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Sensor network localization (SNL) is a challenging problem due to its inherent non-convexity and the effects of noise in inter-node ranging measurements and anchor node position. We formulate a non-convex SNL problem as a multi-player non-convex potential game and investigate the existence and uniqueness of a Nash equilibrium (NE) in both the ideal setting without measurement noise and the practical setting with measurement noise. We first show that the NE exists and is unique in the noiseless case, and corresponds to the precise network localization. Then, we study the SNL for the case with errors affecting the anchor node position and the inter-node distance measurements. Specifically, we establish that in case these errors are sufficiently small, the NE exists and is unique. It is shown that the NE is an approximate solution to the SNL problem, and that the position errors can be quantified accordingly. Based on these findings, we apply the results to case studies involving only inter-node distance measurement errors and only anchor position information inaccuracies., Comment: arXiv admin note: text overlap with arXiv:2311.03326, arXiv:2401.02471

In this note, we investigate the robustness of Nash equilibria (NE) in multi-player aggregative games with coupling constraints. There are many algorithms for computing an NE of an aggregative game given a known aggregator. When the coupling parameters are affected by uncertainty, robust NE need to be computed. We consider a scenario where players' weight in the aggregator is unknown, making the aggregator kind of "a black box". We pursue a suitable learning approach to estimate the unknown aggregator by proposing an inverse variational inequality-based relationship. We then utilize the counterpart to reconstruct the game and obtain first-order conditions for robust NE in the worst case. Furthermore, we characterize the generalization property of the learning methodology via an upper bound on the violation probability. Simulation experiments show the effectiveness of the proposed inverse learning approach.

Consider a sensor network consisting of both anchor and non-anchor nodes. We address the following sensor network localization (SNL) problem: given the physical locations of anchor nodes and relative measurements among all nodes, determine the locations of all non-anchor nodes. The solution to the SNL problem is challenging due to its inherent non-convexity. In this paper, the problem takes on the form of a multi-player non-convex potential game in which canonical duality theory is used to define a complementary dual potential function. After showing the Nash equilibrium (NE) correspondent to the SNL solution, we provide a necessary and sufficient condition for a stationary point to coincide with the NE. An algorithm is proposed to reach the NE and shown to have convergence rate $\mathcal{O}(1/\sqrt{k})$. With the aim of reducing the information exchange within a network, a distributed algorithm for NE seeking is implemented and its global convergence analysis is provided. Extensive simulations show the validity and effectiveness of the proposed approach to solve the SNL problem., Comment: arXiv admin note: text overlap with arXiv:2311.03326

Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results.

In this paper we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed either the absence of constraints or fixed constraints. This work considers a more general setting where the constraints can also dynamically adjust in response to changes in the decision variables. Specifically, we consider linear constraints and analyze the effect of decision-dependent distributions in both the objective function and constraints. Firstly, we establish a sufficient condition for the existence of a constrained equilibrium point, at which the distributions remain invariant under retraining. Morevoer, we propose and analyze two algorithms: repeated constrained optimization and repeated dual ascent. For each algorithm, we provide sufficient conditions for convergence to the constrained equilibrium point. Furthermore, we explore the relationship between the equilibrium point and the optimal point for the constrained decision-dependent optimization problem. Notably, our results encompass previous findings as special cases when the constraints remain fixed. To show the effectiveness of our theoretical analysis, we provide numerical experiments on both a market problem and a dynamic pricing problem for parking based on real-world data.

We revisit an algorithm for distributed consensus optimization proposed in 2010 by J. Wang and N. Elia. By means of a Lyapunov-based analysis, we prove input-to-state stability of the algorithm relative to a closed invariant set composed of optimal equilibria and with respect to perturbations affecting the algorithm's dynamics. In the absence of perturbations, this result implies linear convergence of the local estimates and Lyapunov stability of the optimal steady state. Moreover, we unveil fundamental connections with the well-known Gradient Tracking and with distributed integral control. Overall, our results suggest that a control theoretic approach can have a considerable impact on (distributed) optimization, especially when robustness is considered.

In this paper, we examine the factors that influence the success of false data injection (FDI) attacks in the context of both cyber and physical styles of reinforcement. Many works consider the FDI attack in the context of the ability to change a measurement in a static system only. However, successful attacks will require first intrusion into a system followed by construction of an attack vector that can bypass bad data detection (BDD). In this way, we develop a full service framework for FDI risk assessment. The framework considers both the costs of system intrusion via a weighted graph assessment in combination with a physical, line overload-based vulnerability assessment. We present our simulations on a IEEE 14-bus system with an overlain RTU network to model the true risk of intrusion. The cyber model considers multiple methods of entry for the FDI attack including meter intrusion, RTU intrusion and combined style attacks. Post-intrusion our physical reinforcement model analyses the required level of topology divergence to protect against a branch overload from an optimised attack vector.

State estimation for a class of linear time-invariant systems with distributed output measurements (distributed sensors) and unknown inputs is addressed in this paper. The objective is to design a network of observers such that the state vector of the entire system can be estimated, while each observer (or node) has access to only local output measurements that may not be sufficient on its own to reconstruct the entire system's state. Existing results in the literature on distributed state estimation assume either that the system does not have inputs, or that all the system's inputs are globally known to all the observers. Accordingly, we address this gap by proposing a distributed observer capable of estimating the overall system's state in the presence of inputs, while each node only has limited local information on inputs and outputs. We provide a design method that guarantees convergence of the estimation errors under some mild joint detectability conditions. This design suits undirected communication graphs that may have switching topologies and also applies to strongly connected directed graphs. We also give existence conditions that harmonize with existing results on unknown input observers. Finally, simulation results verify the effectiveness of the proposed estimation scheme for various scenarios.

We consider an intersection zone where autonomous vehicles (AVs) and human-driven vehicles (HDVs) can be present. As a new vehicle arrives, the traffic controller needs to decide and impose an optimal sequence of the vehicles that will exit the intersection zone. The traffic controller can send information regarding the time at which an AV can cross the intersection; however, the traffic controller can not communicate with the HDVs, rather the HDVs can only be controlled using the traffic lights. We formulate the problem as an integer constrained non-linear optimization problem where the traffic-intersection controller only communicates with a subset of the AVs. Since the number of possible combinations increases exponentially with the number of vehicles in the system, we relax the original problem and proposes an algorithm that gives the optimal solution of the relaxed problem and yet only scales linearly with the number of vehicles in the system. The numerical evaluation shows that our algorithm outperforms the First-In-First-Out (FIFO) algorithm.

The ranking of nodes in a network according to their ``importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The current COVID-19 pandemic has recently rejuvenated the interest in this problem, as it is related to the selection of which individuals should be tested in a population of asymptomatic individuals, or which individuals should be vaccinated first. Motivated by the COVID-19 spreading dynamics, in this paper we review the most popular methods for node ranking in undirected unweighted graphs, and compare their performance in a benchmark realistic network, that takes into account the community-based structure of society. Also, we generalize a classic benchmark network originally proposed by Newman for ranking nodes in unweighted graphs, to show how ranks change in the weighted case.

We consider a mixed autonomy scenario where the traffic intersection controller decides whether the traffic light will be green or red at each lane for multiple traffic-light blocks. The objective of the traffic intersection controller is to minimize the queue length at each lane and maximize the outflow of vehicles over each block. We consider that the traffic intersection controller informs the autonomous vehicle (AV) whether the traffic light will be green or red for the future traffic-light block. Thus, the AV can adapt its dynamics by solving an optimal control problem. We model the decision process of the traffic intersection controller as a deterministic delay Markov decision process owing to the delayed action by the traffic controller. We propose Reinforcement-learning based algorithm to obtain the optimal policy. We show - empirically - that our algorithm converges and reduces the energy costs of AVs drastically as the traffic controller communicates with the AVs., Comment: Accepted for Publication at 24th IEEE International Conference on Intelligent Transportation (ITSC'2021)

The paper deals with the distributed minimum sharing problem: a set of decision-makers compute the minimum of some local quantities of interest in a distributed and decentralized way by exchanging information through a communication network. We propose an adjustable approximate solution which enjoys several properties of crucial importance in applications. In particular, the proposed solution has good decentralization properties and it is scalable in that the number of local variables does not grow with the size or topology of the communication network. Moreover, a global and uniform (both in the initial time and in the initial conditions) asymptotic stability result is provided towards a steady state which can be made arbitrarily close to the sought minimum. Exact asymptotic convergence can be recovered at the price of losing uniformity with respect to the initial time.

The problem of mitigating maliciously injected signals in interconnected systems is dealt with in this paper. We consider the class of covert attacks, as they are stealthy and cannot be detected by conventional means in centralized settings. Distributed architectures can be leveraged for revealing such stealthy attacks by exploiting communication and local model knowledge. We show how such detection schemes can be improved to estimate the action of an attacker and we propose an accommodation scheme in order to mitigate or neutralize abnormal behavior of a system under attack.

Testing, tracking and tracing abilities have been identified as pivotal in helping countries to safely reopen activities after the first wave of the COVID-19 virus. Contact tracing apps give the unprecedented possibility to reconstruct graphs of daily contacts, so the question is who should be tested? As human contact networks are known to exhibit community structure, in this paper we show that the Kemeny constant of a graph can be used to identify and analyze bridges between communities in a graph. Our "Kemeny indicator" is the change in Kemeny constant when a node or edge is removed from the graph. We show that testing individuals who are associated with large values of the Kemeny indicator can help in efficiently intercepting new virus outbreaks, when they are still in their early stage. Extensive simulations provide promising results in early identification and in blocking possible "super-spreaders" links that transmit disease between different communities.

This paper examines how moving target defences (MTD) implemented in power systems can be countered by unsupervised learning-based false data injection (FDI) attack and how MTD can be combined with physical watermarking to enhance the system resilience. A novel intelligent attack, which incorporates density-based spatial clustering and dimensionality reduction, is developed and shown to be effective in maintaining stealth in the presence of traditional MTD strategies. In resisting this new type of attack, a novel implementation of MTD combining with physical watermarking is proposed by adding Gaussian watermark into physical plant parameters to drive detection of traditional and intelligent FDI attacks, while remaining hidden to the attackers and limiting the impact on system operation and stability.

Over the last years, Industrial Control Systems (ICS) have become increasingly exposed to a wide range of cyber-physical threats. Efficient models and techniques able to capture their complex structure and identify critical cyber-physical components are therefore essential. AND/OR graphs have proven very useful in this context as they are able to semantically grasp intricate logical interdependencies among ICS components. However, identifying critical nodes in AND/OR graphs is an NP-complete problem. In addition, ICS settings normally involve various cyber and physical security measures that simultaneously protect multiple ICS components in overlapping manners, which makes this problem even harder. In this paper, we present an extended security metric based on AND/OR hypergraphs which efficiently identifies the set of critical ICS components and security measures that should be compromised, with minimum cost (effort) for an attacker, in order to disrupt the operation of vital ICS assets. Our approach relies on MAX-SAT techniques, which we have incorporated in META4ICS, a Java-based security metric analyser for ICS. We also provide a thorough performance evaluation that shows the feasibility of our method. Finally, we illustrate our methodology through a case study in which we analyse the security posture of a realistic Water Transport Network (WTN)., Comment: 10 pages, 10 figures. Keywords: security metrics, cyber-physical security, AND-OR graphs, hypergraphs, MAX-SAT resolution, ICS, CPS

This paper presents a MaxSAT benchmark focused on identifying critical nodes in AND/OR graphs. We use AND/OR graphs to model Industrial Control Systems (ICS) as they are able to semantically grasp intricate logical interdependencies among ICS components. However, identifying critical nodes in AND/OR graphs is an NP-complete problem. We address this problem by efficiently transforming the input AND/OR graph-based model into a weighted logical formula that is then used to build and solve a Weighted Partial MaxSAT problem. The benchmark includes 80 cases with AND/OR graphs of different size and composition as well as the optimal cost and solution for each case., Comment: arXiv admin note: substantial text overlap with arXiv:1905.04796

In recent years, Industrial Control Systems (ICS) have become an appealing target for cyber attacks, having massive destructive consequences. Security metrics are therefore essential to assess their security posture. In this paper, we present a novel ICS security metric based on AND/OR graphs that represent cyber-physical dependencies among network components. Our metric is able to efficiently identify sets of critical cyber-physical components, with minimal cost for an attacker, such that if compromised, the system would enter into a non-operational state. We address this problem by efficiently transforming the input AND/OR graph-based model into a weighted logical formula that is then used to build and solve a Weighted Partial MAX-SAT problem. Our tool, META4ICS, leverages state-of-the-art techniques from the field of logical satisfiability optimisation in order to achieve efficient computation times. Our experimental results indicate that the proposed security metric can efficiently scale to networks with thousands of nodes and be computed in seconds. In addition, we present a case study where we have used our system to analyse the security posture of a realistic water transport network. We discuss our findings on the plant as well as further security applications of our metric., Comment: Keywords: Security metrics, industrial control systems, cyber-physical systems, AND-OR graphs, MAX-SAT resolution

The problem of replay attacks in the communication network between Distributed Generation Units (DGUs) of a DC microgrid is examined. The DGUs are regulated through a hierarchical control architecture, and are networked to achieve secondary control objectives. Following analysis of the detectability of replay attacks by a distributed monitoring scheme previously proposed, the need for a watermarking signal is identified. Hence, conditions are given on the watermark in order to guarantee detection of replay attacks, and such a signal is designed. Simulations are then presented to demonstrate the effectiveness of the technique.

Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using Sum-of-Squares(SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L2-norm. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs.