Recursive reachable set computation for on-line safety assessment of the Cyber-Physical System against stealthy cyber attacks

With recent progress in networked embedded control technology, cyber attacks have become one of the major threats to Cyber-Physical Systems (CPSs) due to their close integration of logical and physical processes. Since the conventional computer security techniques are unable to assure the underlying physical behavior against cyber attacks, this paper considers the safety of the compromised CPS from a controls domain perspective. Specifically, we propose an on-line algorithm to assess the safety of the CPS in the presence of stealthy cyber attacks which can be designed intelligently to avoid detection. The main idea is based on a reachability analysis that computes the reachable set of CPS states possibly reached by all potential stealthy cyber attacks. The reachable set computation typically demands a large computation cost and has mostly relied on the approximation techniques. However, our algorithm analytically derives the exact reachable set solution and further establishes a recursive computation structure that can perform in the real-time CPS operation. This significantly enhances the quality of the on-line safety assessment, enabling more reliable, less conservative, and computationally efficient process. The proposed algorithm is demonstrated with an illustrative example of an unmanned aircraft system (UAS) application.