arXiv subjects

Christoforos Somarakis

Publications and source records attributed to Christoforos Somarakis.

18 recordsLinked to original sources

arXiv2026

Incremental Risk Assessment for Cascading Failures in Large-Scale Multi-Agent Systems

We develop a framework for studying and quantifying the risk of cascading failures in time-delay consensus networks, motivated by a team of agents attempting temporal rendezvous under stochastic disturbances and communication delays. To assess how failures at one or multiple agents amplify the risk of deviation across the network, we employ the Average Value-at-Risk as a systemic measure of cascading uncertainty. Closed-form expressions reveal explicit dependencies of the risk of cascading failure on the Laplacian spectrum, communication delay, and noise statistics. We further establish fundamental lower bounds that characterize the best-achievable network performance under time-delay constraints. These bounds serve as feasibility certificates for assessing whether a desired safety or performance goal can be achieved without exhaustive search across all possible topologies. In addition, we develop an efficient single-step update law that enables scalable propagation of conditional risk as new failures are detected. Analytical and numerical studies demonstrate significant computational savings and confirm the tightness of the theoretical limits across diverse network configurations.

eess.SY↗

arXiv2024

A finite element method to compute the damping rate and frequency of oscillating fluids inside microfluidic nozzles

The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD) microfluidic devices that eject liquid metal droplets, where accurate knowledge of damping rates for the least-damped oscillation modes following droplet ejection is paramount for assessing jetting stability at higher jetting frequencies. Computational fluid dynamics (CFD) simulations often struggle to accurately predict meniscus damping unless a very fine discretization is adopted, so calculations are computationally expensive. The faster alternative we adopt is to compute damping rates directly from the eigenvalues of the linearized problem. The surface tension term in Stokes or sloshing problems requires approximation of meniscus displacements, which introduces additional complexity in their numerical solution. We consider the combined effects of viscosity and surface tension, approximate the meniscus displacements, and construct a finite element method to compute the fluid's oscillation modes. We prove that the method is free of spurious modes with zero or positive damping rates, and we implement it with Taylor-Hood elements for velocity and pressure, and with continuous piecewise quadratic elements for meniscus displacement. We verify the numerical convergence of the method by reproducing the solution to an analytical benchmark problem and two more complex examples with axisymmetric geometry. We obtain the spatial shape and temporal evolution (angular frequency and damping rate) of the set of least-damped oscillation modes in minutes, compared to days for a CFD simulation. The method's ability to quickly generate accurate estimates of fluid oscillation damping rates makes it suitable for integration into design loops for prototyping microfluidic nozzles.

physics.comp-ph↗

arXiv2024

Risk of Cascading Collisions in Network of Vehicles with Delayed Communication

This paper establishes and explores a framework to analyze the risk of cascading failures in a platoon of autonomous vehicles, accounting for communication time-delays and input uncertainty. Our proposed framework yields closed-form expressions for cascading collisions, which we quantify using the coherent Average Value-at-Risk ($\AVAR$) to assess the cascading effect of vehicle collisions within the platoon. We investigate how factors such as network connectivity, system dynamics, communication delays, and uncertainty contribute to the emergence of cascading failures. Our findings are extended to standard communication graphs with symmetries, allowing us to evaluate the risk of cascading collisions from a platoon design perspective. Furthermore, by discovering the boundedness of the inter-vehicle distances, we reveal the best achievable risk of cascading collision with general graph topologies, which is further specified for special communication graph, such as the complete graph. Our theoretical results pave the way for the development of a safety-aware framework aimed at mitigating the risk of cascading collisions in vehicle platoons.

eess.SY↗

arXiv2024

Delay-Induced Watermarking for Detection of Replay Attacks in Linear Systems

A state-feedback watermarking signal design for the detection of replay attacks in linear systems is proposed. The control input is augmented with a random time-delayed term of the system state estimate, in order to secure the system against attacks of replay type. We outline the basic analysis of the closed-loop response of the state-feedback watermarking in a LQG controlled system. Our theoretical results are applied on a temperature process control example. While the proposed secure control scheme requires very involved analysis, it, nevertheless, holds promise of being superior to conventional, feed-forward, watermarking schemes, in both its ability to detect attacks as well as the secured system performance.

eess.SY↗

arXiv2023

Cascading Waves of Fluctuation in Time-delay Multi-agent Rendezvous

We develop a framework to assess the risk of cascading failures when a team of agents aims to rendezvous in time in the presence of exogenous noise and communication time-delay. The notion of value-at-risk (VaR) measure is used to evaluate the risk of cascading failures (i.e., waves of large fluctuations) when agents have failed to rendezvous. Furthermore, an efficient explicit formula is obtained to calculate the risk of higher-order cascading failures recursively. Finally, from a risk-aware design perspective, we report an evaluation of the most vulnerable sequence of agents in various communication graphs.

eess.SY↗

arXiv2022

Co-Design of Watermarking and Robust Control for Security in Cyber-Physical Systems

This work discusses a novel framework for simultaneous synthesis of optimal watermarking signal and robust controllers in cyber-physical systems to minimize the loss in performance due to added watermarking signal and to maximize the detection rate of the attack. A general dynamic controller is designed to improve system performance with respect to the $\mathcal H_2$ norm, while a watermarking signal is added to improve security performance concerning the detection rate of replay attacks. The attack model considered in the paper is a replay attack, a natural attack mode when the dynamics of the system is unknown to the attacker. The paper first generalizes the existing result on the detection rate of $χ^2$ detector from a static-LQR controller to a general dynamic controller. The design improvements on both robustness and security fronts are obtained by iteratively solving the convex subsets of the formulated non-convex problem in terms of the controller and watermarking signal. A semi-definite programming optimization is formulated using Linear Matrix Inequality (LMI) results to solve the larger system-level design optimization problem. We highlight the effectiveness of our method over a simplified three-tank chemical system.

eess.SY↗

arXiv2022

Physics-Based Nozzle Design Rules for High-Frequency Liquid Metal Jetting

We present physics-based nozzle design rules to achieve high-throughput and stable jetting in drop-on-demand liquid metal 3D printing. The design rules are based on scaling laws that capture the change of meniscus oscillation relaxation time with geometric characteristics of the nozzle's inner profile. These characteristics include volume, cross-sectional area, and inner surface area of the nozzle. Using boundary layer theory for a simple geometry, we show that the meniscus settles faster when the ratio of inner surface area to volume is increased. High-fidelity multiphase flow simulations verify this scaling. We use these laws to explore several design concepts with parameterized classes of shapes that reduce the meniscus relaxation time while preserving desired droplet specs. Finally, we show that for various nozzle profile concepts, the optimal performance can be achieved by increasing the ratio of the circumferential surface area to the bulk volume to the extent that is allowable by manufacturing constraints.

physics.flu-dyn↗

arXiv2022

Emergence of Cascading Risk and Role of Spatial Locations of Collisions in Time-Delayed Platoon of Vehicles

We develop a framework to assess the risk of cascading collisions in a platoon of vehicles in the presence of exogenous noise and communication time-delay. The notion of Value-at-Risk (VaR) is adopted to quantify the risk of collision between vehicles in a pair conditioned on the knowledge of multiple previously occurred failures in the platoon. We show that the risk of cascading failures depends on the Laplacian spectrum of the underlying communication graph, time-delay, and noise statistics. Furthermore, we exploit the structure of several standard graphs to show how the risk profile depends on the magnitude and spatial location of the prior collisions (failures). Our theoretical findings are significant as they can be applied to designing safe platoons that minimize the risk of cascading failures. Our theoretical findings are supported by several simulations.

eess.SY↗

arXiv2021

Risk of Phase Incoherence in Wide Area Control of Synchronous Power Networks

We develop a framework to quantify systemic risk measures in a class of Wide-Area-Control (WAC) laws in power networks in the presence of noisy and time-delayed sensory data. A closed-form calculation of the risk of phase incoherence in interconnected power networks is presented, and the effect of network parameters, information flow in WAC architecture, statistics of noise, and time-delays are characterized. We show that in the presence of time-delay and noise, a fundamental trade-off between the best achievable performance (via tuning feedback gains) and value-at-risk emerges. The significance of our results is that they provide a guideline for developing algorithmic design tools to enhance the coherency and robustness of closed-loop power networks simultaneously. Finally, we validate our theoretical findings through extensive simulation examples.

eess.SY↗

arXiv2021

Risk of Cascading Failures in Time-Delayed Vehicle Platooning

We develop a systemic risk framework to explore cascading systemic failures in networked control systems. A time-delayed version of the vehicle platooning problem is used as a benchmark to study the interplay among network connectivity, system dynamics, physical limitations, and uncertainty onto the possibility of cascading failure phenomena. The measure of value-at-risk is employed to investigate the domino effect of failures among pairs of vehicles within the platoon. The systemic risk framework is suitably extended to quantify the robustness of cascading failures via a novel manipulation of bi-variate distribution. We establish closed-form risk formulas that explain the effect of network parameters (e.g., Laplacian eigen-spectrum, time delay), noise statistics, and systemic event sets onto the cascading failures. Our findings can be applied to the design of robust platoons to lower the cascading risk. We support our theoretical results with extensive simulations.

eess.SY↗

arXiv2020

Interpretable machine learning models: a physics-based view

To understand changes in physical systems and facilitate decisions, explaining how model predictions are made is crucial. We use model-based interpretability, where models of physical systems are constructed by composing basic constructs that explain locally how energy is exchanged and transformed. We use the port Hamiltonian (p-H) formalism to describe the basic constructs that contain physically interpretable processes commonly found in the behavior of physical systems. We describe how we can build models out of the p-H constructs and how we can train them. In addition we show how we can impose physical properties such as dissipativity that ensure numerical stability of the training process. We give examples on how to build and train models for describing the behavior of two physical systems: the inverted pendulum and swarm dynamics.

cs.AI↗

arXiv2019

Risk of Collision and Detachment in Vehicle Platooning: Time-Delay-Induced Limitations and Trade-Offs (Extended Version)

We quantify the value-at-risk of inter-vehicle collision and detachment for a class of platoons, which are governed by second-order dynamics in presence of communication time-delay and exogenous stochastic noise. Closed-form expressions for the risk measures are obtained as functions of Laplacian eigen-spectrum as well as their fine explicit approximations using rational polynomial functions. We quantify several hard limits and fundamental tradeoffs among the risk measures, network connectivity, communication time-delay, and statistics of exogenous stochastic noise. Simultaneous presence of stochastic noise and time delay in a platoon imposes some idiosyncratic limitations on the behavior of collision and detachment risks, for instance, weakening (improving) network connectivity may result in lower (higher) levels of risk. Furthermore, a thorough risk analysis and comparison have been conducted for networks with specific graph topology. We support our theoretical findings via extensive simulations.

eess.SY↗

arXiv2019

Koopman Performance Analysis of Nonlinear Consensus Networks

Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative protocols, which consist of multiple agents that are coupled together via an undirected state-dependent graph. We develop a representation of the system solution by decomposing the nonlinear system utilizing ideas from the Koopman operator theory and its spectral analysis. We use recent results on the extensions of the well-known Hartman theorem for hyperbolic systems to establish a connection between the original nonlinear dynamics and the linearized dynamics in terms of Koopman spectral properties. The expected value of the output energy of the nonlinear protocol, which is related to the notions of coherence and robustness in dynamical networks, is evaluated and characterized in terms of Koopman eigenvalues, eigenfunctions, and modes. Spectral representation of the performance measure enables us to develop algorithmic methods to assess the performance of this class of nonlinear dynamical networks as a function of their graph topology. Finally, we propose a scalable computational method for approximation of the components of the Koopman mode decomposition, which is necessary to evaluate the systemic performance measure of the nonlinear dynamic network.

eess.SY↗

arXiv2019

Centrality in Time-Delay Consensus Networks with Structured Uncertainties

We investigate notions of network centrality in terms of the underlying coupling graph of the network, structure of exogenous uncertainties, and communication time-delay. Our focus is on time-delay linear consensus networks, where uncertainty is modeled by structured additive noise on the dynamics of agents. The centrality measures are defined using the $\mathcal H_2$-norm of the network. We quantify the centrality measures as functions of time-delay, the graph Laplacian, and the covariance matrix of the input noise. Several practically relevant uncertainty structures are considered, where we discuss two notions of centrality: one w.r.t intensity of the noise and the other one w.r.t coupling strength between the agents. Furthermore, explicit formulas for the centrality measures are obtained for all types of uncertainty structures. Lastly, we rank agents and communication links based on their centrality indices and highlight the role of time-delay and uncertainty structure in each scenario. Our counter intuitive grasp is that some of centrality measures are highly volatile with respect to time-delay.

eess.SY↗

arXiv2019

Aggregate Fluctuations in Networks with Drift-Diffusion Models Driven by Stable Non-Gaussian Disturbances

The focus of this paper is to quantify measures of aggregate fluctuations for a class of consensus-seeking multiagent networks subject to exogenous noise with alpha-stable distributions. This type of noise is generated by a class of random measures with heavy-tailed probability distributions. We define a cumulative scale parameter using scale parameters of probability distributions of the output variables, as a measure of aggregate fluctuation. Although this class of measures can be characterized implicitly in closed-form in steady-state, finding their explicit forms in terms of network parameters is, in general, almost impossible. We obtain several tractable upper bounds in terms of Laplacian spectrum and statistics of the input noise. Our results suggest that relying on Gaussian-based optimal design algorithms will result in non-optimal solutions for networks that are driven by non-Gaussian noise inputs with alpha-stable distributions. The manuscript has been submitted for publication to IEEE Transactions on Control of Network Systems. It is the extended version of preliminary paper included in the proceedings of the 2018 American Control Conference.

eess.SY↗

arXiv2018

Performance Improvement in Noisy Linear Consensus Networks with Time-Delay

We analyze performance of a class of time-delay first-order consensus networks from a graph topological perspective and present methods to improve it. The performance is measured by network's square of H-2 norm and it is shown that it is a convex function of Laplacian eigenvalues and the coupling weights of the underlying graph of the network. First, we propose a tight convex, but simple, approximation of the performance measure in order to achieve lower complexity in our design problems by eliminating the need for eigen-decomposition. The effect of time-delay reincarnates itself in the form of non-monotonicity, which results in nonintuitive behaviors of the performance as a function of graph topology. Next, we present three methods to improve the performance by growing, re-weighting, or sparsifying the underlying graph of the network. It is shown that our suggested algorithms provide near-optimal solutions with lower complexity with respect to existing methods in literature.

eess.SY↗

arXiv2018

Time-Delay Origins of Fundamental Tradeoffs Between Risk of Large Fluctuations and Network Connectivity

For the class of noisy time-delay linear consensus networks, we obtain explicit formulas for risk of large fluctuations of a scalar observable as a function of Laplacian spectrum and its eigenvectors. It is shown that there is an intrinsic tradeoff between risk and effective resistance of the underlying coupling graph of the network. The main implication is that increasing network connectivity, increases the risk of large fluctuations. For vector-valued observables, we obtain computationally tractable lower and upper bounds for joint risk measures. Then, we study behavior of risk measures for networks with specific graph topologies and show how risk scales with network size.

eess.SY↗

arXiv2017

Convergence Analysis of Classes of Asymmetric Networks of Cucker-Smale Type with Deterministic Perturbations

We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence of identical internal dynamics. The second model describes a similar population of agents that perform velocity alignment with the restriction of collision-free orbits. Although qualitatively different, we explain how these two non-trivial types of perturbations are analyzed under a unified framework. Rigorous analysis is conducted towards establishing new sufficient conditions for asymptotic flocking to a synchronized motion. Applications of our results are compared with simulations to illustrate the effectiveness of our theoretical estimates.

math.OC↗