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.