arXiv subjects

Mohammad Pirani

Publications and source records attributed to Mohammad Pirani.

32 records · Page 2Linked to original sources

arXiv2022

A Survey of Graph-Theoretic Approaches for Analyzing the Resilience of Networked Control Systems

As the scale of networked control systems increases and interactions between different subsystems become more sophisticated, questions of the resilience of such networks increase in importance. The need to redefine classical system and control-theoretic notions using the language of graphs has recently started to gain attention as a fertile and important area of research. This paper presents an overview of graph-theoretic methods for analyzing the resilience of networked control systems. We discuss various distributed algorithms operating on networked systems and investigate their resilience against adversarial actions by looking at the structural properties of their underlying networks. We present graph-theoretic methods to quantify the attack impact, and reinterpret some system-theoretic notions of robustness from a graph-theoretic standpoint to mitigate the impact of the attacks. Moreover, we discuss miscellaneous problems in the security of networked control systems which use graph-theory as a tool in their analyses. We conclude by introducing some avenues for further research in this field.

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arXiv2021

Consensus-Based Distributed Estimation in the Presence of Heterogeneous, Time-Invariant Delays

Classical distributed estimation scenarios typically assume timely and reliable exchanges of information over the sensor network. This paper, in contrast, considers single time-scale distributed estimation via a sensor network subject to transmission time-delays. The proposed discrete-time networked estimator consists of two steps: (i) consensus on (delayed) a-priori estimates, and (ii) measurement update. The sensors only share their a-priori estimates with their out-neighbors over (possibly) time-delayed transmission links. The delays are assumed to be fixed over time, heterogeneous, and known. We assume distributed observability instead of local observability, which significantly reduces the communication/sensing loads on sensors. Using the notions of augmented matrices and Kronecker product, the convergence of the proposed estimator over strongly-connected networks is proved for a specific upper-bound on the time-delay.

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arXiv2021

Resilient Coordinated Movement of Connected Autonomous Vehicles

In this paper, we consider coordinated movement of a network of vehicles consisting of a bounded number of malicious agents, that is, vehicles must reach consensus in longitudinal position and a common predefined velocity. The motions of vehicles are modeled by double-integrator dynamics and communications over the network are asynchronous with delays. Each normal vehicle updates its states by utilizing the information it receives from vehicles in its vicinity. On the other hand, misbehaving vehicles make updates arbitrarily and might threaten the consensus within the network by intentionally changing their moving direction or broadcasting faulty information in their neighborhood. We propose an asynchronous updating strategy for normal vehicles, based on filtering extreme values received from neighboring vehicles, to save them from being misguided by malicious vehicles. We show that there exist topological constraints on the network in terms of graph robustness under which the vehicles resiliently achieve coordinated movement. Numerical simulations are provided to evaluate the results.

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arXiv2019

Attack Resilient Interconnected Second Order Systems: A Game-Theoretic Approach

This paper studies the resilience of second-order networked dynamical systems to strategic attacks. We discuss two widely used control laws, which have applications in power networks and formation control of autonomous agents. In the first control law, each agent receives pure velocity feedback from its neighbor. In the second control law, each agent receives its velocity relative to its neighbors. The attacker selects a subset of nodes in which to inject a signal, and its objective is to maximize the $\mathcal{H}_2$ norm of the system from the attack signal to the output. The defender improves the resilience of the system by adding self-feedback loops to certain nodes of the network with the objective of minimizing the system's $\mathcal{H}_2$ norm. Their decisions comprise a strategic game. Graph-theoretic necessary and sufficient conditions for the existence of Nash equilibria are presented. In the case of no Nash equilibrium, a Stackelberg game is discussed, and the optimal solution when the defender acts as the leader is characterized. For the case of a single attacked node and a single defense node, it is shown that the optimal location of the defense node for each of the control laws is determined by a specific network centrality measure. The extension of the game to the case of multiple attacked and defense nodes is also addressed.

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arXiv2018

Synchronization of Kuramoto oscillators in a bidirectional frequency-dependent tree network

This paper studies the synchronization of a finite number of Kuramoto oscillators in a frequency-dependent bidirectional tree network. We assume that the coupling strength of each link in each direction is equal to the product of a common coefficient and the exogenous frequency of its corresponding head oscillator. We derive a sufficient condition for the common coupling strength in order to guarantee frequency synchronization in tree networks. Moreover, we discuss the dependency of the obtained bound on both the graph structure and the way that exogenous frequencies are distributed. Further, we present an application of the obtained result by means of an event-triggered algorithm for achieving frequency synchronization in a star network assuming that the common coupling coefficient is given.

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arXiv2018

A Game-theoretic Framework for Security-aware Sensor Placement Problem in Networked Control Systems

This paper studies the sensor placement problem in a networked control system for improving its security against cyber-physical attacks. The problem is formulated as a zero-sum game between an attacker and a detector. The attacker's decision is to select $f$ nodes of the network to attack whereas the detector's decision is to place $f$ sensors to detect the presence of the attack signals. In our formulation, the attacker minimizes its visibility, defined as the system $L_2$ gain from the attack signals to the deployed sensors' outputs, and the detector maximizes the visibility of the attack signals. The equilibrium strategy of the game determines the optimal locations of the sensors. The existence of Nash equilibrium for the attacker-detector game is studied when the underlying connectivity graph is a directed or an undirected tree. When the game does not admit a Nash equilibrium, it is shown that the Stackelberg equilibrium of the game, with the detector as the game leader, can be computed efficiently. Finally, the attacker-detector game is studied in a cooperative adaptive cruise control algorithm for vehicle platooning problem. The existence of Nash equilibrium is investigated for both directed and undirected platoons and the effect of the position of the reference vehicle on the game value is studied. Our results show that, under the optimal sensor placement strategy, an undirected topology provides a higher security level for a networked control system compared with its corresponding directed topology.

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arXiv2018

A Graph-Theoretic Approach to the $\mathcal{H}_{\infty}$ Performance of Dynamical Systems on Directed and Undirected Networks

We study a graph-theoretic approach to the $\mathcal{H}_{\infty}$ performance of leader following consensus dynamics on directed and undirected graphs. We first provide graph-theoretic bounds on the system $\mathcal{H}_{\infty}$ norm of the leader following dynamics and show the tightness of the proposed bounds. Then, we discuss the relation between the system $\mathcal{H}_{\infty}$ norm for directed and undirected networks for specific classes of graphs, i.e., balanced digraphs and directed trees. Moreover, we investigate the effects of adding directed edges to a directed tree on the resulting system $\mathcal{H}_{\infty}$ norm. In the end, we apply these theoretical results to a reference velocity tracking problem in a platoon of connected vehicles and discuss the effect of the location of the leading vehicle on the overall $\mathcal{H}_{\infty}$ performance of the system.

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arXiv2018

Resilient Estimation and Control on $k$-Nearest Neighbor Platoons: A Network-Theoretic Approach

This paper is concerned with the network-theoretic properties of so-called $k$-nearest neighbor intelligent vehicular platoons, where each vehicle communicates with $k$ vehicles, both in front and behind. The network-theoretic properties analyzed in this paper play major roles in quantifying the resilience and robustness of three generic distributed estimation and control algorithms against communication failures and disturbances, namely resilient distributed estimation, resilient distributed consensus, and robust network formation. Based on the results for the connectivity measures of the $k$-nearest neighbor platoon, we show that extending the traditional platooning topologies (which were based on interacting with nearest neighbors) to $k$-nearest neighbor platoons increases the resilience of distributed estimation and control algorithms to both communication failures and disturbances. Finally, we discuss how the performance of each algorithm scales with the size of the vehicle platoon.

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arXiv2017

Cooperative Vehicle Speed Fault Diagnostics and Correction

Reliable estimation (or measurement) of vehicle states has always been an active topic of research in the automotive industry and academia. Among the vehicle states, vehicle speed has a priority due to its critical importance in traction and stability control. Moreover, the emergence of new generation of communication technologies has brought a new avenue to traditional studies on vehicle estimation and control. To this end, this paper introduces a set of distributed function calculation algorithms for vehicle networks, robust to communication failures. The introduced algorithms enable each vehicle to gather information from other vehicles in the network in a distributed manner. A procedure to use such a bank of information for a single vehicle to diagnose and correct a possible fault in its own speed estimation/measurement is discussed. The functionality and performance of the proposed algorithms are verified via illustrative examples and simulation results.

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arXiv2017

System-Theoretic Performance Metrics for Low-Inertia Stability of Power Networks

As bulk synchronous generators in the power grid are replaced by distributed generation interfaced through power electronics, inertia is removed from the system, prompting concerns over grid stability. Different metrics are available for quantifying grid stability and performance; however, no theoretical results are available comparing and contrasting these metrics. This paper presents a rigorous system-theoretic study of performance metrics for low-inertia stability. For networks with uniform parameters, we derive explicit expressions for the eigenvalue damping ratios, and for the $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ norms of the linearized swing dynamics, from external power disturbances to different phase/frequency performance outputs.These expressions show the dependence of system performance on inertia constants, damping constants, and on the grid topology. Surprisingly, we find that the $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ norms can display contradictory behavior as functions of the system inertia, indicating that low-inertia performance depends strongly on the chosen performance metric.

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arXiv2016

A Graph Theoretic Approach to the Robustness of k-Nearest Neighbor Vehicle Platoons

We consider a graph theoretic approach to the performance and robustness of a platoon of vehicles, where each vehicle communicates with its $k$-nearest neighbors. In particular, we quantify the platoon's stability margin, robustness to disturbances (in terms of system $\mathcal{H}_{\infty}$ norm), and maximum delay tolerance via graph-theoretic notions such as nodal degrees and (grounded) Laplacian matrix eigenvalues. Our results show that there is a trade-off between robustness to time delay and robustness to disturbances. Both first-order dynamics (reference velocity tracking) and second-order dynamics (controlling inter-vehicular distance) are analyzed in this direction. Theoretical contributions are confirmed via simulation results.

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arXiv2016

Robustness of Leader-Follower Networked Dynamical Systems

We present a graph-theoretic approach to analyzing the robustness of leader-follower consensus dynamics to disturbances and time delays. Robustness to disturbances is captured via the system $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ norms and robustness to time delay is defined as the maximum allowable delay for the system to remain asymptotically stable. Our analysis is built on understanding certain spectral properties of the grounded Laplacian matrix that play a key role in such dynamics. Specifically, we give graph-theoretic bounds on the extreme eigenvalues of the grounded Laplacian matrix which quantify the impact of disturbances and time-delays on the leader-follower dynamics. We then provide tight characterizations of these robustness metrics in Erdos-Renyi random graphs and random regular graphs. Finally, we view robustness to disturbances and time delay as network centrality metrics, and provide conditions under which a leader in a network optimizes each robustness objective. Furthermore, we propose a sufficient condition under which a single leader optimizes both robustness objectives simultaneously.

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arXiv2015

Robustness and Algebraic Connectivity of Random Interdependent Networks

We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and dynamical attacks. We show that random $k$-partite graphs exhibit a threshold for $r$-robustness, and that this threshold is the same as the one for the graph to have minimum degree $r$. We then extend this characterization to random interdependent networks with arbitrary intra-layer topologies. Finally, we characterize the algebraic connectivity of such networks, and provide an asymptotically tight rate of growth of this quantity for a certain range of inter-layer edge formation probabilities. Our results arise from a characterization of the isoperimetric constant of random interdependent networks, and yield new insights into the structure and robustness properties of such networks.

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arXiv2014

On the Smallest Eigenvalue of Grounded Laplacian Matrices

We provide upper and lower bounds on the smallest eigenvalue of grounded Laplacian matrices (which are matrices obtained by removing certain rows and columns of the Laplacian matrix of a given graph). The gap between the upper and lower bounds depends on the ratio of the smallest and largest components of the eigenvector corresponding to the smallest eigenvalue of the grounded Laplacian. We provide a graph-theoretic bound on this ratio, and subsequently obtain a tight characterization of the smallest eigenvalue for certain classes of graphs. Specifically, for Erdos-Renyi random graphs, we show that when a (sufficiently small) set $S$ of rows and columns is removed from the Laplacian, and the probability $p$ of adding an edge is sufficiently large, the smallest eigenvalue of the grounded Laplacian asymptotically almost surely approaches $|S|p$. We also show that for random $d$-regular graphs with a single row and column removed, the smallest eigenvalue is $Θ(\frac{d}{n})$. Our bounds have applications to the study of the convergence rate in continuous-time and discrete-time consensus dynamics with stubborn or leader nodes.

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