arXiv subjects

Sonia Martínez

Publications and source records attributed to Sonia Martínez.

26 records · Page 2Linked to original sources

arXiv2021

High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems

This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with quantifiable probability and can be exploited to formulate robust stochastic optimization problems with out-of-sample guarantees. We assume the random variable evolves in discrete time under uncertain initial conditions and dynamics, and that noisy partial measurements are available. All random elements have unknown probability distributions and we make inferences about the distribution of the state vector using several output samples from multiple realizations of the process. To this end, we leverage an observer to estimate the state of each independent realization and exploit the outcome to construct the ambiguity sets. We illustrate our results in an economic dispatch problem involving distributed energy resources over which the scheduler has no direct control.

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arXiv2020

High-Confidence Attack Detection via Wasserstein-Metric Computations

This paper considers a sensor attack and fault detection problem for linear cyber-physical systems, which are subject to system noise that can obey an unknown light-tailed distribution. We propose a new threshold-based detection mechanism that employs the Wasserstein metric, and which guarantees system performance with high confidence employing a finite number of measurements. The proposed detector may generate false alarms with a rate $Δ$ in normal operation, where $Δ$ can be tuned to be arbitrarily small by means of a benchmark distribution which is part of our mechanism. Thus, the proposed detector is sensitive to sensor attacks and faults which have a statistical behavior that is different from that of the system's noise. We quantify the impact of stealthy attacks---which aim to perturb the system operation while producing false alarms that are consistent with the natural system's noise---via a probabilistic reachable set. To enable tractable implementation of our methods, we propose a linear optimization problem that computes the proposed detection measure and a semidefinite program that produces the proposed reachable set.

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arXiv2020

Dynamics of Data-driven Ambiguity Sets for Hyperbolic Conservation Laws with Uncertain Inputs

Ambiguity sets of probability distributions are used to hedge against uncertainty about the true probabilities of random quantities of interest (QoIs). When available, these ambiguity sets are constructed from both data (collected at the initial time and along the boundaries of the physical domain) and concentration-of-measure results on the Wasserstein metric. To propagate the ambiguity sets into the future, we use a physics-dependent equation governing the evolution of cumulative distribution functions (CDF) obtained through the method of distributions. This study focuses on the latter step by investigating the spatio-temporal evolution of data-driven ambiguity sets and their associated guarantees when the random QoIs they describe obey hyperbolic partial-differential equations with random inputs. For general nonlinear hyperbolic equations with smooth solutions, the CDF equation is used to propagate the upper and lower envelopes of pointwise ambiguity bands. For linear dynamics, the CDF equation allows us to construct an evolution equation for tighter ambiguity balls. We demonstrate that, in both cases, the ambiguity sets are guaranteed to contain the true (unknown) distributions within a prescribed confidence.

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arXiv2019

A Probabilistic Framework for Moving-Horizon Estimation: Stability and Privacy Guarantees

This work proposes a unifying probabilistic framework for the design of robustly asymptotically stable moving-horizon estimators (MHE) for discrete-time nonlinear systems, and a mechanism to incorporate differential privacy in moving-horizon estimation. We begin with an investigation of the classical notion of strong local observability of nonlinear systems and its relationship to optimization-based state estimation. We then present a general moving-horizon estimation framework for strongly locally observable systems, as an iterative minimization scheme in the space of probability measures. This framework allows for the minimization of the estimation cost with respect to different metrics. In particular, we consider two variants, which we name $W_2$-MHE and KL-MHE, where the minimization scheme uses the 2-Wasserstein distance and the KL-divergence, respectively. The $W_2$-MHE yields a gradient-based estimator whereas the KL-MHE yields a particle filter, for which we investigate asymptotic stability and robustness properties. Stability results for these moving-horizon estimators are derived in the probabilistic setting, against the backdrop of the classical notion of strong local observability which, to the best of our knowledge, differentiates it from other previous works. We then propose a mechanism to encode differential privacy of the measurements used by the estimator via an entropy regularization of the MHE objective functional. In particular, we find sufficient bounds on the regularization parameter to achieve the desired level of differential privacy. Numerical simulations demonstrate the performance of these estimators.

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arXiv2019

Identification of critical nodes in large-scale spatial networks

The notion of network connectivity is used to characterize the robustness and failure tolerance of networks, with high connectivity being a desirable feature. In this paper, we develop a novel approach to the problem of identifying critical nodes in large-scale networks, with algebraic connectivity (the second smallest eigenvalue of the graph Laplacian) as the chosen metric. Employing a graph-embedding technique, we reduce the class of considered weight-balanced graphs to spatial networks with uniformly distributed nodes and nearest-neighbors communication topologies. Through a continuum approximation, we consider the Laplace operator on a manifold (with the Neumann boundary condition) as the limiting case of the graph Laplacian. We then reduce the critical node set identification problem to that of finding a ball of fixed radius, whose removal minimizes the second (Neumann) eigenvalue of the Laplace operator on the residual domain. This leads us to consider two functional and nested optimization problems. Resorting to the min-max theorem, we first treat the problem of determining the second smallest eigenvalue for a fixed domain by minimizing an energy functional. We then obtain a projected gradient flow that converges to the set of points satisfying the KKT conditions and prove that the only locally asymptotically stable critical point is the second eigenfunction of the Laplace operator. Building on these results, we consider the critical ball identification problem and construct a dynamics to converge asymptotically to these points. Finally, we provide a characterization of the location of critical nodes (for infinitesimally-small balls) as those points which belong to the nodal set of the second eigenfunction of the Laplace operator.

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arXiv2019

Data-driven ambiguity sets with probabilistic guarantees for dynamic processes

Distributional ambiguity sets provide quantifiable ways to characterize the uncertainty about the true probability distribution of random variables of interest. This makes them a key element in data-driven robust optimization by exploiting high-confidence guarantees to hedge against uncertainty. This paper explores the construction of Wasserstein ambiguity sets in dynamic scenarios where data is collected progressively and may only reveal partial information about the unknown random variable. For random variables evolving according to known dynamics, we leverage assimilated samples to make inferences about their unknown distribution at the end of the sampling horizon. Under exact knowledge of the flow map, we provide sufficient conditions that relate the growth of the trajectories with the sampling rate to establish a reduction of the ambiguity set size as the horizon increases. Further, we characterize the exploitable sample history that results in a guaranteed reduction of ambiguity sets under errors in the computation of the flow and when the dynamics is subject to bounded unknown disturbances. Our treatment deals with both full- and partial-state measurements and, in the latter case, exploits the sampled-data observability properties of linear time-varying systems under irregular sampling. Simulations on a UAV detection application show the superior performance resulting from the proposed dynamic ambiguity sets.

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arXiv2018

Distributed Control for Spatial Self-Organization of Multi-Agent Swarms

In this work, we design distributed control laws for spatial self-organization of multi-agent swarms in 1D and 2D spatial domains. The objective is to achieve a desired density distribution over a simply-connected spatial domain. Since individual agents in a swarm are not themselves of interest and we are concerned only with the macroscopic objective, we view the network of agents in the swarm as a discrete approximation of a continuous medium and design control laws to shape the density distribution of the continuous medium. The key feature of this work is that the agents in the swarm do not have access to position information. Each individual agent is capable of measuring the current local density of agents and can communicate with its spatial neighbors. The network of agents implement a Laplacian-based distributed algorithm, which we call pseudo-localization, to localize themselves in a new coordinate frame, and a distributed control law to converge to the desired spatial density distribution. We start by studying self-organization in one-dimension, which is then followed by the two-dimensional case.

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arXiv2012

On Single-Input Controllable Linear Systems Under Periodic DoS Jamming Attacks

In this paper, we study remotely-controlled single-input controllable linear systems, subject to periodic Denial-of-Service (DoS) attacks. We propose a control strategy which can beat any partially identified jammer by properly placing the closed-loop poles. This is proven theoretically for systems of dimension 4 or less. Nevertheless, simulations show the practicality of this strategy for systems up to order 5.

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