arXiv subjects

Shreyas Sundaram

Publications and source records attributed to Shreyas Sundaram.

At least 37 records · Page 2Linked to original sources

arXiv2023

Resilience for Distributed Consensus with Constraints

This paper proposes a new approach that enables multi-agent systems to achieve resilient \textit{constrained} consensus in the presence of Byzantine attacks, in contrast to existing literature that is only applicable to \textit{unconstrained} resilient consensus problems. The key enabler for our approach is a new device called a \textit{$(γ_i,α_i)$-resilient convex combination}, which allows normal agents in the network to utilize their locally available information to automatically isolate the impact of the Byzantine agents. Such a resilient convex combination is computable through linear programming, whose complexity scales well with the size of the overall system. By applying this new device to multi-agent systems, we introduce network and constraint redundancy conditions under which resilient constrained consensus can be achieved with an exponential convergence rate. We also provide insights on the design of a network such that the redundancy conditions are satisfied. Finally, numerical simulations and an example of safe multi-agent learning are provided to demonstrate the effectiveness of the proposed results.

eess.SY↗

arXiv2023

Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guarantees

The problem of online change point detection is to detect abrupt changes in properties of time series, ideally as soon as possible after those changes occur. Existing work on online change point detection either assumes i.i.d data, focuses on asymptotic analysis, does not present theoretical guarantees on the trade-off between detection accuracy and detection delay, or is only suitable for detecting single change points. In this work, we study the online change point detection problem for linear dynamical systems with unknown dynamics, where the data exhibits temporal correlations and the system could have multiple change points. We develop a data-dependent threshold that can be used in our test that allows one to achieve a pre-specified upper bound on the probability of making a false alarm. We further provide a finite-sample-based bound for the probability of detecting a change point. Our bound demonstrates how parameters used in our algorithm affect the detection probability and delay, and provides guidance on the minimum required time between changes to guarantee detection.

cs.LG↗

arXiv2023

Reverse Engineering the Reproduction Number: A Framework for Data-Driven Counterfactual Analysis, Strategy Evaluation, and Feedback Control of Epidemics

During the COVID-19 pandemic, different countries, regions, and communities constructed various epidemic models to evaluate spreading behaviors and assist in making mitigation policies. Model uncertainties, introduced by complex transmission behaviors, contact-tracing networks, time-varying spreading parameters, and human factors, as well as insufficient data, have posed arduous challenges for model-based approaches. To address these challenges, we propose a novel framework for data-driven counterfactual analysis, strategy evaluation, and feedback control of epidemics, which leverages statistical information from epidemic testing data instead of constructing a specific model. Through reverse engineering the reproduction number by quantifying the impact of the intervention strategy, this framework tackles three primary problems: 1) How severe would an outbreak have been without the implemented intervention strategies? 2) What impact would varying the intervention strength have had on an outbreak? 3) How can we adjust the intervention intensity based on the current state of an outbreak? Specifically, we consider the epidemic intervention policies such as the testing-for-isolation strategy as an example, which was successfully implemented by the University of Illinois Urbana-Champaign (UIUC) and Purdue University (Purdue) during the COVID-19 pandemic. By leveraging data collected by UIUC and Purdue, we validate the effectiveness of the proposed data-driven framework.

physics.soc-ph↗

arXiv2023

Robust Online Covariance and Sparse Precision Estimation Under Arbitrary Data Corruption

Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an online scenario even in the presence of arbitrary and adversarial data attacks. At each time step, data points, drawn nominally independently and identically from a multivariate Gaussian distribution, arrive. However, a certain fraction of these points may have been arbitrarily corrupted. We propose an online algorithm to estimate the sparse inverse covariance (i.e., precision) matrix despite this corruption. We provide the error-bound and convergence properties of the estimates to the true precision matrix under our algorithms.

cs.LG↗

arXiv2023

Learning Linearized Models from Nonlinear Systems with Finite Data

Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs, and assumes that the underlying dynamics is truly linear. In contrast, we consider the problem of identifying a linearized model when the true underlying dynamics is nonlinear. We provide a multiple trajectories-based deterministic data acquisition algorithm followed by a regularized least squares algorithm, and provide a finite sample error bound on the learned linearized dynamics. Our error bound demonstrates a trade-off between the error due to nonlinearity and the error due to noise, and shows that one can learn the linearized dynamics with arbitrarily small error given sufficiently many samples. We validate our results through experiments, where we also show the potential insufficiency of linear system identification using a single trajectory with i.i.d random inputs, when nonlinearity does exist.

eess.SY↗

arXiv2023

Deep Reinforcement Learning Based Framework for Mobile Energy Disseminator Dispatching to Charge On-the-Road Electric Vehicles

The exponential growth of electric vehicles (EVs) presents novel challenges in preserving battery health and in addressing the persistent problem of vehicle range anxiety. To address these concerns, wireless charging, particularly, Mobile Energy Disseminators (MEDs) have emerged as a promising solution. The MED is mounted behind a large vehicle and charges all participating EVs within a radius upstream of it. Unfortuantely, during such V2V charging, the MED and EVs inadvertently form platoons, thereby occupying multiple lanes and impairing overall corridor travel efficiency. In addition, constrained budgets for MED deployment necessitate the development of an effective dispatching strategy to determine optimal timing and locations for introducing the MEDs into traffic. This paper proposes a deep reinforcement learning (DRL) based methodology to develop a vehicle dispatching framework. In the first component of the framework, we develop a realistic reinforcement learning environment termed "ChargingEnv" which incorporates a reliable charging simulation system that accounts for common practical issues in wireless charging deployment, specifically, the charging panel misalignment. The second component, the Proximal-Policy Optimization (PPO) agent, is trained to control MED dispatching through continuous interactions with ChargingEnv. Numerical experiments were carried out to demonstrate the demonstrate the efficacy of the proposed MED deployment decision processor. The experiment results suggest that the proposed model can significantly enhance EV travel range while efficiently deploying a optimal number of MEDs. The proposed model is found to be not only practical in its applicability but also has promises of real-world effectiveness. The proposed model can help travelers to maximize EV range and help road agencies or private-sector vendors to manage the deployment of MEDs efficiently.

cs.RO↗

arXiv2023

On the Benefits of Leveraging Structural Information in Planning Over the Learned Model

Model-based Reinforcement Learning (RL) integrates learning and planning and has received increasing attention in recent years. However, learning the model can incur a significant cost (in terms of sample complexity), due to the need to obtain a sufficient number of samples for each state-action pair. In this paper, we investigate the benefits of leveraging structural information about the system in terms of reducing sample complexity. Specifically, we consider the setting where the transition probability matrix is a known function of a number of structural parameters, whose values are initially unknown. We then consider the problem of estimating those parameters based on the interactions with the environment. We characterize the difference between the Q estimates and the optimal Q value as a function of the number of samples. Our analysis shows that there can be a significant saving in sample complexity by leveraging structural information about the model. We illustrate the findings by considering several problems including controlling a queuing system with heterogeneous servers, and seeking an optimal path in a stochastic windy gridworld.

cs.LG↗

arXiv2023

Multi-Robot Persistent Monitoring: Minimizing Latency and Number of Robots with Recharging Constraints

In this paper we study multi-robot path planning for persistent monitoring tasks. We consider the case where robots have a limited battery capacity with a discharge time $D$. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum allowable time between robot visits, called the latency. The objective is to find the minimum number of robots that can satisfy these latency constraints while also ensuring that the robots periodically charge at a recharging depot. The decision version of this problem is known to be PSPACE-complete. We present a $O(\frac{\log D}{\log \log D}\log ρ)$ approximation algorithm for the problem where $ρ$ is the ratio of the maximum and the minimum latency constraints. We also present an orienteering based heuristic to solve the problem and show empirically that it typically provides higher quality solutions than the approximation algorithm. We extend our results to provide an algorithm for the problem of minimizing the maximum weighted latency given a fixed number of robots. We evaluate our algorithms on large problem instances in a patrolling scenario and in a wildfire monitoring application. We also compare the algorithms with an existing solver on benchmark instances.

cs.RO↗

arXiv2022

Robust Online and Distributed Mean Estimation Under Adversarial Data Corruption

We study robust mean estimation in an online and distributed scenario in the presence of adversarial data attacks. At each time step, each agent in a network receives a potentially corrupted data point, where the data points were originally independent and identically distributed samples of a random variable. We propose online and distributed algorithms for all agents to asymptotically estimate the mean. We provide the error-bound and the convergence properties of the estimates to the true mean under our algorithms. Based on the network topology, we further evaluate each agent's trade-off in convergence rate between incorporating data from neighbors and learning with only local observations.

cs.CR↗

arXiv2022

Finite Sample Guarantees for Distributed Online Parameter Estimation with Communication Costs

We study the problem of estimating an unknown parameter in a distributed and online manner. Existing work on distributed online learning typically either focuses on asymptotic analysis, or provides bounds on regret. However, these results may not directly translate into bounds on the error of the learned model after a finite number of time-steps. In this paper, we propose a distributed online estimation algorithm which enables each agent in a network to improve its estimation accuracy by communicating with neighbors. We provide non-asymptotic bounds on the estimation error, leveraging the statistical properties of the underlying model. Our analysis demonstrates a trade-off between estimation error and communication costs. Further, our analysis allows us to determine a time at which the communication can be stopped (due to the costs associated with communications), while meeting a desired estimation accuracy. We also provide a numerical example to validate our results.

eess.SY↗

arXiv2022

Optimal Mitigation of SIR Epidemics Under Model Uncertainty

We study the impact of model parameter uncertainty on optimally mitigating the spread of epidemics. We capture the epidemic spreading process using a susceptible-infected-removed (SIR) epidemic model and consider testing for isolation as the control strategy. We use a testing strategy to remove (isolate) a portion of the infected population. Our goal is to maintain the daily infected population below a certain level, while minimizing the total number of tests. Distinct from existing works on leveraging control strategies in epidemic spreading, we propose a testing strategy by overestimating the seriousness of the epidemic and study the feasibility of the system under the impact of model parameter uncertainty. Compared to the optimal testing strategy, we establish that the proposed strategy under model parameter uncertainty will flatten the curve effectively but require more tests and a longer time period.

eess.SY↗

arXiv2022

A Survey of Graph-Theoretic Approaches for Analyzing the Resilience of Networked Control Systems

As the scale of networked control systems increases and interactions between different subsystems become more sophisticated, questions of the resilience of such networks increase in importance. The need to redefine classical system and control-theoretic notions using the language of graphs has recently started to gain attention as a fertile and important area of research. This paper presents an overview of graph-theoretic methods for analyzing the resilience of networked control systems. We discuss various distributed algorithms operating on networked systems and investigate their resilience against adversarial actions by looking at the structural properties of their underlying networks. We present graph-theoretic methods to quantify the attack impact, and reinterpret some system-theoretic notions of robustness from a graph-theoretic standpoint to mitigate the impact of the attacks. Moreover, we discuss miscellaneous problems in the security of networked control systems which use graph-theory as a tool in their analyses. We conclude by introducing some avenues for further research in this field.

eess.SY↗

arXiv2022

Identifying the Dynamics of a System by Leveraging Data from Similar Systems

We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and provide finite sample performance guarantees on the quality of the identified dynamics. Our results show that one can effectively use the auxiliary data generated by the similar system to reduce the estimation error due to the process noise, at the cost of adding a portion of error that is due to intrinsic differences in the models of the true and auxiliary systems. We also provide numerical experiments to validate our theoretical results. Our analysis can be applied to a variety of important settings. For example, if the system dynamics change at some point in time (e.g., due to a fault), how should one leverage data from the prior system in order to learn the dynamics of the new system? As another example, if there is abundant data available from a simulated (but imperfect) model of the true system, how should one weight that data compared to the real data from the system? Our analysis provides insights into the answers to these questions.

eess.SY↗

arXiv2022

Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectories

We consider the problem of learning the dynamics of autonomous linear systems (i.e., systems that are not affected by external control inputs) from observations of multiple trajectories of those systems, with finite sample guarantees. Existing results on learning rate and consistency of autonomous linear system identification rely on observations of steady state behaviors from a single long trajectory, and are not applicable to unstable systems. In contrast, we consider the scenario of learning system dynamics based on multiple short trajectories, where there are no easily observed steady state behaviors. We provide a finite sample analysis, which shows that the dynamics can be learned at a rate $\mathcal{O}(\frac{1}{\sqrt{N}})$ for both stable and unstable systems, where $N$ is the number of trajectories, when the initial state of the system has zero mean (which is a common assumption in the existing literature). We further generalize our result to the case where the initial state has non-zero mean. We show that one can adjust the length of the trajectories to achieve a learning rate of $\mathcal{O}(\sqrt{\frac{\log{N}}{N})}$ for strictly stable systems and a learning rate of $\mathcal{O}(\frac{(\log{N})^d}{\sqrt{N}})$ for marginally stable systems, where $d$ is some constant.

eess.SY↗

arXiv2021

On a Network SIS Epidemic Model with Cooperative and Antagonistic Opinion Dynamics

We propose a mathematical model to study coupled epidemic and opinion dynamics in a network of communities. Our model captures SIS epidemic dynamics whose evolution is dependent on the opinions of the communities toward the epidemic, and vice versa. In particular, we allow both cooperative and antagonistic interactions, representing similar and opposing perspectives on the severity of the epidemic, respectively. We propose an Opinion-Dependent Reproduction Number to characterize the mutual influence between epidemic spreading and opinion dissemination over the networks. Through stability analysis of the equilibria, we explore the impact of opinions on both epidemic outbreak and eradication, characterized by bounds on the Opinion-Dependent Reproduction Number. We also show how to eradicate epidemics by reshaping the opinions, offering researchers an approach for designing control strategies to reach target audiences to ensure effective epidemic suppression.

eess.SY↗

arXiv2021

Planning for Package Deliveries in Risky Environments Over Multiple Epochs

We study a risk-aware robot planning problem where a dispatcher must construct a package delivery plan that maximizes the expected reward for a robot delivering packages across multiple epochs. Each package has an associated reward for delivery and a risk of failure. If the robot fails while delivering a package, no future packages can be delivered and the cost of replacing the robot is incurred. The package delivery plan takes place over the course of either a finite or an infinite number of epochs, denoted as the finite horizon problem and infinite horizon problem, respectively. The dispatcher has to weigh the risk and reward of delivering packages during any given epoch against the potential loss of any future epoch's reward. By using the ratio between a package's reward and its risk of failure, we prove an optimal, greedy solution to both the infinite and finite horizon problems. The finite horizon problem can be solved optimally in $O(K n\log n)$ time where $K$ is the number of epochs and $n$ is the number of packages. We show an isomorphism between the infinite horizon problem and Markov Decision Processes to prove an optimal $O(n)$ time algorithm for the infinite horizon problem.

math.OC↗

arXiv2021

Distributed Estimation of Sparse Inverse Covariances

Learning the relationships between various entities from time-series data is essential in many applications. Gaussian graphical models have been studied to infer these relationships. However, existing algorithms process data in a batch at a central location, limiting their applications in scenarios where data is gathered by different agents. In this paper, we propose a distributed sparse inverse covariance algorithm to learn the network structure (i.e., dependencies among observed entities) in real-time from data collected by distributed agents. Our approach is built on an online graphical alternating minimization algorithm, augmented with a consensus term that allows agents to learn the desired structure cooperatively. We allow the system designer to select the number of communication rounds and optimization steps per data point. We characterize the rate of convergence of our algorithm and provide simulations on synthetic datasets.

cs.LG↗

arXiv2021

Peak Infection Time for a Networked SIR Epidemic with Opinion Dynamics

We propose an SIR epidemic model coupled with opinion dynamics to study an epidemic and opinions spreading in a network of communities. Our model couples networked SIR epidemic dynamics with opinions towards the severity of the epidemic, and vice versa. We develop an epidemic-opinion based threshold condition to capture the moment when a weighted average of the epidemic states starts to decrease exponentially fast over the network, namely the peak infection time. We define an effective reproduction number to characterize the behavior of the model through the peak infection time. We use both analytical and simulation-based results to illustrate that the opinions reflect the recovered levels within the communities after the epidemic dies out.

eess.SY↗