arXiv subjects

Sonia Martinez

Publications and source records attributed to Sonia Martinez.

At least 19 recordsLinked to original sources

arXiv2025

Distributed Time-Varying Coverage Control via Singular Perturbations

This paper presents a novel dynamic coverage control algorithm allowing a group of robots to track an optimal-deployment configuration for arbitrary time-varying density functions. Building on singular perturbation theory, the proposed design employs a two-time scale separation approach, with a fast time scale corresponding to communication and a slow time scale corresponding to agent motion. The resulting algorithm is distributed over the 2-hop Delaunay graph and, for small enough values of the perturbation parameter, achieves the same performance as its centralized counterpart. We also introduce three discrete-time versions that rely only on 1-hop communication at the cost of having to use delayed information and formally establish their asymptotic convergence properties. Our technical approach combines computational geometry, singular perturbation theory, generating functions, and linear iterations with delayed updates. Various simulations illustrate the performance of the proposed algorithms.

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arXiv2025

Baseline-improved Economic Model Predictive Control for Optimal Microgrid Dispatch

Economic Model Predictive Control (EMPC) optimizes economic performance over a prediction horizon rather than stabilizing to a reference, making it attractive for microgrid (MG) dispatch. However, since load and generation forecasts are known only 24-48 h ahead, economically optimal steady states or periodic trajectories are unavailable, and EMPC works relying on such signals are inadequate. Moreover, demand charges, based on the maximum monthly grid import, cannot be easily cast as an additive cost, which prevents a naive application of the principle of optimality. We propose to close this mismatch between the EMPC prediction horizon and monthly timescales via an appropriately generated baseline reference trajectory. We first propose an EMPC formulation for a generic deterministic discrete nonlinear time-varying system subject to hard state and input constraints. We then show that, under appropriate terminal ingredients -- sequential control invariance of the terminal region and a terminal control law causing a Lyapunov-like decrease of the terminal cost -- the asymptotic average economic cost of the proposed method is no worse than a baseline given by any arbitrary reference trajectory known only online. This yields a practical, finite-time upper bound on the average economic cost difference with the baseline that decreases linearly to zero as time goes to infinity. We then show how the framework solves optimal MG dispatch problems, introducing costs and constraints that conform to the required assumptions. Using data from the Port of San Diego MG, realistic simulations demonstrate that the proposed method reduces monthly electricity costs in closed loop relative to reference trajectories generated either by optimizing the electricity cost over the prediction horizon or by tracking an ideal grid import curve.

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arXiv2025

Robust Output-Feedback MPC for Nonlinear Systems with Applications to Robotic Exploration

This paper introduces a novel method for robust output-feedback model predictive control (MPC) for a class of nonlinear discrete-time systems. We propose a novel interval-valued predictor which, given an initial estimate of the state, produces intervals which are guaranteed to contain the future trajectory of the system. By parameterizing the control input with an initial stabilizing feedback term, we are able to reduce the width of the predicted state intervals compared to existing methods. We demonstrate this through a numerical comparison where we show that our controller performs better in the presence of large amounts of noise. Finally, we present a simulation study of a robot navigation scenario, where we incorporate a time-varying entropy term into the cost function in order to autonomously explore an uncertain area.

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arXiv2025

Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densities

In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability distributions over continuous variables, and (ii) leverage these results to obtain new distributed estimators restricted to subsets of variables observed by individual agents. This relates to applications such as cooperative localization and federated learning, where the data collected at any agent depends on a subset of all variables of interest. We present Bayesian density estimation algorithms using data from non-linear likelihoods at agents in centralized, distributed, and marginal distributed settings. After setting up a distributed estimation objective, we prove almost-sure convergence to the optimal set of pdfs at each agent. Then, we prove the same for a storage-aware algorithm estimating densities only over relevant variables at each agent. Finally, we present a Gaussian version of these algorithms and implement it in a mapping problem using variational inference to handle non-linear likelihood models associated with LiDAR sensing.

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arXiv2025

Robotic Exploration using Generalized Behavioral Entropy

This work presents and evaluates a novel strategy for robotic exploration that leverages human models of uncertainty perception. To do this, we introduce a measure of uncertainty that we term "Behavioral entropy", which builds on Prelec's probability weighting from Behavioral Economics. We show that the new operator is an admissible generalized entropy, analyze its theoretical properties and compare it with other common formulations such as Shannon's and Renyi's. In particular, we discuss how the new formulation is more expressive in the sense of measures of sensitivity and perceptiveness to uncertainty introduced here. Then we use Behavioral entropy to define a new type of utility function that can guide a frontier-based environment exploration process. The approach's benefits are illustrated and compared in a Proof-of-Concept and ROS-Unity simulation environment with a Clearpath Warthog robot. We show that the robot equipped with Behavioral entropy explores faster than Shannon and Renyi entropies.

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arXiv2024

Guaranteed Privacy-Preserving $\mathcal{H}_{\infty}$-Optimal Interval Observer Design for Bounded-Error LTI Systems

This paper furthers current research into the notion of guaranteed privacy, which provides a deterministic characterization of the privacy of output signals of a dynamical system or mechanism. Unlike stochastic differential privacy, guaranteed privacy offers strict bounds on the proximity between the ranges of two sets of estimated data. Our approach relies on synthesizing an interval observer for a perturbed linear time-invariant (LTI) bounded-error system. The design procedure incorporates a bounded noise perturbation factor computation and observer gains synthesis. Consequently, the observer simultaneously provides guaranteed private and stable interval-valued estimates for a desired variable. We demonstrate the optimality of our design by minimizing the $\mathcal{H}_{\infty}$ norm of the observer error system. Furthermore, we assess the accuracy of our proposed mechanism by quantifying the loss incurred when considering guaranteed privacy specifications. Finally, we illustrate the outperformance of the proposed approach to differential privacy through simulations.

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arXiv2024

Data-driven mode detection and stabilization of unknown switched linear systems

This paper considers the stabilization of unknown switched linear systems using data. Instead of a full system model, we have access to a finite number of trajectories of each of the different modes prior to the online operation of the system. On the basis of informative enough measurements, formally characterized in terms of linear matrix inequalities, we design an online switched controller that alternates between a mode detection phase and a stabilization phase. Since the specific currently-active mode is unknown, the controller employs the most recent online measurements to determine it by implementing computationally efficient tests that check compatibility with the set of systems consistent with the pre-collected measurements. The stabilization phase applies the stabilizing feedback gain corresponding to the identified active mode and monitors the evolution of the associated Lyapunov function to detect switches. When a switch is detected, the controller returns to the mode-detection phase. Under average dwell- and activation-time assumptions on the switching signal, we show that the proposed controller guarantees a practical stability property of the closed-loop switched system. Various simulations illustrate our results.

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arXiv2024

Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems

This paper proposes a novel approach to construct data-driven online solutions to optimization problems (P) subject to a class of distributionally uncertain dynamical systems. The introduced framework allows for the simultaneous learning of distributional system uncertainty via a parameterized, control-dependent ambiguity set using a finite historical data set, and its use to make online decisions with probabilistic regret function bounds. Leveraging the merits of Machine Learning, the main technical approach relies on the theory of Distributional Robust Optimization (DRO), to hedge against uncertainty and provide less conservative results than standard Robust Optimization approaches. Starting from recent results that describe ambiguity sets via parameterized, and control-dependent empirical distributions as well as ambiguity radii, we first present a tractable reformulation of the corresponding optimization problem while maintaining the probabilistic guarantees. We then specialize these problems to the cases of 1) optimal one-stage control of distributionally uncertain nonlinear systems, and 2) resource allocation under distributional uncertainty. A novelty of this work is that it extends DRO to online optimization problems subject to a distributionally uncertain dynamical system constraint, handled via a control-dependent ambiguity set that leads to online-tractable optimization with probabilistic guarantees on regret bounds. Further, we introduce an online version of Nesterov's accelerated-gradient algorithm, and analyze its performance to solve this class of problems via dissipativity theory.

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arXiv2024

Multi-agent Coverage Control: From Discrete Assignments to Continuous Multi-agent Distribution Matching

The multi-agent spatial coverage control problem encompasses a broad research domain, dealing with both dynamic and static deployment strategies, discrete-task assignments, and spatial distribution-matching deployment. Coverage control may involve the deployment of a finite number of agents or a continuum through centralized or decentralized, locally-interacting schemes. All these problems can be solved via a different taxonomy of deployment algorithms for multiple agents. Depending on the application scenario, these problems involve from purely discrete descriptions of tasks (finite loads) and agents (finite resources), to a mixture of discrete and continuous elements, to fully continuous descriptions of the same. Yet, it is possible to find common features that underline all the above formulations, which we aim to illustrate here. By doing so, we aim to point the reader to novel references related to these problems. The short article outline is the following: Static coverage via concurrent area partitioning and assignment; Static coverage as a discrete task assignment; and Continuum task assignment for large-scale swarms.

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arXiv2024

Fine-Tuned Convex Approximations of Probabilistic Reachable Sets under Data-driven Uncertainties

This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded reachable set of the system. Instead, we turn to find a PRS that bounds system states with high confidence. Our data-driven approach builds on a kernel density estimator (KDE) accelerated by a fast Fourier transform (FFT), which is customized to model the uncertainties and obtain the PRS efficiently. However, the non-convex shape of the PRS can make it impractical for subsequent optimal designs. Motivated by this, we formulate a mixed integer nonlinear programming (MINLP) problem whose solution result is an optimal $n$ sided convex polygon that approximates the PRS. Leveraging this formulation, we propose a heuristic algorithm to find this convex set efficiently while ensuring accuracy. The algorithm is tested on comprehensive case studies that demonstrate its near-optimality, accuracy, efficiency, and robustness. The benefits of this work pave the way for promising applications to safety-critical, real-time motion planning of uncertain dynamic systems.

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arXiv2024

Distributed Resilient Interval Observer Synthesis for Nonlinear Discrete-Time Systems

This paper introduces a novel recursive distributed estimation algorithm aimed at synthesizing input and state interval observers for nonlinear bounded-error discrete-time multi-agent systems. The considered systems have sensors and actuators that are susceptible to unknown or adversarial inputs. To solve this problem, we first identify conditions that allow agents to obtain nonlinear bounded-error equations characterizing the input. Then, we propose a distributed interval-valued observer that is guaranteed to contain the disturbance and system states. To do this, we first detail a gain design procedure that uses global problem data to minimize an upper bound on the $\ell_1$ norm of the observer error. We then propose a gain design approach that does not require global information, using only values that are local to each agent. The second method improves on the computational tractability of the first, at the expense of some added conservatism. Further, we discuss some possible ways of extending the results to a broader class of systems. We conclude by demonstrating our observer on two examples. The first is a unicycle system, for which we apply the first gain design method. The second is a 145-bus power system, which showcases the benefits of the second method, due to the first approach being intractable for systems with high dimensional state spaces.

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arXiv2023

Distributed Variational Inference for Online Supervised Learning

Developing efficient solutions for inference problems in intelligent sensor networks is crucial for the next generation of location, tracking, and mapping services. This paper develops a scalable distributed probabilistic inference algorithm that applies to continuous variables, intractable posteriors and large-scale real-time data in sensor networks. In a centralized setting, variational inference is a fundamental technique for performing approximate Bayesian estimation, in which an intractable posterior density is approximated with a parametric density. Our key contribution lies in the derivation of a separable lower bound on the centralized estimation objective, which enables distributed variational inference with one-hop communication in a sensor network. Our distributed evidence lower bound (DELBO) consists of a weighted sum of observation likelihood and divergence to prior densities, and its gap to the measurement evidence is due to consensus and modeling errors. To solve binary classification and regression problems while handling streaming data, we design an online distributed algorithm that maximizes DELBO, and specialize it to Gaussian variational densities with non-linear likelihoods. The resulting distributed Gaussian variational inference (DGVI) efficiently inverts a $1$-rank correction to the covariance matrix. Finally, we derive a diagonalized version for online distributed inference in high-dimensional models, and apply it to multi-robot probabilistic mapping using indoor LiDAR data.

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arXiv2023

Control of Discrete-Time LTI Systems using Stochastic Ensemble Systems

In this paper, we study the control properties of a new class of stochastic ensemble systems that consists of families of random variables. These random variables provide an increasingly good approximation of an unknown discrete, linear-time invariant (DLTI) system, and can be obtained by a standard, data-driven procedure. Our first result relates the reachability properties of the stochastic ensemble system with that of the limiting DLTI system. We then provide a method to combine the control inputs obtained from the stochastic ensemble systems to compute a control input for the DLTI system. Later, we deal with a particular kind of stochastic ensemble system generated from realizing Bernoulli random variables. For this, we characterize the variance of the computed state and control. We also do the same for a situation where the data is updated sequentially in a streaming fashion. We illustrate the results numerically in various simulation examples.

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arXiv2023

Distributed Resilient Interval Observers for Bounded-Error LTI Systems Subject to False Data Injection Attacks

This paper proposes a novel distributed interval-valued simultaneous state and input observer for linear time-invariant (LTI) systems that are subject to attacks or unknown inputs injected both on their sensors and actuators. Each agent in the network leverages a singular value decomposition (SVD) based transformation to decompose its observations into two components, one of them unaffected by the attack signal, which helps to obtain local interval estimates of the state and unknown input and then uses intersection to compute the best interval estimate among neighboring nodes. We show that the computed intervals are guaranteed to contain the true state and input trajectories, and we provide conditions under which the observer is stable. Furthermore, we provide a method for designing stabilizing gains that minimize an upper bound on the worst-case steady-state observer error. We demonstrate our algorithm on an IEEE 14-bus power system.

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arXiv2023

Robot Navigation in Risky, Crowded Environments: Understanding Human Preferences

Risky and crowded environments (RCE) contain abstract sources of risk and uncertainty, which are perceived differently by humans, leading to a variety of behaviors. Thus, robots deployed in RCEs, need to exhibit diverse perception and planning capabilities in order to interpret other human agents' behavior and act accordingly in such environments. To understand this problem domain, we conducted a study to explore human path choices in RCEs, enabling better robotic navigational explainable AI (XAI) designs. We created a novel COVID-19 pandemic grocery shopping scenario which had time-risk tradeoffs, and acquired users' path preferences. We found that participants showcase a variety of path preferences: from risky and urgent to safe and relaxed. To model users' decision making, we evaluated three popular risk models (Cumulative Prospect Theory (CPT), Conditional Value at Risk (CVAR), and Expected Risk (ER). We found that CPT captured people's decision making more accurately than CVaR and ER, corroborating theoretical results that CPT is more expressive and inclusive than CVaR and ER. We also found that people's self assessments of risk and time-urgency do not correlate with their path preferences in RCEs. Finally, we conducted thematic analysis of open-ended questions, providing crucial design insights for robots is RCE. Thus, through this study, we provide novel and critical insights about human behavior and perception to help design better navigational explainable AI (XAI) in RCEs.

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arXiv2022

Guaranteed Privacy of Distributed Nonconvex Optimization via Mixed-Monotone Functional Perturbations

In this paper, we introduce a new notion of guaranteed privacy that requires that the change of the range of the corresponding inclusion function to the true function is small. In particular, leveraging mixed-monotone inclusion functions, we propose a privacy-preserving mechanism for nonconvex distributed optimization, which is based on deterministic, but unknown, affine perturbation of the local objective functions, which is stronger than probabilistic differential privacy. The design requires a robust optimization method to characterize the best accuracy that can be achieved by an optimal perturbation. Subsequently, this is used to guide the refinement of a guaranteed-private perturbation mechanism that can achieve a quantifiable accuracy via a theoretical upper bound that is shown to be independent of the chosen optimization algorithm.

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arXiv2022

Using data informativity for online stabilization of unknown switched linear systems

This work studies data-driven switched controller design for discrete-time switched linear systems. Instead of having access to the full system dynamics, an initialization phase is performed, during which noiseless measurements of the state and the input are collected for each mode. Under certain conditions on these measurements, we develop a stabilizing switched controller for the switched system. To be precise, the controller switches between identifying the active mode of the system and applying a predetermined stabilizing feedback. We prove that if the system switches according to certain specifications, this controller stabilizes the closed-loop system. Simulations on a network example illustrate our approach.

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arXiv2022

Distributed Interval Observers for Bounded-Error LTI Systems

This paper proposes a novel distributed interval observer design for linear time-invariant (LTI) discrete-time systems subject to bounded disturbances. In the proposed observer algorithm, each agent in a networked group exchanges locally-computed framers or interval-valued state estimates with neighbors, and coordinates its update via an intersection operation. We show that the proposed framers are guaranteed to bound the true state trajectory of the system by construction, i.e., without imposing any additional assumptions or constraints. Moreover, we provide necessary and sufficient conditions for the collective stability of the distributed observer, i.e., to guarantee the uniform boundedness of the observer error sequence. In particular, we show that such conditions can be tractably satisfied through a constructive and distributed approach. Moreover, we provide an algorithm to verify some structural conditions for a given system, which guarantee the existence of the proposed observer. Finally, simulation results demonstrate the effectiveness of our proposed method compared to an existing distributed observer in the literature.

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