Rahul Dhal

Vulnerability of continuous-time network synchronization processes: A minimum energy perspective

We characterize the vulnerability of a linear network synchronization process to intrusion by an adversary that can actuate a single network component. Specifically, we model the intruder as seeking to move the state of the synchronization process to an undesirable value or set (which may or may not be known to system operators) via a local actuation. We evaluate the network vulnerability in terms of the whether or not the intruder can achieve its goal, and also the minimum actuation energy (or expected minimum energy, if the goal is unknown) required of the adversary to achieve the goal. We formalize that the required energy is related to the inverse of the controllability Gramian for the process, and statistics defined thereof (e.g., its trace and determinant). We then obtain explicit formulas for the Gramian inverse and its associated statistics. These explicit formulae yield interesting structural and graph-theoretic characterizations of the energy-based vulnerability measures.

Link-failure detection in network synchronization processes

We study the detection of link failures in network synchronization processes. In particular, for a canonical linear network synchronization model, we consider detection of a critical links failure by a monitor that makes noisy local measurements of the process. We characterize Maximum A-Posteriori (MAP) detection of the link failure, for both the case that the monitor has information about the networks initial state and the random-initial-condition case. Several algebraic, spectral and graph theoretic characterizations of the detector and its performance are provided. These include conditions under which the link failure is completely hidden from the monitor and, conversely, conditions that permit perfect detection with sufficient data. Our analyses highlight that rather effective detection is possible with limited and noisy observation data.

Forecasting Weather-Impacted Airport Capacities for Flow Contingency Management: Advanced Methods and Integration

ne goal of the Next Generation Air Transportation System (NextGen) is to develop strategic decision-making capabilities, which facilitate allocation of traffic management initiatives (TMIs) across the United States National Airspace System (NAS) over a full-day look-ahead horizon. In recent years, several promising concepts and methodologies for such strategic traffic management have been advanced, including our teams flow contingency management (FCM) solution. A key thrust of these strategic traffic management solutions, including FCM, is the development of stochastic forecasts of weather impact in both the en route and terminal area airspace. FCM, in particular, requires forecast scenarios (possible futures) of weather-constrained capacities, including sector capacities and airport arrival and departure rates (AARs and ADRs), over a full day forecast horizon. Several recent studies have introduced promising techniques for forecasting weather impacts and generating impact scenarios 1–3 , however many challenges remain in developing and validating useful and accurate models. The work presented here contributes to the research effort on strategic forecasting of weather-impacted airport capacities (specifically, AARs). Although AAR and ADR forecasting has been extensively studied, most efforts have focused on shorter time horizons (up to four hours 4 ) or are terminal-specific (e.g., the stratus forecast for San Francisco International Airport 5 ). However, FCM requires a generic probabilistic methodology for AAR prediction, albeit one that only needs to predict significant capacity reductions rather than detailed trends in runway configurations and capacity. Recently, Buxi and Hansen introduced two methodologies for probabilistic forecasting of AAR scenarios over a full-day horizon from terminal-area forecasts 6 . These approaches are promising for FCM, but depend on the presence of similar full-day TAF profiles in the historical record, and also do not account for convective weather. In our previous works, we introduced alternative regression-based approaches for prediction in the context of several case studies, and studied the incorporation of convective-weather forecasts in terminal capacity prediction. However, these initial studies stopped short of introducing a generic prediction algorithm, and also did not consider the wide range of forecast products that could be leveraged in AAR prediction. In this study, we introduce a multinomial-logistic-regression-based methodology for full-day AAR prediction for arbitrary airports, for use in the FCM solution. The paper is organized as follows. In Section II, we introduce the proposed regression methodology in generality, including both regression-model construction and model deployment for FCM. In Section III, we present two case studies for Boston Logan International Airport (KBOS)

Local open- and closed-loop manipulation of multi-agent networks

We explore the manipulation of networked cyber-physical devices via external actuation or feedback control at a single location, in the context of a canonical multi-agent system model known as the double integrator network. One main focus is to understand whether or not, and how easily, a stakeholder can manipulate networks full dynamics by designing the actuation signal for one agent (in an open-loop sense). Additionally, we investigate the ability of the stakeholder to manipulate the multi-agent system, and achieve control objectives, via local feedback control. For both problems, we find that manipulation of the dynamics is crucially dependent on the networks graph and associated spectrum.

Security of airborne network dynamics and algorithms: a graph-theoretic perspective

A comprehensive framework for analyzing the security and robustness of airborne networks is envisioned, that acknowledges both their physical dynamics and cyber- functions. The framework is developed in three aspects, first by developing models for meshed physical- and cyber- dynamics, then envisioning possible adversarial conduct, and finally defining security and robustness formally. After introducing the framework, we overview promising tools for characterizing/designing security and robustness; these tools critically expose the role of the networks sensing/communication topology in its threat response.

Layered Moment-Linear Network Models as Tools for Strategic Air Traffic Flow Management.

For strategic traffic flow management, models are needed that allow NAS stakeholders to characterize the joint evolution of weather (and/or its impact on air traffic operating capabilities) in conjunction with the evolution of traffic flows. While queueing models show some promise for permitting meshed analysis of weather and traffic (including flow management initiatives), they are mathematically and computationally unwieldy when either the weather evolution or the airspace topology are modeled at realistic scale. Here, we investigate whether a new class of models known as layered moment-linear networks that approximate queueing-network models can serve as tractable albeit abstracted models for weather and traffic dynamics. As a first step toward constructing layered moment-linear models for traffic/weather, we develop a linear approximation for an M/D/1 queue with variable service rate. We evaluate the accuracy of the approximation using simulations, and then use it to analyze a traffic bottleneck that is modulated by a complex (networked) weather-propagation event.

Majorisations for the eigenvectors of graph-adjacency matrices

We develop majorisation results that characterise changes in eigenvector components of a graphs adjacency matrix when its topology is changed. Specifically, for general (weighted, directed) graphs, we characterise changes in dominant eigenvector components for single- and multi-row incrementations. We also show that topology changes can be tailored to set ratios between the components of the dominant eigenvector. For more limited graph classes (specifically, undirected, and reversibly-structured ones), majorisations for components of the subdominant and other eigenvectors upon graph modifications are also obtained.

Vulnerability of Network Synchronization Processes: A Minimum Energy Perspective

We study the vulnerability of a linear network synchronization process to intrusion at a single network component, from a graph-theoretic perspective. Specifically, we model the intruder as seeking to move the state of the synchronization process to an undesirable value or set via a local actuation. We measure the network vulnerability in terms of the minimum or expected minimum actuation energy required of the adversary to achieve the goal, which is related to the inverse of the controllability Gramian for the process and statistics defined thereof (e.g., its trace and determinant). Using explicit formulas for the Gramian inverse and its associated statistics together with algebraic graph-theory concepts, we then develop structural and graph-theoretic characterizations of the energy-based vulnerability measures.

Leveraging Airborne Networks: Scene Reconstruction Using Incidental Measurements

Unmanned aerial systems, and specifically airborne networking technology, can provide unique capabilities for the monitoring and management of large-scale environmental and geopolitical events (e.g., forest fires, oil slicks, battlefields, urban warfare, etc). In particular, these technologies hold promise for permitting pervasive sensing of large-scale spatiotemporal dynamical processes, by permitting high density measurement at relatively low cost. The measurements can potentially be leveraged to reconstruct and forecast the dynamical processes of interest, and these estimates/forecasts in turn can be used to facilitate management. While this use of UAS technology is potentially transformative, significant challenges remain in developing algorithms for the inference of complex dynamical processes from pervasive measurements. The research presented here aims to contribute to the development and characterization of such inference algorithms. The inference of spatiotemporal processes using UAS-based measurements (including from airborne networks) is complicated by several factors:

Performance analysis of an influence-model-based graph partitioning algorithm

Recently, a stochastic automaton known as the influence model was advanced as a tool for flexible and distributed graph partitioning, which can find optimal solutions to numerous hard partitioning problems in an almost-sure sense. Here, we provide a performance analysis of the influence model-based partitioner, for the hard problem of m-way partitioning with reference vertices. Specifically, we show that the influence model algorithm finds the optimal partition quickly with high probability, whenever the optimal cut-set is sufficiently weak compared to other cuts in the graph.