Jackeline Abad Torres

Graph-theoretic characterisations of zeros for the input–output dynamics of complex network processes

We examine linear network dynamics in which an input can be applied at only one network component and measurements can only be made at one (in general different) component. The infinite-zero and finite-zero structures of these dynamics are characterised explicitly in terms of the networks graph matrix, using the special coordinate basis for linear system. These algebraic characterisations are then used to identify relationships between features of the networks graph topology and the state matrix of its finite zero dynamics.

Sparse allocation of resources in dynamical networks with application to spread control

Sparse resource allocation to shape a network dynamical process is studied. Specifically, we consider allocating limited distributed control resources among a subset of a networks components, to minimize the dominant eigenvalue of a linear dynamical process associated with the network. Structural characterizations of the closed-loop dynamics at the optimum are obtained. These results are then used to 1) develop constructive algorithms for optimal resource allocation, 2) identify limits on the control performance, and 3) understand the relationship between the networks graph and the optimal resource profile. This study advances a research thrust on disease spread control in networks, toward the realistic paradigm that control resources can only be allocated at a subset of network locations.

Graph-theoretic analysis of network input-output processes

The control of dynamical processes in networks is considered, in the case where measurement and actuation capabilities are sparse and possibly remote. Specifically, we study control of a canonical network dynamics, when only one network components state can be measured and only one (in general different) component can be actuated. To do so, we characterize the finite- and infinite-zeros of the resulting SISO system in terms of the graph topology. Using these results, we establish graph-theoretic conditions under which there are zeros in the closed right-half plane. These conditions depend on the length, strength, and number of the paths from the component where the input is applied to the component where the measurements are made. Then, we present the implications of these conditions on the controller design task focusing in stabilizations/destabilization of network processes under static negative feedback.

Fast fault location in power transmission networks using transient signatures from sparsely-placed synchrophasors

This paper explores real-time fault location in a power transmission network using measurements of transients from sparsely-placed synchrophasors. The fault-location problem is abstracted to a statistical hypothesis-testing or detection problem, wherein the linearized dynamical models corresponding to different fault conditions must be distinguished in the face of fault-clearing and measurement uncertainty. A maximum a posteriori probability (MAP) detector is constructed. A strategy for real-time implementation of the fault-locator is discussed, which is based on pre-computation of detector parameters using state-estimator and contingency-analysis data, along with on-line collection of synchrophrasor data and implementation of the hypothesis test. Numerical case studies of the 11-Bus two area power system verify that the proposed fault-location algorithm can locate a faulted line accurately and quickly.

Stabilization and destabilization of network processes by sparse remote feedback: Graph-theoretic approach

The control of dynamical processes in networks is considered, in the case where measurement and actuation capabilities are sparse and possibly remote. Specifically, we study control of a canonical network dynamics, when only one network components state can be measured and only one (in general different) component can be actuated. To do so, we characterize the finite- and infinite- zeros of the resulting SISO system in terms of the graph topology. Using these results, we establish graphical conditions under which a network dynamics is stable/unstable upon application of any static linear feedback. We also give graphical conditions for destabilization of a stable networks dynamics with high-gain static feedback. These conditions depend on the length, strength, and number of the paths from the component where the input is applied to the component where the measurements are made.

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.

Connecting network graph structure to linear-system zero structure

We examine linear network dynamics in which an input can be applied at only one network component and measurements can only be made at one (in general different) component. The infinite-zero- and finite-invariant-zero-structure of these dynamics are characterized explicitly in terms of the networks graph matrix, using the special coordinate basis for linear system. These algebraic characterizations are then used to identify relationships between features of the networks graph topology and the state matrix of its finite zero dynamics.

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.

A two-layer transformation for characterizing the zeros of a network input-output dynamics

Many networks can be modeled as collections of subsystems with complex internal dynamics, which are dynamically coupled according to a weighted digraph. This article characterizes the input-output behavior of a network of coupled homogeneous single-input single-output subsystems, in the case where external actuation and measurement are each applied at a single (but possibly different) component. Precisely, a two-layer transformation of the networks dynamics is undertaken, which makes explicit the roles of 1) the local subsystem model, 2) the networks global interconnections (graph), and 3) the input and output locations, in determining the zeros of the input-output model. The analysis of the zeros via this special-coordinate-basis decomposition shows a parallel with the spectral analysis of the coupled-subsystem model, and directly gives insight into the networks input-output dynamics and its feedback control.

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.