Observability Robustness under Sensor Failures: Complexities and algorithms

The problem of determining the minimal number of sensors whose removal destroys observability of a linear time invariant system is studied. This problem is closely related to the ability of unique state reconstruction of a system under adversarial sensor attacks, and the dual of it is the inverse to the recently studied minimal controllability problems. It is proven that this problem is NP-hard both for a numerically specific system, and for a generic system whose nonzero entries of its system matrices are unknown but can take values freely (also called structured system). Two polynomial time algorithms are provided to solve this problem, respectively, on a numerical system with bounded maximum geometric multiplicities, and on a structured system with bounded matching deficiencies, which are often met by practical engineering systems. The proposed algorithms can be easily extended to the case where each sensor has a non-negative cost. Numerical experiments show that the structured system based algorithm could be alternative when the exact values of system matrices are not accessible.Comment: 8 pages, 2 figures, add some materials, fix some type error

Edge Selection in Bilinear Dynamical Networks

In large-scale networks, agents (e.g., sensors and actuators) and links (e.g., couplings and communication links) can fail or be (cyber-)attacked. In this paper, we focus on continuous-time bilinear networks, where additive disturbances model attack/uncertainty on agents/states (a.k.a. node disturbances) and multiplicative disturbances model attack/uncertainty on couplings between agents/states (a.k.a. link disturbances). We then investigate a network robustness notion in terms of the underlying digraph of the network, and structure of exogenous uncertainties/attacks. Specifically, we define the robustness measure using the H2-norm of the network and calculate it in terms of the reachability Gramian of the bilinear system. The main result shows that under certain conditions, the measure is supermodular over the set of all possible attacked links. The supermodular property facilitates the efficient solution finding of the optimization problem. We conclude the paper with a few examples illustrating how different structures can make the system more or less vulnerable to malicious attacks on links and present our concluding remarks.Comment: 6 pages, 2 figure

CNN-based Prediction of Network Robustness With Missing Edges

Connectivity and controllability of a complex network are two important issues that guarantee a networked system to function. Robustness of connectivity and controllability guarantees the system to function properly and stably under various malicious attacks. Evaluating network robustness using attack simulations is time consuming, while the convolutional neural network (CNN)-based prediction approach provides a cost-efficient method to approximate the network robustness. In this paper, we investigate the performance of CNN-based approaches for connectivity and controllability robustness prediction, when partial network information is missing, namely the adjacency matrix is incomplete. Extensive experimental studies are carried out. A threshold is explored that if a total amount of more than 7.29\% information is lost, the performance of CNN-based prediction will be significantly degenerated for all cases in the experiments. Two scenarios of missing edge representations are compared, 1) a missing edge is marked `no edge' in the input for prediction, and 2) a missing edge is denoted using a special marker of `unknown'. Experimental results reveal that the first representation is misleading to the CNN-based predictors.Comment: In Proceedings of the IEEE 2022 International Joint Conference on Neural Networks (IJCNN

Cyber-Threat Assessment for the Air Traffic Management System: A Network Controls Approach

Air transportation networks are being disrupted with increasing frequency by failures in their cyber- (computing, communication, control) systems. Whether these cyber- failures arise due to deliberate attacks or incidental errors, they can have far-reaching impact on the performance of the air traffic control and management systems. For instance, a computer failure in the Washington DC Air Route Traffic Control Center (ZDC) on August 15, 2015, caused nearly complete closure of the Centers airspace for several hours. This closure had a propagative impact across the United States National Airspace System, causing changed congestion patterns and requiring placement of a suite of traffic management initiatives to address the capacity reduction and congestion. A snapshot of traffic on that day clearly shows the closure of the ZDC airspace and the resulting congestion at its boundary, which required augmented traffic management at multiple locations. Cyber- events also have important ramifications for private stakeholders, particularly the airlines. During the last few months, computer-system issues have caused several airlines fleets to be grounded for significant periods of time: these include United Airlines (twice), LOT Polish Airlines, and American Airlines. Delays and regional stoppages due to cyber- events are even more common, and may have myriad causes (e.g., failure of the Department of Homeland Security systems needed for security check of passengers, see [3]). The growing frequency of cyber- disruptions in the air transportation system reflects a much broader trend in the modern society: cyber- failures and threats are becoming increasingly pervasive, varied, and impactful. In consequence, an intense effort is underway to develop secure and resilient cyber- systems that can protect against, detect, and remove threats, see e.g. and its many citations. The outcomes of this wide effort on cyber- security are applicable to the air transportation infrastructure, and indeed security solutions are being implemented in the current system. While these security solutions are important, they only provide a piecemeal solution. Particular computers or communication channels are protected from particular attacks, without a holistic view of the air transportation infrastructure. On the other hand, the above-listed incidents highlight that a holistic approach is needed, for several reasons. First, the air transportation infrastructure is a large scale cyber-physical system with multiple stakeholders and diverse legacy assets. It is impractical to protect every cyber- asset from known and unknown disruptions, and instead a strategic view of security is needed. Second, disruptions to the cyber- system can incur complex propagative impacts across the air transportation network, including its physical and human assets. Also, these implications of cyber- events are exacerbated or modulated by other disruptions and operational specifics, e.g. severe weather, operator fatigue or error, etc. These characteristics motivate a holistic and strategic perspective on protecting the air transportation infrastructure from cyber- events. The analysis of cyber- threats to the air traffic system is also inextricably tied to the integration of new autonomy into the airspace. The replacement of human operators with cyber functions leaves the network open to new cyber threats, which must be modeled and managed. Paradoxically, the mitigation of cyber events in the airspace will also likely require additional autonomy, given the fast time scale and myriad pathways of cyber-attacks which must be managed. The assessment of new vulnerabilities upon integration of new autonomy is also a key motivation for a holistic perspective on cyber threats

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control

Can Competition Outperform Collaboration? The Role of Misbehaving Agents

We investigate a novel approach to resilient distributed optimization with quadratic costs in a multi-agent system prone to unexpected events that make some agents misbehave. In contrast to commonly adopted filtering strategies, we draw inspiration from phenomena modeled through the Friedkin-Johnsen dynamics and argue that adding competition to the mix can improve resilience in the presence of misbehaving agents. Our intuition is corroborated by analytical and numerical results showing that (i) there exists a nontrivial trade-off between full collaboration and full competition and (ii) our competition-based approach can outperform state-of-the-art algorithms based on Weighted Mean Subsequence Reduced. We also study impact of communication topology and connectivity on resilience, pointing out insights to robust network design.Comment: Submitted to IEEE TAC - first revisio

Structural engineering of evolving complex dynamical networks

Networks are ubiquitous in nature and many natural and man-made systems can be modelled as networked systems. Complex networks, systems comprising a number of nodes that are connected through edges, have been frequently used to model large-scale systems from various disciplines such as biology, ecology, and engineering. Dynamical systems interacting through a network may exhibit collective behaviours such as synchronisation, consensus, opinion formation, flocking and unusual phase transitions. Evolution of such collective behaviours is highly dependent on the structure of the interaction network. Optimisation of network topology to improve collective behaviours and network robustness can be achieved by intelligently modifying the network structure. Here, it is referred to as "Engineering of the Network". Although coupled dynamical systems can develop spontaneous synchronous patterns if their coupling strength lies in an appropriate range, in some applications one needs to control a fraction of nodes, known as driver nodes, in order to facilitate the synchrony. This thesis addresses the problem of identifying the set of best drivers, leading to the best pinning control performance. The eigen-ratio of the augmented Laplacian matrix, that is the largest eigenvalue divided by the second smallest one, is chosen as the controllability metric. The approach introduced in this thesis is to obtain the set of optimal drivers based on sensitivity analysis of the eigen-ratio, which requires only a single computation of the eigenvector associated with the largest eigenvalue, and thus is applicable for large-scale networks. This leads to a new "controllability centrality" metric for each subset of nodes. Simulation results reveal the effectiveness of the proposed metric in predicting the most important driver(s) correctly.     Interactions in complex networks might also facilitate the propagation of undesired effects, such as node/edge failure, which may crucially affect the performance of collective behaviours. In order to study the effect of node failure on network synchronisation, an analytical metric is proposed that measures the effect of a node removal on any desired eigenvalue of the Laplacian matrix. Using this metric, which is based on the local multiplicity of each eigenvalue at each node, one can approximate the impact of any node removal on the spectrum of a graph. The metric is computationally efficient as it only needs a single eigen-decomposition of the Laplacian matrix. It also provides a reliable approximation for the "Laplacian energy" of a network. Simulation results verify the accuracy of this metric in networks with different topologies. This thesis also considers formation control as an application of network synchronisation and studies the "rigidity maintenance" problem, which is one of the major challenges in this field. This problem is to preserve the rigidity of the sensing graph in a formation during motion, taking into consideration constraints such as line-of-sight requirements, sensing ranges and power limitations. By introducing a "Lattice of Configurations" for each node, a distributed rigidity maintenance algorithm is proposed to preserve the rigidity of the sensing network when failure in a sensing link would result in loss of rigidity. The proposed algorithm recovers rigidity by activating, almost always, the minimum number of new sensing links and considers real-time constraints of practical formations. A sufficient condition for this problem is proved and tested via numerical simulations. Based on the above results, a number of other areas and applications of network dynamics are studied and expounded upon in this thesis