arXiv subjects

Fabio Pasqualetti

Publications and source records attributed to Fabio Pasqualetti.

At least 73 records · Page 4Linked to original sources

arXiv2020

Network Theoretic Analysis of Maximum a Posteriori Detectors for Optimal Input Detection

This paper considers maximum-a-posteriori (MAP) and linear discriminant based MAP detectors to detect changes in the mean and covariance of a stochastic input, driving specific network nodes, using noisy measurements from sensors non-collocated with the input nodes. We explicitly characterize both detectors' performance in terms of the network edge weights and input and sensor nodes' location. In the asymptotic measurement regime, when the input and measurement noise are jointly Gaussian, we show that the detectors' performance can be studied using the input to output gain of the system's transfer function matrix. Using this result, we obtain conditions for which the detection performance associated with the sensors on a given network cut is better (or worse) than that of the sensors associated with the subnetwork induced by the cut and not containing the input nodes. Our results also provide structural insights into the sensor placement from a detection-theoretic viewpoint. We validate our theoretical findings via multiple numerical examples.

math.OC↗

arXiv2020

Lipschitz Bounds and Provably Robust Training by Laplacian Smoothing

In this work we propose a graph-based learning framework to train models with provable robustness to adversarial perturbations. In contrast to regularization-based approaches, we formulate the adversarially robust learning problem as one of loss minimization with a Lipschitz constraint, and show that the saddle point of the associated Lagrangian is characterized by a Poisson equation with weighted Laplace operator. Further, the weighting for the Laplace operator is given by the Lagrange multiplier for the Lipschitz constraint, which modulates the sensitivity of the minimizer to perturbations. We then design a provably robust training scheme using graph-based discretization of the input space and a primal-dual algorithm to converge to the Lagrangian's saddle point. Our analysis establishes a novel connection between elliptic operators with constraint-enforced weighting and adversarial learning. We also study the complementary problem of improving the robustness of minimizers with a margin on their loss, formulated as a loss-constrained minimization problem of the Lipschitz constant. We propose a technique to obtain robustified minimizers, and evaluate fundamental Lipschitz lower bounds by approaching Lipschitz constant minimization via a sequence of gradient $p$-norm minimization problems. Ultimately, our results show that, for a desired nominal performance, there exists a fundamental lower bound on the sensitivity to adversarial perturbations that depends only on the loss function and the data distribution, and that improvements in robustness beyond this bound can only be made at the expense of nominal performance. Our training schemes provably achieve these bounds both under constraints on performance and~robustness.

cs.LG↗

arXiv2020

Path-dependent Dynamics Induced by Rewiring Networks of Inertial Oscillators

In networks of coupled oscillators, it is of interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static networks. However, new questions arise when network structure is time-varying or when the oscillator system is multistable, the latter of which can occur when an inertial term is added to the Kuramoto model. While the consequences of evolving topology and multistability on collective behavior have been examined separately, real-world systems such as gene regulatory networks and the brain can exhibit these properties simultaneously. How does the rewiring of network connectivity affect synchronization in systems with multistability, where different paths of network evolution may differentially impact system dynamics? To address this question, we study the effects of time-evolving network topology on coupled Kuramoto oscillators with inertia. We show that hysteretic synchronization behavior occurs when the network density of coupled inertial oscillators is slowly varied as the dynamics evolve. Moreover, we find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony, and that these changes remain after the network returns to its initial configuration and are robust to a wide range of network perturbations. Our findings suggest that the specific progression of network topology, in addition to its initial or final static structure, can play a considerable role in modulating the collective behavior of systems evolving on complex networks.

nlin.AO↗

arXiv2020

Minimum-gain Pole Placement with Sparse Static Feedback

The minimum-gain eigenvalue assignment/pole placement problem (MGEAP) is a classical problem in LTI systems with static state feedback. In this paper, we study the MGEAP when the state feedback has arbitrary sparsity constraints. We formulate the sparse MGEAP problem as an equality-constrained optimization problem and present an analytical characterization of its locally optimal solution in terms of eigenvector matrices of the closed loop system. This result is used to provide a geometric interpretation of the solution of the non-sparse MGEAP, thereby providing additional insights for this classical problem. Further, we develop an iterative projected gradient descent algorithm to obtain local solutions for the sparse MGEAP using a parametrization based on the Sylvester equation. We present a heuristic algorithm to compute the projections, which also provides a novel method to solve the sparse EAP. Also, a relaxed version of the sparse MGEAP is presented and an algorithm is developed to obtain approximately sparse local solutions to the MGEAP. Finally, numerical studies are presented to compare the properties of the algorithms, which suggest that the proposed projection algorithm converges in most cases.

math.OC↗

arXiv2020

Data-Driven Control of Complex Networks

Our ability to manipulate the behavior of complex networks depends on the design of efficient control algorithms and, critically, on the availability of an accurate and tractable model of the network dynamics. While the design of control algorithms for network systems has seen notable advances in the past few years, knowledge of the network dynamics is a ubiquitous assumption that is difficult to satisfy in practice, especially when the network topology is large and, possibly, time-varying. In this paper we overcome this limitation, and develop a data-driven framework to control a complex dynamical network optimally and without requiring any knowledge of the network dynamics. Our optimal controls are constructed using a finite set of experimental data, where the unknown complex network is stimulated with arbitrary and possibly random inputs. In addition to optimality, we show that our data-driven formulas enjoy favorable computational and numerical properties even compared to their model-based counterpart. Although our controls are provably correct for networks with linear dynamics, we also characterize their performance against noisy experimental data and in the presence of nonlinear dynamics, as they arise when mitigating cascading failures in power-grid networks and when manipulating neural activity in brain networks.

eess.SY↗

arXiv2020

Mediated Remote Synchronization of Kuramoto-Sakaguchi Oscillators: the Number of Mediators Matters

Cortical regions without direct neuronal connections have been observed to exhibit synchronized dynamics. A recent empirical study has further revealed that such regions that share more common neighbors are more likely to behave coherently. To analytically investigate the underlying mechanisms, we consider that a set of n oscillators, which have no direct connections, are linked through m intermediate oscillators (called mediators), forming a complete bipartite network structure. Modeling the oscillators by the Kuramoto-Sakaguchi model, we rigorously prove that mediated remote synchronization, i.e., synchronization between those n oscillators that are not directly connected, becomes more robust as the number of mediators increases. Simulations are also carried out to show that our theoretical findings can be applied to other general and complex networks.

nlin.AO↗

arXiv2020

Habit learning supported by efficiently controlled network dynamics in naive macaque monkeys

Primates display a marked ability to learn habits in uncertain and dynamic environments. The associated perceptions and actions of such habits engage distributed neural circuits. Yet, precisely how such circuits support the computations necessary for habit learning remain far from understood. Here we construct a formal theory of network energetics to account for how changes in brain state produce changes in sequential behavior. We exercise the theory in the context of multi-unit recordings spanning the caudate nucleus, prefrontal cortex, and frontal eyefields of female macaque monkeys engaged in 60-180 sessions of a free scan task that induces motor habits. The theory relies on the determination of effective connectivity between recording channels, and on the stipulation that a brain state is taken to be the trial-specific firing rate across those channels. The theory then predicts how much energy will be required to transition from one state into another, given the constraint that activity can spread solely through effective connections. Consistent with the theory's predictions, we observed smaller energy requirements for transitions between more similar and more complex trial saccade patterns, and for sessions characterized by less entropic selection of saccade patterns. Using a virtual lesioning approach, we demonstrate the resilience of the observed relationships between minimum control energy and behavior to significant disruptions in the inferred effective connectivity. Our theoretically principled approach to the study of habit learning paves the way for future efforts examining how behavior arises from changing patterns of activity in distributed neural circuitry.

q-bio.NC↗

arXiv2020

On a Security vs Privacy Trade-off in Interconnected Dynamical Systems

We study a security problem for interconnected systems, where each subsystem aims to detect local attacks using local measurements and information exchanged with neighboring subsystems. The subsystems also wish to maintain the privacy of their states and, therefore, use privacy mechanisms that share limited or noisy information with other subsystems. We quantify the privacy level based on the estimation error of a subsystem's state and propose a novel framework to compare different mechanisms based on their privacy guarantees. We develop a local attack detection scheme without assuming the knowledge of the global dynamics, which uses local and shared information to detect attacks with provable guarantees. Additionally, we quantify a trade-off between security and privacy of the local subsystems. Interestingly, we show that, for some instances of the attack, the subsystems can achieve a better detection performance by being more private. We provide an explanation for this counter-intuitive behavior and illustrate our results through numerical examples.

eess.SY↗

arXiv2020

Learning Minimum-Energy Controls from Heterogeneous Data

In this paper we study the problem of learning minimum-energy controls for linear systems from heterogeneous data. Specifically, we consider datasets comprising input, initial and final state measurements collected using experiments with different time horizons and arbitrary initial conditions. In this setting, we first establish a general representation of input and sampled state trajectories of the system based on the available data. Then, we leverage this data-based representation to derive closed-form data-driven expressions of minimum-energy controls for a wide range of control horizons. Further, we characterize the minimum number of data required to reconstruct the minimum-energy inputs, and discuss the numerical properties of our expressions. Finally, we investigate the effect of noise on our data-driven formulas, and, in the case of noise with known second-order statistics, we provide corrected expressions that converge asymptotically to the true optimal control inputs.

math.OC↗

arXiv2020

The control of brain network dynamics across diverse scales of space and time

The human brain is composed of distinct regions that are each associated with particular functions and distinct propensities for the control of neural dynamics. However, the relation between these functions and control profiles is poorly understood, as is the variation in this relation across diverse scales of space and time. Here we probe the relation between control and dynamics in brain networks constructed from diffusion tensor imaging data in a large community based sample of young adults. Specifically, we probe the control properties of each brain region and investigate their relationship with dynamics across various spatial scales using the Laplacian eigenspectrum. In addition, through analysis of regional modal controllability and partitioning of modes, we determine whether the associated dynamics are fast or slow, as well as whether they are alternating or monotone. We find that brain regions that facilitate the control of energetically easy transitions are associated with activity on short length scales and slow time scales. Conversely, brain regions that facilitate control of difficult transitions are associated with activity on long length scales and fast time scales. Built on linear dynamical models, our results offer parsimonious explanations for the activity propagation and network control profiles supported by regions of differing neuroanatomical structure.

q-bio.NC↗

arXiv2020

Time-evolving controllability of effective connectivity networks during seizure progression

Over one third of the estimated 3 million people with epilepsy in the US are medication resistant. Responsive neurostimulation from chronically implanted electrodes provides a promising treatment option and alternative to resective surgery. However, determining personalized optimal stimulation parameters, including when and where to intervene to guarantee a positive patient outcome, is a major open challenge. Network neuroscience and control theory offer useful tools that may guide improvements in parameter selection for control of anomalous neural activity. Here we use a novel method to characterize dynamic controllability across consecutive effective connectivity (EC) networks based on regularized partial correlations between implanted electrodes during the onset, propagation, and termination phases of thirty-four seizures. We estimate regularized partial correlation adjacency matrices from one-second time windows of intracranial electrocorticography recordings using the Graphical Least Absolute Shrinkage and Selection Operator (GLASSO). Average and modal controllability metrics calculated from each resulting EC network track the time-varying controllability of the brain on an evolving landscape of conditionally dependent network interactions. We show that average controllability increases throughout a seizure and is negatively correlated with modal controllability throughout. Furthermore, our results support the hypothesis that the energy required to drive the brain to a seizure-free state from an ictal state is smallest during seizure onset; yet, we find that applying control energy at electrodes in the seizure onset zone may not always be energetically favorable. Our work suggests that a low-complexity model of time-evolving controllability may offer new insights for developing and improving control strategies targeting seizure suppression.

q-bio.NC↗

arXiv2020

Data-Driven Attack Detection for Linear Systems

This paper studies the attack detection problem in a data-driven and model-free setting, for deterministic systems with linear and time-invariant dynamics. Differently from existing studies that leverage knowledge of the system dynamics to derive security bounds and monitoring schemes, we focus on the case where the system dynamics, as well as the attack strategy and attack location, are unknown. We derive fundamental security limitations as a function of only the observed data and without estimating the system dynamics (in fact, no assumption is made on the identifiability of the system). In particular, (i) we derive detection limitations as a function of the informativity and length of the observed data, (ii) provide a data-driven characterization of undetectable attacks, and (iii) construct a data-driven detection monitor. Surprisingly, and in accordance with recent studies on data-driven control, our results show that model-based and data-driven security techniques share the same fundamental limitations, provided that the collected data remains sufficiently informative.

eess.SY↗

arXiv2020

Accuracy Prevents Robustness in Perception-based Control

In this paper we prove the existence of a fundamental trade-off between accuracy and robustness in perception-based control, where control decisions rely solely on data-driven, and often incompletely trained, perception maps. In particular, we consider a control problem where the state of the system is estimated from measurements extracted from a high-dimensional sensor, such as a camera. We assume that a map between the camera's readings and the state of the system has been learned from a set of training data of finite size, from which the noise statistics are also estimated. We show that algorithms that maximize the estimation accuracy (as measured by the mean squared error) using the learned perception map tend to perform poorly in practice, where the sensor's statistics often differ from the learned ones. Conversely, increasing the variability and size of the training data leads to robust performance, however limiting the estimation accuracy, and thus the control performance, in nominal conditions. Ultimately, our work proves the existence and the implications of a fundamental trade-off between accuracy and robustness in perception-based control, which, more generally, affects a large class of machine learning and data-driven algorithms.

math.OC↗

arXiv2020

Models of communication and control for brain networks: distinctions, convergence, and future outlook

Recent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work.

q-bio.NC↗

arXiv2019

On the Robustness of Data-Driven Controllers for Linear Systems

This paper proposes a new framework and several results to quantify the performance of data-driven state-feedback controllers for linear systems against targeted perturbations of the training data. We focus on the case where subsets of the training data are randomly corrupted by an adversary, and derive lower and upper bounds for the stability of the closed-loop system with compromised controller as a function of the perturbation statistics, size of the training data, sensitivity of the data-driven algorithm to perturbation of the training data, and properties of the nominal closed-loop system. Our stability and convergence bounds are probabilistic in nature, and rely on a first-order approximation of the data-driven procedure that designs the state-feedback controller, which can be computed directly using the training data. We illustrate our findings via multiple numerical studies.

eess.SY↗

arXiv2019

Secure Trajectory Planning Against Undetectable Spoofing Attacks

This paper studies, for the first time, the trajectory planning problem in adversarial environments, where the objective is to design the trajectory of a robot to reach a desired final state despite the unknown and arbitrary action of an attacker. In particular, we consider a robot moving in a two-dimensional space and equipped with two sensors, namely, a Global Navigation Satellite System (GNSS) sensor and a Radio Signal Strength Indicator (RSSI) sensor. The attacker can arbitrarily spoof the readings of the GNSS sensor and the robot control input so as to maximally deviate his trajectory from the nominal precomputed path. We derive explicit and constructive conditions for the existence of undetectable attacks, through which the attacker deviates the robot trajectory in a stealthy way. Conversely, we characterize the existence of secure trajectories, which guarantee that the robot either moves along the nominal trajectory or that the attack remains detectable. We show that secure trajectories can only exist between a subset of states, and provide a numerical mechanism to compute them. We illustrate our findings through several numerical studies, and discuss that our methods are applicable to different models of robot dynamics, including unicycles. More generally, our results show how control design affects security in systems with nonlinear dynamics.

math.OC↗

arXiv2019

A Framework to Control Functional Connectivity in the Human Brain

In this paper, we propose a framework to control brain-wide functional connectivity by selectively acting on the brain's structure and parameters. Functional connectivity, which measures the degree of correlation between neural activities in different brain regions, can be used to distinguish between healthy and certain diseased brain dynamics and, possibly, as a control parameter to restore healthy functions. In this work, we use a collection of interconnected Kuramoto oscillators to model oscillatory neural activity, and show that functional connectivity is essentially regulated by the degree of synchronization between different clusters of oscillators. Then, we propose a minimally invasive method to correct the oscillators' interconnections and frequencies to enforce arbitrary and stable synchronization patterns among the oscillators and, consequently, a desired pattern of functional connectivity. Additionally, we show that our synchronization-based framework is robust to parameter mismatches and numerical inaccuracies, and validate it using a realistic neurovascular model to simulate neural activity and functional connectivity in the human brain.

eess.SY↗

arXiv2019

A practical guide to methodological considerations in the controllability of structural brain networks

Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool from the physical and engineering sciences that can provide insights regarding that relationship; it formalizes the study of how the dynamics of a complex system can arise from its underlying structure of interconnected units. Given the recent use of network control theory in neuroscience, it is now timely to offer a practical guide to methodological considerations in the controllability of structural brain networks. Here we provide a systematic overview of the framework, examine the impact of modeling choices on frequently studied control metrics, and suggest potentially useful theoretical extensions. We ground our discussions, numerical demonstrations, and theoretical advances in a dataset of high-resolution diffusion imaging with 730 diffusion directions acquired over approximately 1 hour of scanning from ten healthy young adults. Following a didactic introduction of the theory, we probe how a selection of modeling choices affects four common statistics: average controllability, modal controllability, minimum control energy, and optimal control energy. Next, we extend the current state of the art in two ways: first, by developing an alternative measure of structural connectivity that accounts for radial propagation of activity through abutting tissue, and second, by defining a complementary metric quantifying the complexity of the energy landscape of a system. We close with specific modeling recommendations and a discussion of methodological constraints.

q-bio.NC↗