Analysis and Design of Actuation-Sensing-Communication Interconnection Structures towards Secured/Resilient Closed-loop Systems

This paper considers the analysis and design of resilient/robust decentralized control systems. Specifically, we aim to assess how the pairing of sensors and actuators lead to architectures that are resilient to attacks/hacks for industrial control systems and other complex cyber-physical systems. We consider inherent structural properties such as internal fixed modes of a dynamical system depending on actuation, sensing, and interconnection/communication structure for linear discrete time-invariant dynamical systems. We introduce the notion of resilient fixed-modes free system that ensures the non-existence of fixed modes when the actuation-sensing-communication structure is compromised due to attacks by a malicious agent on actuators, sensors, or communication components and natural failures. Also, we provide a graph-theoretical characterization for the resilient structurally fixed modes that enables to capture the non-existence of resilient fixed modes for almost all possible systems' realizations. Additionally, we address the minimum actuation-sensing-communication co-design ensuring the non-existence of resiliently structurally fixed modes, which we show to be NP-hard. Notwithstanding, we identify conditions that are often satisfied in engineering settings and under which the co-design problem is solvable in polynomial-time complexity. Furthermore, we leverage the structural insights and properties to provide a convex optimization method to design the gain for a parametrized system and satisfying the sparsity of a given information pattern. Thus, exploring the interplay between structural and non-structural systems to ensure their resilience. Finally, the efficacy of the proposed approach is demonstrated on a power grid example.