in the environment of the controller. An effective way to address this problem is to make system state estimation accurate enough for control regardless of the compromised components. This work follows this way and develops a procedure named CPS checkpointing and recovery, which leverages historical data to recover failed system states. Specially, we first propose a new concept of physical-state recovery. The essential operation is defined as rolling the system forward starting from a consistent historical system state. Second, we design a checkpointing protocol that defines how to record system states for the recovery. The protocol introduces a sliding window that accommodates attack-detection delay to improve the correctness of stored states. Third, we present a use case of CPS checkpointing and recovery that deals with compromised sensor measurements. At last, we evaluate our design through conducting simulator-based experiments and illustrating the use of our design with an unmanned vehicle case study