Identifying and Analyzing Dependencies in and among Complex Cyber Physical Systems

Abstract

Contemporary Critical Infrastructures (CIs), such as the power grid, comprise cyber physical systems that are tightly coupled, to form a complex system of interconnected components with interacting dependencies. Modelling methodologies have been suggested as proper tools to provide better insight into the dependencies and behavioural characteristics of these complex systems. In order to facilitate the study of interconnections in and among critical infrastructures, and to provide a clear view of the interdependencies among their cyber and physical components, this paper proposes a novel method, based on a graphical model called Modified Dependency Structure Matrix (MDSM). The MDSM provides a compact perspective of both inter-dependency and intra-dependency between subsystems of one complex system or two distinct systems. Additionally, we propose four parameters that allow the quantitative assessment of the characteristics of dependencies, including multi-order dependencies in large scale CIs. We illustrate the workings of the proposed method by applying it to a micro-distribution network based on the G2ELAB 14-Bus model. The results provide valuable insight into the dependencies among the network components and substantiate the applicability of the proposed method for analyzing large scale cyber physical systems.

Cyber-Physical Vulnerability Assessment in Smart Grids Based on Multilayer Complex Networks

“…− To determine the vulnerabilities of the cybercomplex network centrality indexes which all encies between power and ICT systems. Thes ered in monolayer centrality indexes [12][13][14][15][16][17][18][19]2 interconnection between power and ICT netw The content of the paper is organized as follows network theory and their centrality indexes used fo layer networks. In Section 3, a Cyber-physical sma composed of two interconnected heterogeneous netw and by the coupling layer between both networks.…”

“…where ⊕ α A [α] is the intra-layer adjacency matrix and ⊕ α,β A [α,β] is the inter-layer adjacency matrix corresponding to the connectivity matrix C. Figure 1 presents an example of a system with two layers; the physical layer contains two OT nodes (1,2) and the cyber layer comprises three IT nodes (3, 4, and 5). The intralayer adjacency matrices, corresponding to each layer as well as the intra-layer matrix, are defined by the matrices A [1] (4), A [2] (5), and ⊕ α A [α] (6). Similarly, the connectivity matrix between the layers is expressed by C (7), and it is obtained from the inter-layer adjacency matrices A [1,2] (8), where A [2,1] = A [1,2]T .…”

“…The intralayer adjacency matrices, corresponding to each layer as well as the intra-layer matrix, are defined by the matrices A [1] (4), A [2] (5), and ⊕ α A [α] (6). Similarly, the connectivity matrix between the layers is expressed by C (7), and it is obtained from the inter-layer adjacency matrices A [1,2] (8), where A [2,1] = A [1,2]T . Finally, the supra-adjacency matrix corresponding to the multilayer system in Figure 1 is represented by A M (9).…”

“…Finally, the supra-adjacency matrix corresponding to the multilayer system in Figure 1 is represented by ̅ ℳ (9). [2,1] 0 (7)…”

“…Smart grids are characterized by high digitisation that facilitates modernisation in electrical network infrastructure, active grid management, control and real-time communication with consumers, prosumers, and DSOs [ 1 ]. Smart grid digitisation has created new areas of work, in which the electrical and communications infrastructures are neither independent nor operate in isolation [ 2 , 3 ]. Consequently, both infrastructures must be integrated into a single cyber-physical system (CPS) that must be analysed holistically to identify potential vulnerabilities that may affect the security and continuity of the power supply.…”