pwc-archive/papers-with-abstracts huggingface dataset:
Quadratic Regularization of Data-Enabled Predictive Control: Theory and Application to Power Converter Experiments
Authors: Linbin Huang, Jianzhe Zhen, John Lygeros, Florian Dörfler
Date: 2020-12-08 00:00:00

Data-driven control that circumvents the process of system identification by providing optimal control inputs directly from system data has attracted renewed attention in recent years. In this paper, we focus on understanding the effects of the regularization on the data-enabled predictive control (DeePC) algorithm. We provide theoretical motivation and interpretation for including a quadratic regularization term. Our analysis shows that the quadratic regularization term leads to robust and optimal solutions with regards to disturbances affecting the data. Moreover, when the input/output constraints are inactive, the quadratic regularization leads to a closed-form solution of the DeePC algorithm and thus enables fast calculations. On this basis, we propose a framework for data-driven synchronization and power regulations of power converters, which is tested by high-fidelity simulations and experiments.
Large Deviations Principle for Discrete-time Mean-field Games
Authors: Naci Saldi
Date: 2021-02-15 00:00:00

In this paper, we establish a large deviations principle (LDP) for interacting particle systems that arise from state and action dynamics of discrete-time mean-field games under the equilibrium policy of the infinite-population limit. The LDP is proved under weak Feller continuity of state and action dynamics. The proof is based on transferring LDP for empirical measures of initial states and noise variables under setwise topology to the original game model via contraction principle, which was first suggested by Delarue, Lacker, and Ramanan to establish LDP for continuous-time mean-field games under common noise. We also compare our work with LDP results established in prior literature for interacting particle systems, which are in a sense uncontrolled versions of mean-field games.
Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound
Authors: Sebastian A. Nugroho, Ahmad F. Taha
Date: 2020-12-27 00:00:00
Tasks: valid

Sensor and actuator selection problems (SASP) are some of the core problems in dynamic systems design and control. These problems correspond to determining the optimal selection of sensors (measurements) or actuators (control nodes) such that certain estimation/control objectives can be achieved. While the literature on SASP is indeed inveterate, the vast majority of the work focuses on linear(ized) representation of the network dynamics, resulting in the placements of sensors or actuators (SA) that are valid for confined operating regions. As an alternative, herein we propose a new general framework for addressing SASP in nonlinear dynamic systems (NDS), assuming that the inputs and outputs are linearly coupled with the nonlinear dynamics. This is investigated through (i) classifying and parameterizing the NDS into various nonlinear function sets, (ii) utilizing rich Lyapunov theoretic formulations, and (iii) designing a new customized branch-and-bound (BnB) algorithm that exploits problem structure of the SASP. The newly designed BnB routines are computationally more attractive than the standard one and also directly applicable to solve SASP for linear systems. In contrast with contemporary approaches from the literature, our approach is suitable for finding the optimal SA combination for stable/unstable NDS that ensures stabilization of estimation error and closed-loop dynamics through a simple linear feedback control policy.
Equivariant Systems Theory and Observer Design for Second Order Kinematic Systems on Matrix Lie Groups
Authors: Yonhon Ng, Pieter van Goor, Tarek Hamel, Robert Mahony
Date: 2021-05-11 00:00:00

This paper presents the equivariant systems theory and observer design for second order kinematic systems on matrix Lie groups. The state of a second order kinematic system on a matrix Lie group is naturally posed on the tangent bundle of the group with the inputs lying in the tangent of the tangent bundle known as the double tangent bundle. We provide a simple parameterization of both the tangent bundle state space and the input space (the fiber space of the double tangent bundle) and then introduce a semi-direct product group and group actions onto both the state and input spaces. We show that with the proposed group actions the second order kinematics are equivariant. An equivariant lift of the kinematics onto the symmetry group is defined and used to design a nonlinear observer on the lifted state space using nonlinear constructive design techniques. A simple hovercraft simulation verifies the performance of our observer.
A Simple Bound for Resilient Submodular Maximization with Curvature
Authors: Micah Corah
Date: 2021-05-11 00:00:00

Resilient submodular maximization refers to the combinatorial problems studied by Nemhauser and Fisher and asks how to maximize an objective given a number of adversarial removals. For example, one application of this problem is multi-robot sensor planning with adversarial attacks. However, more general applications of submodular maximization are also relevant. Tzoumas et al. obtain near-optimal solutions to this problem by taking advantage of a property called curvature to produce a mechanism which makes certain bait elements interchangeable with other elements of the solution that are produced via typical greedy means. This document demonstrates that -- at least in theory -- applying the method for selection of bait elements to the entire solution can improve that guarantee on solution quality.
HAPS-ITS: Enabling Future ITS Services in Trans-Continental Highways
Authors: Wael Jaafar, Halim Yanikomeroglu
Date: 2021-05-11 00:00:00
Tasks: Autonomous Vehicles

With the advent of rapid globalization and the inter-border supply chain network, the reliability and efficiency of transportation systems have become even more critical. Indeed, trans-continental highways need particular attention due to their important role in sustaining globalization. In this context, intelligent transportation systems (ITS) can actively enhance the safety, mobility, productivity, and comfort of trans-continental highways. However, ITS efficiency depends greatly on the roads where they are deployed, on the availability of power and connectivity, and on the integration of future connected and autonomous vehicles. To this end, high altitude platform station (HAPS) systems, due to their mobility, sustainability, payload capacity, and communication/caching/computing capabilities, are seen as a key enabler of future ITS services for trans-continental highways; this paradigm is referred to as HAPS-ITS. The latter is envisioned as an active component of ITS systems to support a plethora of transportation applications, such as traffic monitoring, accident reporting, and platooning. This paper discusses how HAPS systems can enable advanced ITS services for trans-continental highways, presenting the main requirements of HAPS-ITS and a detailed case study of the Trans-Sahara highway.
Parameter Estimation in Epidemic Spread Networks Using Limited Measurements
Authors: Lintao Ye, Philip E. Paré, Shreyas Sundaram
Date: 2021-05-11 00:00:00
Tasks: parameter estimation

We study the problem of estimating the parameters (i.e., infection rate and recovery rate) governing the spread of epidemics in networks. Such parameters are typically estimated by measuring various characteristics (such as the number of infected and recovered individuals) of the infected populations over time. However, these measurements also incur certain costs, depending on the population being tested and the times at which the tests are administered. We thus formulate the epidemic parameter estimation problem as an optimization problem, where the goal is to either minimize the total cost spent on collecting measurements, or to optimize the parameter estimates while remaining within a measurement budget. We show that these problems are NP-hard to solve in general, and then propose approximation algorithms with performance guarantees. We validate our algorithms using numerical examples.
Optimal Online Algorithms for Peak-Demand Reduction Maximization with Energy Storage
Authors: Yanfang Mo, Qiulin Lin, Minghua Chen, Si-Zhao Joe Qin
Date: 2021-05-11 00:00:00
Tasks: Decision Making

The high proportions of demand charges in electric bills motivate large-power customers to leverage energy storage for reducing the peak procurement from the outer grid. Given limited energy storage, we expect to maximize the peak-demand reduction in an online fashion, challenged by the highly uncertain demands and renewable injections, the non-cumulative nature of peak consumption, and the coupling of online decisions. In this paper, we propose an optimal online algorithm that achieves the best competitive ratio, following the idea of maintaining a constant ratio between the online and the optimal offline peak-reduction performance. We further show that the optimal competitive ratio can be computed by solving a linear number of linear-fractional programs. Moreover, we extend the algorithm to adaptively maintain the best competitive ratio given the revealed inputs and actions at each decision-making round. The adaptive algorithm retains the optimal worst-case guarantee and attains improved average-case performance. We evaluate our proposed algorithms using real-world traces and show that they obtain up to 81% peak reduction of the optimal offline benchmark. Additionally, the adaptive algorithm achieves at least 20% more peak reduction against baseline alternatives.
Different Environment Feedback in Fast-slow Eco-evolutionary Dynamics
Authors: Lulu Gong, Ming Cao
Date: 2021-05-10 00:00:00

The fast-slow dynamics of an eco-evolutionary system are studied, where we consider the feedback actions of environmental resources that are classified into those that are self-renewing and those externally supplied. We show although these two types of resources are drastically different, the resulting closed-loop systems bear close resemblances, which include the same equilibria and their stability conditions on the boundary of the phase space, and the similar appearances of equilibria in the interior. After closer examination of specific choices of parameter values, we disclose that the global dynamical behaviors of the two types of closed-loop systems can be fundamentally different in terms of limit cycles: the system with self-renewing resources undergoes a generalized Hopf bifurcation such that one stable limit cycle and one unstable limit cycle can coexist; the system with externally supplied resources can only have the stable limit cycle induced by a supercritical Hopf bifurcation. Finally, the explorative analysis is carried out to show the discovered dynamic behaviors are robust in even larger parameter space.
Travelling wave analysis of cellular invasion into surrounding tissues
Authors: Maud El-Hachem, Scott W McCue, Matthew J Simpson
Date: 2021-05-11 00:00:00

Single-species reaction-diffusion equations, such as the Fisher-KPP and Porous-Fisher equations, support travelling wave solutions that are often interpreted as simple mathematical models of biological invasion. Such travelling wave solutions are thought to play a role in various applications including development, wound healing and malignant invasion. One criticism of these single-species equations is that they do not explicitly describe interactions between the invading population and the surrounding environment. In this work we study a reaction-diffusion equation that describes malignant invasion which has been used to interpret experimental measurements describing the invasion of malignant melanoma cells into surrounding human skin tissues. This model explicitly describes how the population of cancer cells degrade the surrounding tissues, thereby creating free space into which the cancer cells migrate and proliferate to form an invasion wave of malignant tissue that is coupled to a retreating wave of skin tissue. We analyse travelling wave solutions of this model using a combination of numerical simulation, phase plane analysis and perturbation techniques. Our analysis shows that the travelling wave solutions involve a range of very interesting properties that resemble certain well-established features of both the Fisher-KPP and Porous-Fisher equations, as well as a range of novel properties that can be thought of as extensions of these well-studied single-species equations. Of particular interest is that travelling wave solutions of the invasion model are very well approximated by trajectories in the Fisher-KPP phase plane that are normally disregarded. This observation establishes a previously unnoticed link between coupled multi-species reaction diffusion models of invasion and a different class of models of invasion that involve moving boundary problems.
Automated quantitative analysis of first-pass myocardial perfusion magnetic resonance imaging data
Authors: Cian M Scannell
Date: 2021-05-10 00:00:00
Tasks: Diagnostic, Image Registration, Management

Coronary artery disease (CAD) remains the world's leading cause of mortality and the disease burden is continually expanding as the population ages. Recently, the MR-INFORM randomised trial has demonstrated that the management of patients with stable CAD can be guided by stress perfusion cardiovascular magnetic resonance (CMR) imaging and it is non-inferior to the using the invasive reference standard of fractional flow reserve. The benefits of using stress perfusion CMR include that it is non-invasive and significantly reduces the number of unnecessary coronary revascularisations. As compared to other ischaemia tests, it boasts a high spatial resolution and does not expose the patient to ionising radiation. However, the main limitation of stress perfusion CMR is that the diagnostic accuracy is highly dependent on the level of training of the operator, resulting in the test only being performed routinely in experienced tertiary centres. The clinical translation of stress perfusion CMR would be greatly aided by a fully automated, user-independent, quantitative evaluation of myocardial blood flow. This thesis presents major steps towards this goal: robust motion correction, automated image processing, reliable quantitative modelling, and thorough validation. The motion correction scheme makes use of data decomposition techniques, such as robust principal component analysis, to mitigate the difficulties in image registration caused by the dynamic contrast enhancement. The motion corrected image series are input to a processing pipeline which leverages the recent advances in image processing facilitated by deep learning. The pipeline utilises convolutional neural networks to perform a series of computer vision tasks including myocardial segmentation and right ventricular insertion point detection...
COVID-19 transmission risk factors
Authors: Alessio Notari, Giorgio Torrieri
Date: 2020-05-07 00:00:00

We analyze risk factors correlated with the initial transmission growth rate of the recent COVID-19 pandemic in different countries. The number of cases follows in its early stages an almost exponential expansion; we chose as a starting point in each country the first day $d_i$ with 30 cases and we fitted for 12 days, capturing thus the early exponential growth. We looked then for linear correlations of the exponents $\alpha$ with other variables, for a sample of 126 countries. We find a positive correlation, {\it i.e. faster spread of COVID-19}, with high confidence level with the following variables, with respective $p$-value: low Temperature ($4\cdot10^{-7}$), high ratio of old vs.~working-age people ($3\cdot10^{-6}$), life expectancy ($8\cdot10^{-6}$), number of international tourists ($1\cdot10^{-5}$), earlier epidemic starting date $d_i$ ($2\cdot10^{-5}$), high level of physical contact in greeting habits ($6 \cdot 10^{-5}$), lung cancer prevalence ($6 \cdot 10^{-5}$), obesity in males ($1 \cdot 10^{-4}$), share of population in urban areas ($2\cdot10^{-4}$), cancer prevalence ($3 \cdot 10^{-4}$), alcohol consumption ($0.0019$), daily smoking prevalence ($0.0036$), UV index ($0.004$, 73 countries). We also find a correlation with low Vitamin D levels ($0.002-0.006$, smaller sample, $\sim 50$ countries, to be confirmed on a larger sample). There is highly significant correlation also with blood types: positive correlation with types RH- ($3\cdot10^{-5}$) and A+ ($3\cdot10^{-3}$), negative correlation with B+ ($2\cdot10^{-4}$). Several of the above variables are intercorrelated and likely to have common interpretations. We performed a Principal Component Analysis, in order to find their significant independent linear combinations. We also analyzed a possible bias: countries with low GDP-per capita might have less testing and we discuss correlation with the above variables.
Economic analysis of tidal stream turbine arrays: a review
Authors: Zoe Goss, Daniel Coles, Matthew Piggott
Date: 2021-05-11 00:00:00

This tidal stream energy industry has to date been comprised of small demonstrator projects made up of one to a four turbines. However, there are currently plans to expand to commercially sized projects with tens of turbines or more. As the industry moves to large-scale arrays for the first time, there has been a push to develop tools to optimise the array design and help bring down the costs. This review investigates different methods of modelling the economic performance of tidal-stream arrays, for use within these optimisation tools. The different cost reduction pathways are discussed from costs falling as the global installed capacity increases, due to greater experience, improved power curves through larger-diameter higher-rated turbines, to economic efficiencies that can be found by moving to large-scale arrays. A literature review is conducted to establish the most appropriate input values for use in economic models. This includes finding a best case, worst case and typical values for costs and other related parameters. The information collated in this review can provide a useful steering for the many optimisation tools that have been developed, especially when cost information is commercially sensitive and a realistic parameter range is difficult to obtain.
Correlation-Robust Optimal Auctions
Authors: Wanchang Zhang
Date: 2021-05-10 00:00:00

I study the design of auctions in which the auctioneer is assumed to have information only about the marginal distribution of a generic bidder's valuation, but does not know the correlation structure of the joint distribution of bidders' valuations. I assume that a generic bidder's valuation is bounded and $\bar{v}$ is the maximum valuation of a generic bidder. The performance of a mechanism is evaluated in the worst case over the uncertainty of joint distributions that are consistent with the marginal distribution. For the two-bidder case, the second-price auction with the uniformly distributed random reserve maximizes the worst-case expected revenue across all dominant-strategy mechanisms under certain regularity conditions. For the $N$-bidder ($N\ge3$) case, the second-price auction with the $\bar{v}-$scaled $Beta (\frac{1}{N-1},1)$ distributed random reserve maximizes the worst-case expected revenue across standard (a bidder whose bid is not the highest will never be allocated) dominant-strategy mechanisms under certain regularity conditions. When the probability mass condition (part of the regularity conditions) does not hold, the second-price auction with the $s^*-$scaled $Beta (\frac{1}{N-1},1)$ distributed random reserve maximizes the worst-case expected revenue across standard dominant-strategy mechanisms, where $s^*\in (0,\bar{v})$.
On Plug-and-Play Regularization using Linear Denoisers
Authors: Ruturaj G. Gavaskar, Chirayu D. Athalye, Kunal N. Chaudhury
Date: 2021-05-11 00:00:00

In plug-and-play (PnP) regularization, the knowledge of the forward model is combined with a powerful denoiser to obtain state-of-the-art image reconstructions. This is typically done by taking a proximal algorithm such as FISTA or ADMM, and formally replacing the proximal map associated with a regularizer by nonlocal means, BM3D or a CNN denoiser. Each iterate of the resulting PnP algorithm involves some kind of inversion of the forward model followed by denoiser-induced regularization. A natural question in this regard is that of optimality, namely, do the PnP iterations minimize some f+g, where f is a loss function associated with the forward model and g is a regularizer? This has a straightforward solution if the denoiser can be expressed as a proximal map, as was shown to be the case for a class of linear symmetric denoisers. However, this result excludes kernel denoisers such as nonlocal means that are inherently non-symmetric. In this paper, we prove that a broader class of linear denoisers (including symmetric denoisers and kernel denoisers) can be expressed as a proximal map of some convex regularizer g. An algorithmic implication of this result for non-symmetric denoisers is that it necessitates appropriate modifications in the PnP updates to ensure convergence to a minimum of f+g. Apart from the convergence guarantee, the modified PnP algorithms are shown to produce good restorations.
Mitigating Smart Meter Asynchrony Error Via Multi-Objective Low Rank Matrix Recovery
Authors: Yuxuan Yuan, Kaveh Dehghanpour, Zhaoyu Wang
Date: 2021-05-11 00:00:00

Smart meters (SMs) are being widely deployed by distribution utilities across the U.S. Despite their benefits in real-time monitoring. SMs suffer from certain data quality issues; specifically, unlike phasor measurement units (PMUs) that use GPS for data synchronization, SMs are not perfectly synchronized. The asynchrony error can degrade the monitoring accuracy in distribution networks. To address this challenge, we propose a principal component pursuit (PCP)-based data recovery strategy. Since asynchrony results in a loss of temporal correlation among SMs, the key idea in our solution is to leverage a PCP-based low rank matrix recovery technique to maximize the temporal correlation between multiple data streams obtained from SMs. Further, our approach has a novel multi-objective structure, which allows utilities to precisely refine and recover all SM-measured variables, including voltage and power measurements, while incorporating their inherent dependencies through power flow equations. We have performed numerical experiments using real SM data to demonstrate the effectiveness of the proposed strategy in mitigating the impact of SM asynchrony on distribution grid monitoring.