Robust Optimal Network Topology Switching for Zero Dynamics Attacks

Abstract: The intrinsic, sampling, and enforced zero dynamics attacks (ZDAs) are among the most detrimental stealthy attacks in robotics, aerospace, and cyber-physical systems. They exploit internal dynamics, discretization, redundancy/asynchronous actuation and sensing, to construct disruptive attacks that are completely stealthy in the measurement. They work even when the systems are both controllable and observable. This paper presents a novel framework to robustly and optimally detect and mitigate ZDAs for networked linear control systems. We utilize controllability, observability, robustness, and sensitivity metrics written explicitly in terms of the system topology, thereby proposing a robust and optimal switching topology formulation for resilient ZDA detection and mitigation. Our main contribution is the reformulation of this problem into an equivalent rank-constrained optimization problem (i.e., optimization with a convex objective function subject to convex constraints and rank constraints), which can be solved using convex rank minimization approaches. The effectiveness of our method is demonstrated using networked double integrators subject to ZDAs.