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Network control theory (NCT) offers a robust analytical framework for understanding the influence of network topology on dynamic behaviors, enabling researchers to decipher how certain patterns of external control measures can steer system dynamics towards desired states. Distinguished from other structure-function methodologies, NCT's predictive capabilities can be coupled with deploying Graph Neural Networks (GNNs), which have demonstrated exceptional utility in various network-based learning tasks. However, the performance of GNNs heavily relies on the expressiveness of node features, and the lack of node features can greatly degrade their performance. Furthermore, many real-world systems may lack node-level information, posing a challenge for GNNs.To tackle this challenge, we introduce a novel approach, NCT-based Enhanced Feature Augmentation (NCT-EFA), that assimilates average controllability, along with other centrality indices, into the feature augmentation pipeline to enhance GNNs performance. Our evaluation of NCT-EFA, on six benchmark GNN models across two experimental setting. solely employing average controllability and in combination with additional centrality metrics. showcases an improved performance reaching as high as 11%. Our results demonstrate that incorporating NCT into feature enrichment can substantively extend the applicability and heighten the performance of GNNs in scenarios where node-level information is unavailable., Comment: Conference paper

This paper presents a novel approach for resilient distributed consensus in multiagent networks when dealing with adversarial agents imprecision in states observed by normal agents. Traditional resilient distributed consensus algorithms often presume that agents have exact knowledge of their neighbors' states, which is unrealistic in practical scenarios. We show that such existing methods are inadequate when agents only have access to imprecise states of their neighbors. To overcome this challenge, we adapt a geometric approach and model an agent's state by an `imprecision region' rather than a point in $\mathbb{R}^d$. From a given set of imprecision regions, we first present an efficient way to compute a region that is guaranteed to lie in the convex hull of true, albeit unknown, states of agents. We call this region the \emph{invariant hull} of imprecision regions and provide its geometric characterization. Next, we use these invariant hulls to identify a \emph{safe point} for each normal agent. The safe point of an agent lies within the convex hull of its \emph{normal} neighbors' states and hence is used by the agent to update it's state. This leads to the aggregation of normal agents' states to safe points inside the convex hull of their initial states, or an approximation of consensus. We also illustrate our results through simulations. Our contributions enhance the robustness of resilient distributed consensus algorithms by accommodating state imprecision without compromising resilience against adversarial agents., Comment: American Control Conference (ACC), 2024

In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of 'augmented' graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph's structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning., Comment: Accepted in 2024 American Control Conference (ACC), July 8-12, 2024 in Toronto, ON, Canada

Graph Neural Networks (GNNs) have shown remarkable merit in performing various learning-based tasks in complex networks. The superior performance of GNNs often correlates with the availability and quality of node-level features in the input networks. However, for many network applications, such node-level information may be missing or unreliable, thereby limiting the applicability and efficacy of GNNs. To address this limitation, we present a novel approach denoted as Ego-centric Spectral subGraph Embedding Augmentation (ESGEA), which aims to enhance and design node features, particularly in scenarios where information is lacking. Our method leverages the topological structure of the local subgraph to create topology-aware node features. The subgraph features are generated using an efficient spectral graph embedding technique, and they serve as node features that capture the local topological organization of the network. The explicit node features, if present, are then enhanced with the subgraph embeddings in order to improve the overall performance. ESGEA is compatible with any GNN-based architecture and is effective even in the absence of node features. We evaluate the proposed method in a social network graph classification task where node attributes are unavailable, as well as in a node classification task where node features are corrupted or even absent. The evaluation results on seven datasets and eight baseline models indicate up to a 10% improvement in AUC and a 7% improvement in accuracy for graph and node classification tasks, respectively., Comment: 22nd IEEE International Conference on Machine Learning and Applications 2023

This paper studies the controllability backbone problem in dynamical networks defined over graphs. The main idea of the controllability backbone is to identify a small subset of edges in a given network such that any subnetwork containing those edges/links has at least the same network controllability as the original network while assuming the same set of input/leader vertices. We consider the strong structural controllability (SSC) in our work, which is useful but computationally challenging. Thus, we utilize two lower bounds on the network's SSC based on the zero forcing notion and graph distances. We provide algorithms to compute controllability backbones while preserving these lower bounds. We thoroughly analyze the proposed algorithms and compute the number of edges in the controllability backbones. Finally, we compare and numerically evaluate our methods on random graphs., Comment: Accepted in 62nd IEEE Conference on Decision and Control, Dec. 13-15, 2023, Singapore

Graph unlearning emerges as a crucial advancement in the pursuit of responsible AI, providing the means to remove sensitive data traces from trained models, thereby upholding the right to be forgotten. It is evident that graph machine learning exhibits sensitivity to data privacy and adversarial attacks, necessitating the application of graph unlearning techniques to address these concerns effectively. In this comprehensive survey paper, we present the first systematic review of graph unlearning approaches, encompassing a diverse array of methodologies and offering a detailed taxonomy and up-to-date literature overview to facilitate the understanding of researchers new to this field. Additionally, we establish the vital connections between graph unlearning and differential privacy, augmenting our understanding of the relevance of privacy-preserving techniques in this context. To ensure clarity, we provide lucid explanations of the fundamental concepts and evaluation measures used in graph unlearning, catering to a broader audience with varying levels of expertise. Delving into potential applications, we explore the versatility of graph unlearning across various domains, including but not limited to social networks, adversarial settings, and resource-constrained environments like the Internet of Things (IoT), illustrating its potential impact in safeguarding data privacy and enhancing AI systems' robustness. Finally, we shed light on promising research directions, encouraging further progress and innovation within the domain of graph unlearning. By laying a solid foundation and fostering continued progress, this survey seeks to inspire researchers to further advance the field of graph unlearning, thereby instilling confidence in the ethical growth of AI systems and reinforcing the responsible application of machine learning techniques in various domains., Comment: 22 page review paper on graph unlearning

This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes $N$, the number of leaders $N_L$, and diameter $D$, where $2 \le D \le N/N_L$, we propose graph constructions generating strong structurally controllable networks. We also compute the number of edges in graphs, which are maximal for improved robustness measured by the algebraic connectivity and Kirchhoff index. For the controllability analysis, we utilize the notion of zero forcing sets in graphs. Additionally, we present graph grammars, which are sets of rules that agents apply in a distributed manner to construct the graphs mentioned above. We also numerically evaluate our methods. This work exploits the trade-off between network controllability and robustness and generates networks satisfying multiple design criteria., Comment: American Control Conference (ACC 2023)

This paper studies the problem of selecting input nodes (leaders) to make networks strong structurally controllable despite misbehaving nodes and edges. We utilize a graph-based characterization of network strong structural controllability (SSC) in terms of zero forcing in graphs, which is a dynamic coloring of nodes. We consider three types of misbehaving nodes and edges that disrupt the zero forcing process in graphs, thus, deteriorating the network SSC. Then, we examine a leader selection guaranteeing network SSC by ensuring the accuracy of the zero forcing process, despite $k$ misbehaving nodes/edges. Our main result shows that a network is resilient to $k$ misbehaving nodes/edges under one threat model if and only if it is resilient to the same number of failures under the other threat models. Thus, resilience against one threat model implies resilience against the other models. We then discuss the computational aspects of leader selection for resilient SSC and present a numerical evaluation.

Feature extraction is an essential task in graph analytics. These feature vectors, called graph descriptors, are used in downstream vector-space-based graph analysis models. This idea has proved fruitful in the past, with spectral-based graph descriptors providing state-of-the-art classification accuracy. However, known algorithms to compute meaningful descriptors do not scale to large graphs since: (1) they require storing the entire graph in memory, and (2) the end-user has no control over the algorithm's runtime. In this paper, we present streaming algorithms to approximately compute three different graph descriptors capturing the essential structure of graphs. Operating on edge streams allows us to avoid storing the entire graph in memory, and controlling the sample size enables us to keep the runtime of our algorithms within desired bounds. We demonstrate the efficacy of the proposed descriptors by analyzing the approximation error and classification accuracy. Our scalable algorithms compute descriptors of graphs with millions of edges within minutes. Moreover, these descriptors yield predictive accuracy comparable to the state-of-the-art methods but can be computed using only 25% as much memory., Comment: Extension of work accepted to PAKDD 2020. Accepted to ACM TKDD in 2023

In this paper, we study the maximum edge augmentation problem in directed Laplacian networks to improve their robustness while preserving lower bounds on their strong structural controllability (SSC). Since adding edges could adversely impact network controllability, the main objective is to maximally densify a given network by selectively adding missing edges while ensuring that SSC of the network does not deteriorate beyond certain levels specified by the SSC bounds. We consider two widely used bounds: first is based on the notion of zero forcing (ZF), and the second relies on the distances between nodes in a graph. We provide an edge augmentation algorithm that adds the maximum number of edges in a graph while preserving the ZF-based SSC bound, and also derive a closed-form expression for the exact number of edges added to the graph. Then, we examine the edge augmentation problem while preserving the distance-based bound and present a randomized algorithm that guarantees an approximate solution with high probability. Finally, we numerically evaluate and compare these edge augmentation solutions.

Distributed multi-task learning provides significant advantages in multi-agent networks with heterogeneous data sources where agents aim to learn distinct but correlated models simultaneously.However, distributed algorithms for learning relatedness among tasks are not resilient in the presence of Byzantine agents. In this paper, we present an approach for Byzantine resilient distributed multi-task learning. We propose an efficient online weight assignment rule by measuring the accumulated loss using an agent's data and its neighbors' models. A small accumulated loss indicates a large similarity between the two tasks. In order to ensure the Byzantine resilience of the aggregation at a normal agent, we introduce a step for filtering out larger losses. We analyze the approach for convex models and show that normal agents converge resiliently towards the global minimum.Further, aggregation with the proposed weight assignment rule always results in an improved expected regret than the non-cooperative case. Finally, we demonstrate the approach using three case studies, including regression and classification problems, and show that our method exhibits good empirical performance for non-convex models, such as convolutional neural networks.

In this paper, we study the relationship between resilience and accuracy in the resilient distributed multi-dimensional consensus problem. We consider a network of agents, each of which has a state in $\mathbb{R}^d$. Some agents in the network are adversarial and can change their states arbitrarily. The normal (non-adversarial) agents interact locally and update their states to achieve consensus at some point in the convex hull $\calC$ of their initial states. This objective is achievable if the number of adversaries in the neighborhood of normal agents is less than a specific value, which is a function of the local connectivity and the state dimension $d$. However, to be resilient against adversaries, especially in the case of large $d$, the desired local connectivity is large. We discuss that resilience against adversarial agents can be improved if normal agents are allowed to converge in a bounded region $\calB\supseteq\calC$, which means normal agents converge at some point close to but not necessarily inside $\calC$ in the worst case. The accuracy of resilient consensus can be measured by the Hausdorff distance between $\calB$ and $\calC$. As a result, resilience can be improved at the cost of accuracy. We propose a resilient bounded consensus algorithm that exploits the trade-off between resilience and accuracy by projecting $d$-dimensional states into lower dimensions and then solving instances of resilient consensus in lower dimensions. We analyze the algorithm, present various resilience and accuracy bounds, and also numerically evaluate our results., Comment: IEEE Conference on Decision and Control (CDC) 2020

We study the strong structural controllability (SSC) of diffusively coupled networks, where the external control inputs are injected to only some nodes, namely the leaders. For such systems, one measure of controllability is the dimension of strong structurally controllable subspace, which is equal to the smallest possible rank of controllability matrix under admissible (positive) coupling weights. In this paper, we compare two tight lower bounds on the dimension of strong structurally controllable subspace: one based on the distances of followers to leaders, and the other based on the graph coloring process known as zero forcing. We show that the distance-based lower bound is usually better than the zero-forcing-based bound when the leaders do not constitute a zero-forcing set. On the other hand, we also show that any set of leaders that can be shown to achieve complete SSC via the distance-based bound is necessarily a zero-forcing set. These results indicate that while the zero-forcing based approach may be preferable when the focus is only on verifying complete SSC, the distance-based approach is usually more informative when partial SSC is also of interest. Furthermore, we also present a novel bound based on the combination of these two approaches, which is always at least as good as, and in some cases strictly greater than, the maximum of the two bounds. We support our analysis with numerical results for various graphs and leader sets., Comment: Accepted to the 59th IEEE Conference on Decision and Control

In this paper, we study resilient distributed diffusion for multi-task estimation in the presence of adversaries where networked agents must estimate distinct but correlated states of interest by processing streaming data. We show that in general diffusion strategies are not resilient to malicious agents that do not adhere to the diffusion-based information processing rules. In particular, by exploiting the adaptive weights used for diffusing information, we develop time-dependent attack models that drive normal agents to converge to states selected by the attacker. We show that an attacker that has complete knowledge of the system can always drive its targeted agents to its desired estimates. Moreover, an attacker that does not have complete knowledge of the system including streaming data of targeted agents or the parameters they use in diffusion algorithms, can still be successful in deploying an attack by approximating the needed information. The attack models can be used for both stationary and non-stationary state estimation.In addition, we present and analyze a resilient distributed diffusion algorithm that is resilient to any data falsification attack in which the number of compromised agents in the local neighborhood of a normal agent is bounded. The proposed algorithm guarantees that all normal agents converge to their true target states if appropriate parameters are selected. We also analyze trade-off between the resilience of distributed diffusion and its performance in terms of steady-state mean-square-deviation (MSD) from the correct estimates. Finally, we evaluate the proposed attack models and resilient distributed diffusion algorithm using stationary and non-stationary multi-target localization.

In this paper, we study the resilient vector consensus problem in networks with adversarial agents and improve resilience guarantees of existing algorithms. A common approach to achieving resilient vector consensus is that every non-adversarial (or normal) agent in the network updates its state by moving towards a point in the convex hull of its \emph{normal} neighbors' states. Since an agent cannot distinguish between its normal and adversarial neighbors, computing such a point, often called as \emph{safe point}, is a challenging task. To compute a safe point, we propose to use the notion of \emph{centerpoint}, which is an extension of the median in higher dimensions, instead of Tverberg partition of points, which is often used for this purpose. We discuss that the notion of centerpoint provides a complete characterization of safe points in $\mathbb{R}^d$. In particular, we show that a safe point is essentially an interior centerpoint if the number of adversaries in the neighborhood of a normal agent $i$ is less than $\frac{N_i}{d+1} $, where $d$ is the dimension of the state vector and $N_i$ is the total number of agents in the neighborhood of $i$. Consequently, we obtain necessary and sufficient conditions on the number of adversarial agents to guarantee resilient vector consensus. Further, by considering the complexity of computing centerpoints, we discuss improvements in the resilience guarantees of vector consensus algorithms and compare with the other existing approaches. Finally, we numerically evaluate the performance of our approach through experiments.

In this paper, we consider a network of agents with Laplacian dynamics, and study the problem of improving network robustness by adding a maximum number of edges within the network while preserving a lower bound on its strong structural controllability (SSC) at the same time. Edge augmentation increases network's robustness to noise and structural changes, however, it could also deteriorate network controllability. Thus, by exploiting relationship between network controllability and distances between nodes in graphs, we formulate an edge augmentation problem with a constraint to preserve distances between certain node pairs, which in turn guarantees that a lower bound on SSC is maintained even after adding edges. In this direction, first we choose a node pair and maximally add edges while maintaining the distance between selected nodes. We show that an optimal solution belongs to a certain class of graphs called clique chains. Then, we present an algorithm to add edges while preserving distances between a certain collection of nodes. Further, we present a randomized algorithm that guarantees a desired approximation ratio with high probability to solve the edge augmentation problem. Finally, we evaluate our results on various networks., Comment: American Control Conference (ACC)2020, Denver

Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity between graphs. This enables applying data mining algorithms (e.g classification, clustering, or anomaly detection) on graph-structured data which have numerous applications in multiple domains. State-of-the-art algorithms for computing descriptors require the entire graph to be in memory, entailing a huge memory footprint, and thus do not scale well to increasing sizes of real-world networks. In this work, we propose streaming algorithms to efficiently approximate descriptors by estimating counts of sub-graphs of order $k\leq 4$, and thereby devise extensions of two existing graph comparison paradigms: the Graphlet Kernel and NetSimile. Our algorithms require a single scan over the edge stream, have space complexity that is a fraction of the input size, and approximate embeddings via a simple sampling scheme. Our design exploits the trade-off between available memory and estimation accuracy to provide a method that works well for limited memory requirements. We perform extensive experiments on real-world networks and demonstrate that our algorithms scale well to massive graphs., Comment: Accepted to PAKDD 2020

We address the problem of distributed state estimation of a linear dynamical process in an attack-prone environment. Recent attempts to solve this problem impose stringent redundancy requirements on the measurement and communication resources of the network. In this paper, we take a step towards alleviating such strict requirements by exploring two complementary directions: (i) making a small subset of the nodes immune to attacks, or "trusted", and (ii) incorporating diversity into the network. We define graph-theoretic constructs that formally capture the notions of redundancy, diversity, and trust. Based on these constructs, we develop a resilient estimation algorithm and demonstrate that even relatively sparse networks that either exhibit node-diversity, or contain a small subset of trusted nodes, can be just as resilient to adversarial attacks as more dense networks. Finally, given a finite budget for network design, we focus on characterizing the complexity of (i) selecting a set of trusted nodes, and (ii) allocating diversity, so as to achieve a desired level of robustness. We establish that, unfortunately, each of these problems is NP-complete.

Retinal blood vessels are considered to be the reliable diagnostic biomarkers of ophthalmologic and diabetic retinopathy. Monitoring and diagnosis totally depends on expert analysis of both thin and thick retinal vessels which has recently been carried out by various artificial intelligent techniques. Existing deep learning methods attempt to segment retinal vessels using a unified loss function optimized for both thin and thick vessels with equal importance. Due to variable thickness, biased distribution, and difference in spatial features of thin and thick vessels, unified loss function are more influential towards identification of thick vessels resulting in weak segmentation. To address this problem, a conditional patch-based generative adversarial network is proposed which utilizes a generator network and a patch-based discriminator network conditioned on the sample data with an additional loss function to learn both thin and thick vessels. Experiments are conducted on publicly available STARE and DRIVE datasets which show that the proposed model outperforms the state-of-the-art methods.

In this paper, we study the problem of computing a tight lower bound on the dimension of the strong structurally controllable subspace (SSCS) in networks with Laplacian dynamics. The bound is based on a sequence of vectors containing the distances between leaders (nodes with external inputs) and followers (remaining nodes) in the underlying network graph. Such vectors are referred to as the distance-to-leaders vectors. {We give exact and approximate algorithms to compute the longest sequences of distance-to-leaders vectors, which directly provide distance-based bounds on the dimension of SSCS. The distance-based bound is known to outperform the other known bounds (for instance, based on zero-forcing sets), especially when the network is partially strong structurally controllable. Using these results, we discuss an application of the distance-based bound in solving the leader selection problem for strong structural controllability. Further, we characterize strong structural controllability in path and cycle graphs with a given set of leader nodes using sequences of distance-to-leaders vectors. Finally, we numerically evaluate our results on various graphs.

We investigate how the graph topology influences the robustness to noise in undirected linear consensus networks. We measure the structural robustness by using the smallest possible value of steady state population variance of states under the noisy consensus dynamics with edge weights from the unit interval. We derive tight upper and lower bounds on the structural robustness of networks based on the average distance between nodes and the average node degree. Using the proposed bounds, we characterize the networks with different types of robustness scaling under increasing size. Furthermore, we present a fundamental trade-off between the structural robustness and the average degree of networks. While this trade-off implies that a desired level of structural robustness can only be achieved by graphs with a sufficiently large average degree, we also show that there exist dense graphs with poor structural robustness. We then show that, random k-regular graphs (the degree of each node is k) with n nodes typically have near-optimal structural robustness among all the graphs with size n and average degree k for sufficiently large n and k. We also show that when k increases properly with n, random k-regular graphs maintain a structural robustness within a constant factor of the complete graph's while also having the minimum average degree required for such robustness., Comment: Accepted for publication in IEEE Transactions on Automatic Control

A networked system can be made resilient against adversaries and attacks if the underlying network graph is structurally robust. For instance, to achieve distributed consensus in the presence of adversaries, the underlying network graph needs to satisfy certain robustness conditions. A typical approach to making networks structurally robust is to strategically add extra links between nodes, which might be prohibitively expensive. In this paper, we propose an alternative way of improving network's robustness, that is by considering heterogeneity of nodes. Nodes in a network can be of different types and can have multiple variants. As a result, different nodes can have disjoint sets of vulnerabilities, which means that an attacker can only compromise a particular type of nodes by exploiting a particular vulnerability. We show that, by such a diversification of nodes, attacker's ability to change the underlying network structure is significantly reduced. Consequently, even a sparse network with heterogeneous nodes can exhibit the properties of a structurally robust network. Using these ideas, we propose a distributed control policy that utilizes heterogeneity in the network to achieve resilient consensus in adversarial environment. We extend the notion of $(r,s)$-robustness to incorporate the diversity of nodes and provide necessary and sufficient conditions to guarantee resilient distributed consensus in heterogeneous networks. Finally we study the properties and construction of robust graphs with heterogeneous nodes., Comment: 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys) 2019

Neuroscience has traditionally relied on manually observing lab animals in controlled environments. Researchers usually record animals behaving in free or restrained manner and then annotate the data manually. The manual annotation is not desirable for three reasons; one, it is time consuming, two, it is prone to human errors and three, no two human annotators will 100\% agree on annotation, so it is not reproducible. Consequently, automated annotation of such data has gained traction because it is efficient and replicable. Usually, the automatic annotation of neuroscience data relies on computer vision and machine leaning techniques. In this article, we have covered most of the approaches taken by researchers for locomotion and gesture tracking of lab animals. We have divided these papers in categories based upon the hardware they use and the software approach they take. We also have summarized their strengths and weaknesses., Comment: 41 pages, 2 figures

In this paper, we demonstrate a conflicting relationship between two crucial properties---controllability and robustness---in linear dynamical networks of diffusively coupled agents. In particular, for any given number of nodes $N$ and diameter $D$, we identify networks that are maximally robust using the notion of Kirchhoff index and then analyze their strong structural controllability. For this, we compute the minimum number of leaders, which are the nodes directly receiving external control inputs, needed to make such networks controllable under all feasible coupling weights between agents. Then, for any $N$ and $D$, we obtain a sharp upper bound on the minimum number of leaders needed to design strong structurally controllable networks with $N$ nodes and diameter $D$. We also discuss that the bound is best possible for arbitrary $N$ and $D$. Moreover, we construct a family of graphs for any $N$ and $D$ such that the graphs have maximal edge sets (maximal robustness) while being strong structurally controllable with the number of leaders in the proposed sharp bound. We then analyze the robustness of this graph family. The results suggest that optimizing robustness increases the number of leaders needed for strong structural controllability. Our analysis is based on graph-theoretic methods and can be applied to exploit network structure to co-optimize robustness and controllability in networks., Comment: IEEE Transactions on Control of Network Systems

As the Industrial Internet of Things (IIot) becomes more prevalent in critical application domains, ensuring security and resilience in the face of cyber-attacks is becoming an issue of paramount importance. Cyber-attacks against critical infrastructures, for example, against smart water-distribution and transportation systems, pose serious threats to public health and safety. Owing to the severity of these threats, a variety of security techniques are available. However, no single technique can address the whole spectrum of cyber-attacks that may be launched by a determined and resourceful attacker. In light of this, we consider a multi-pronged approach for designing secure and resilient IIoT systems, which integrates redundancy, diversity, and hardening techniques. We introduce a framework for quantifying cyber-security risks and optimizing IIoT design by determining security investments in redundancy, diversity, and hardening. To demonstrate the applicability of our framework, we present two case studies in water distribution and transportation a case study in water-distribution systems. Our numerical evaluation shows that integrating redundancy, diversity, and hardening can lead to reduced security risk at the same cost.

In recent years, state-of-the-art traffic-control devices have evolved from standalone hardware to networked smart devices. Smart traffic control enables operators to decrease traffic congestion and environmental impact by acquiring real-time traffic data and changing traffic signals from fixed to adaptive schedules. However, these capabilities have inadvertently exposed traffic control to a wide range of cyber-attacks, which adversaries can easily mount through wireless networks or even through the Internet. Indeed, recent studies have found that a large number of traffic signals that are deployed in practice suffer from exploitable vulnerabilities, which adversaries may use to take control of the devices. Thanks to the hardware-based failsafes that most devices employ, adversaries cannot cause traffic accidents directly by setting compromised signals to dangerous configurations. Nonetheless, an adversary could cause disastrous traffic congestion by changing the schedule of compromised traffic signals, thereby effectively crippling the transportation network. To provide theoretical foundations for the protection of transportation networks from these attacks, we introduce a game-theoretic model of launching, detecting, and mitigating attacks that tamper with traffic-signal schedules. We show that finding optimal strategies is a computationally challenging problem, and we propose efficient heuristic algorithms for finding near optimal strategies. We also introduce a Gaussian-process based anomaly detector, which can alert operators to ongoing attacks. Finally, we evaluate our algorithms and the proposed detector using numerical experiments based on the SUMO traffic simulator.

Cyber-Physical Systems (CPS) allow us to manipulate objects in the physical world by providing a communication bridge between computation and actuation elements. In the current scheme of things, this sought-after control is marred by limitations inherent in the underlying communication network(s) as well as by the uncertainty found in the physical world. These limitations hamper fine-grained control of elements that may be separated by large-scale distances. In this regard, soft computing is an emerging paradigm that can help to overcome the vulnerabilities, and unreliability of CPS by using techniques including fuzzy systems, neural network, evolutionary computation, probabilistic reasoning and rough sets. In this paper, we present a comprehensive contemporary review of soft computing techniques for CPS dependability modeling, analysis, and improvement. This paper provides an overview of CPS applications, explores the foundations of dependability engineering, and highlights the potential role of soft computing techniques for CPS dependability with various case studies, while identifying common pitfalls and future directions. In addition, this paper provides a comprehensive survey on the use of various soft computing techniques for making CPS dependable., Comment: IEEE Access