Towards Robustness for Cyber-Physical Systems

While the importance of robustness in engineering design is well accepted, it is less clear how to design cyber-physical systems (CPS) for robustness. With the objective of developing a robustness theory for CPS, we introduce a notion of robustness for cyber systems inspired by existing notions of input-output stability in control theory. We show that the proposed notion of robustness captures two intuitive goals: bounded disturbances lead to bounded deviations from nominal behavior, and the effect of a sporadic disturbance disappears in finitely many steps. For cyber systems modeled as finite-state transducers, the proposed notion of robustness can be verified in pseudo-polynomial time. The synthesis problem, consisting of designing a controller enforcing robustness, can also be solved in pseudo-polynomial time.