Analysis and Design of Actuation–Sensing–Communication Interconnection Structures Toward Secured/Resilient LTI 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 a resilient fixed-modes free system that ensures the nonexistence 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 nonexistence of resilient fixed modes for almost all possible systems' realizations. Additionally, we address the minimum actuation-sensing-communication codesign ensuring the nonexistence 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 codesign 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 parameterized system and satisfying the sparsity of a given information pattern. Thus, exploring the interplay between structural and nonstructural systems to ensure their resilience. Finally, the efficacy of the proposed approach is demonstrated on a power grid example.