pwc-archive/papers-with-abstracts huggingface dataset:
Reverse Kron reduction of Multi-phase Radial Network
Authors: Steven H. Low
Date: 2024-03-26 00:00:00

We consider the problem of identifying the admittance matrix of a three-phase radial network from voltage and current measurements at a subset of nodes. These measurements are used to estimate a virtual network represented by the Kron reduction (Schur complement) of the full admittance matrix. We focus on recovering exactly the full admittance matrix from its Kron reduction, i.e., computing the inverse of Schur complement. The key idea is to decompose Kron reduction into a sequence of iterations that maintains an invariance structure, and exploit this structure to reverse each step of the iterative Kron reduction.
Destination-Constrained Linear Dynamical System Modeling in Set-Valued Frameworks
Authors: Xiaowei Yang, Haiqi Liu, Fanqin Meng, Xiaojing Shen
Date: 2024-03-26 00:00:00

Directional motion towards a specified destination is a common occurrence in physical processes and human societal activities. Utilizing this prior information can significantly improve the control and predictive performance of system models. This paper primarily focuses on reconstructing linear dynamic system models based on destination constraints in the set-valued framework. We treat destination constraints as inherent information in the state evolution process and employ convex optimization techniques to construct a coherent and robust state model. This refined model effectively captures the impact of destination constraints on the state evolution at each time step. Furthermore, we design an optimal weight matrix for the reconstructed model to ensure smoother and more natural trajectories of state evolution. We also analyze the theoretical guarantee of optimality for this weight matrix and the properties of the reconstructed model. Finally, simulation experiments verify that the reconstructed model has significant advantages over the unconstrained and unoptimized weighted models and constrains the evolution of state trajectories with different starting and ending points.
Optimal Operation of Reconfigurable Active Distribution Networks Aiming at Resiliency Improvement
Authors: Saeed Behzadi, Amir Bagheri, Abbas Rabiee
Date: 2024-03-25 00:00:00
Tasks: Scheduling

As natural disasters bring about power outage and financial losses, network resiliency is an important challenge for distribution network operators (DNOs). On the other side, power loss reduction during normal operating condition is a major concern of DNOs. In this paper, optimal scheduling of active distribution network (ADN) is addressed through simultaneous minimization of power loss in normal condition and load shedding in critical condition after natural disasters. A new formulation is developed for the network reconfiguration to optimize the system operation in both normal and emergency conditions in the presence of conventional and renewable-energy-based distributed generation (DG) as well as energy storage systems (ESSs). The line flow based (LFB) algorithm is used for the AC power flow calculations, and all the developed relations have been convexified to construct a mixed-integer quadratically-constrained programming (MIQCP) optimization model. The simulations have been implemented on the IEEE 33-bus system in GAMS, and the results are investigated.
A Discrete-Time Least-Squares Adaptive State Tracking Control Scheme with A Mobile-Robot System Study
Authors: Qianhong Zhao, Gang Tao
Date: 2024-03-25 00:00:00
Tasks: Collision Avoidance, parameter estimation

This paper develops an adaptive state tracking control scheme for discrete-time systems, using the least-squares algorithm, as the new solution to the long-standing discrete-time adaptive state tracking control problem to which the Lyapunov method (well-developed for the continuous-time adaptive state tracking problem) is not applicable. The new adaptive state tracking scheme is based on a recently-developed new discrete-time error model which has been used for gradient algorithm based state tracking control schemes, and uses the least-squares algorithm for parameter adaptation. The new least-squares algorithm is derived to minimize an accumulative estimation error, to ensure certain optimality for parameter estimation. The system stability and output tracking properties are studied. Technical results are presented in terms of plant-model matching, error model, adaptive law, optimality formulation, and stability and tracking analysis. The developed adaptive control scheme is applied to a discrete-time multiple mobile robot system to meet an adaptive state tracking objective. In addition, a collision avoidance mechanism is proposed to prevent collisions in the whole tracking process. Simulation results are presented, which verify the desired system state tracking properties under the developed least-squares algorithm based adaptive control scheme.
High-dimensional continuification control of large-scale multi-agent systems under limited sensing and perturbations
Authors: Gian Carlo Maffettone, Mario di Bernardo, Maurizio Porfiri
Date: 2024-03-25 00:00:00

This paper investigates the robustness of a novel high-dimensional continuification control method for complex multi-agent systems. We begin by formulating a partial differential equation describing the spatio-temporal density dynamics of swarming agents. A stable control action for the density is then derived and validated under nominal conditions. Subsequently, we discretize this macroscopic strategy into actionable velocity inputs for the system's agents. Our analysis demonstrates the robustness of the approach beyond idealized assumptions of unlimited sensing and absence of perturbations.
State-Augmented Linear Games with Antagonistic Error for High-Dimensional, Nonlinear Hamilton-Jacobi Reachability
Authors: Will Sharpless, Yat Tin Chow, Sylvia Herbert
Date: 2024-03-25 00:00:00

Hamilton-Jacobi Reachability (HJR) is a popular method for analyzing the liveness and safety of a dynamical system with bounded control and disturbance. The corresponding HJ value function offers a robust controller and characterizes the reachable sets, but is traditionally solved with Dynamic Programming (DP) and limited to systems of dimension less than six. Recently, the space-parallelizeable, generalized Hopf formula has been shown to also solve the HJ value with a nearly three-log increase in dimension limit, but is limited to linear systems. To extend this potential, we demonstrate how state-augmented (SA) spaces, which are well-known for their improved linearization accuracy, may be used to solve tighter, conservative approximations of the value function with any linear model in this SA space. Namely, we show that with a representation of the true dynamics in the SA space, a series of inequalities confirms that the value of a SA linear game with antagonistic error is a conservative envelope of the true value function. It follows that if the optimal controller for the HJ SA linear game with error may succeed, it will also succeed in the true system. Unlike previous methods, this result offers the ability to safely approximate reachable sets and their corresponding controllers with the Hopf formula in a non-convex manner. Finally, we demonstrate this in the slow manifold system for clarity, and in the controlled Van der Pol system with different lifting functions.
Spline Trajectory Tracking and Obstacle Avoidance for Mobile Agents via Convex Optimization
Authors: Akua Dickson, Christos G. Cassandras, Roberto Tron
Date: 2024-03-25 00:00:00
Tasks: Motion Planning

We propose an output feedback control-based motion planning technique for agents to enable them to converge to a specified polynomial trajectory while imposing a set of safety constraints on our controller to avoid collisions within the free configuration space (polygonal environment). To achieve this, we 1) decompose our polygonal environment into different overlapping cells 2) write out our polynomial trajectories as the output of a reference dynamical system with given initial conditions 3) formulate convergence and safety constraints as Linear Matrix Inequalities (LMIs) on our controller using Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs) and 4) solve a semi-definite programming (SDP) problem with convergence and safety constraints imposed to synthesize a controller for each convex cell. Extensive simulations are included to test our motion planning method under different initial conditions and different reference trajectories. The synthesized controller is robust to changes in initial conditions and is always safe relative to the boundaries of the polygonal environment.
Energy Efficiency Optimization Method of WDM Visible Light Communication System for Indoor Broadcasting Networks
Authors: Dayu Shi, Xun Zhang, Ziqi Liu, Xuanbang Chen, Jianghao Li, Xiaodong Liu, William Shieh
Date: 2024-03-25 00:00:00

This paper introduces a novel approach to optimize energy efficiency in wavelength division multiplexing (WDM) Visible Light Communication (VLC) systems designed for indoor broadcasting networks. A physics-based LED model is integrated into system energy efficiency optimization, enabling quantitative analysis of the critical issue of VLC energy efficiency: the nonlinear interplay between illumination and communication performance. The optimization jointly incorporates constraints on communication quality of each channel, and illumination performance, standardized by the International Commission on Illumination (CIE). The formulated nonlinear optimization problem is solved by the Sequential Quadratic Programming (SQP) algorithm in an experiment-based simulation. An integrated Red-Green-Blue-Yellow Light Emitting Diode (RGBY-LED) is measured for model calibration and three different scenarios are simulated to evaluate the generality of the proposed method. Results demonstrate a double enhancement in performance and a high versatility in accommodating various scenarios. Furthermore, it highlights the importance of balancing communication and illumination imperatives in VLC systems, challenging conventional perceptions focused solely on minimizing power consumption.
Scheduling Power-Intensive Operations of Battery Energy Storage Systems and Application to Hybrid Hydropower Plants
Authors: Stefano Cassano, Fabrizio Sossan
Date: 2024-03-25 00:00:00
Tasks: Scheduling

This paper proposes a novel set of power constraints for Battery Energy Storage Systems (BESSs), referred to as Dynamic Power Constraints (DPCs), that account for the voltage and current limits of the BESS as a function of its State of Charge (SOC). These constraints are formulated for integration into optimization-based BESS scheduling problems, providing a significant improvement over traditional static constraints. It is shown that, under mild assumptions typically verified during practical operations, DPCs can be expressed as a linear function of the BESS power, thus making it possible to retrofit existing scheduling problems without altering their tractability property (i.e., convexity). The DCPs unify voltage and current constraints into a single framework, filling a gap between simplified models used in BESS schedulers and more advanced models in real-time controllers and Battery Management Systems (BMSs). By improving the representation of the BESS's power capability, the proposed constraints enable schedulers to make more reliable and feasible decision, especially in power-intensive applications where the BESS operates near its rated power. To demonstrate the effectiveness of the DPCs, a simulation-based performance evaluation is conducted using a hybrid system comprising a 230 MW Hydropower Plant (HPP) and a 750 kVA/500 kWh BESS. Compared to state-of-the-art formulations such as static power constraints and DPC formulations without voltage constraints the proposed method reduces BESS constraint violations by 93% during real-time operations.
Privacy Preservation by Intermittent Transmission in Cooperative LQG Control Systems
Authors: Wenhao Lin, Yuqing Ni, Wen Yang, Chao Yang
Date: 2024-03-25 00:00:00

In this paper, we study a cooperative linear quadratic Gaussian (LQG) control system with a single user and a server. In this system, the user runs a process and employs the server to meet the needs of computation. However, the user regards its state trajectories as privacy. Therefore, we propose a privacy scheme, in which the user sends data to the server intermittently. By this scheme, the server's received information of the user is reduced, and consequently the user's privacy is preserved. In this paper, we consider a periodic transmission scheme. We analyze the performance of privacy preservation and LQG control of different transmission periods. Under the given threshold of the control performance loss, a trade-off optimization problem is proposed. Finally, we give the solution to the optimization problem.
Policy Gradient-based Model Free Optimal LQG Control with a Probabilistic Risk Constraint
Authors: Arunava Naha, Subhrakanti Dey
Date: 2024-03-25 00:00:00
Tasks: Model Predictive Control

In this paper, we investigate a model-free optimal control design that minimizes an infinite horizon average expected quadratic cost of states and control actions subject to a probabilistic risk or chance constraint using input-output data. In particular, we consider linear time-invariant systems and design an optimal controller within the class of linear state feedback control. Three different policy gradient (PG) based algorithms, natural policy gradient (NPG), Gauss-Newton policy gradient (GNPG), and deep deterministic policy gradient (DDPG), are developed, and compared with the optimal risk-neutral linear-quadratic regulator (LQR) and a scenario-based model predictive control (MPC) technique via numerical simulations. The convergence properties and the accuracy of all the algorithms are compared numerically. We also establish analytical convergence properties of the NPG and GNPG algorithms under the known model scenario, while the proof of convergence for the unknown model scenario is part of our ongoing work.
A Blotto Game Approach to Ride-hailing Markets with Electric Vehicles
Authors: Marko Maljkovic, Gustav Nilsson, Nikolas Geroliminis
Date: 2024-03-25 00:00:00
Tasks: Decision Making

When a centrally operated ride-hailing company considers to enter a market already served by another company, it has to make a strategic decision about how to distribute its fleet among different regions in the area. This decision will be influenced by the market share the company can secure and the costs associated with charging the vehicles in each region, all while competing with the company already operating in the area. In this paper, we propose a Colonel Blotto-like game to model this decision-making. For the class of games that we study, we first prove the existence and uniqueness of a Nash Equilibrium. Subsequently, we provide its general characterization and present an algorithm for computing the ones in the feasible set's interior. Additionally, for a simplified scenario involving two regions, which would correspond to a city area with a downtown and a suburban region, we also provide a method to check for the equilibria on the feasible set's boundary. Finally, through a numerical case study, we illustrate the impact of charging prices on the position of the Nash equilibrium.
A Branch and Bound method for the exact parameter identification of the PK/PD model for anesthetic drugs
Authors: Giulia Di Credico, Luca Consolini, Mattia Laurini, Marco Locatelli, Marco Milanesi, Michele Schiavo, Antonio Visioli
Date: 2024-03-25 00:00:00
Tasks: global-optimization

We address the problem of parameter identification for the standard pharmacokinetic/pharmacodynamic (PK/PD) model for anesthetic drugs. Our main contribution is the development of a global optimization method that guarantees finding the parameters that minimize the one-step ahead prediction error. The method is based on a branch-and-bound algorithm, that can be applied to solve a more general class of nonlinear regression problems. We present some simulation results, based on a dataset of twelve patients. In these simulations, we are always able to identify the exact parameters, despite the non-convexity of the overall identification problem.
A data-based comparison of methods for reducing the peak volume flow rate in a district heating system
Authors: Felix Agner, Ulrich Trabert, Anders Rantzer, Janybek Orozaliev
Date: 2024-03-25 00:00:00

This work concerns reduction of the peak flow rate of a district heating grid, a key system property which is bounded by pipe dimensions and pumping capacity. The peak flow rate constrains the number of additional consumers that can be connected, and may be a limiting factor in reducing supply temperatures when transitioning to the 4th generation of district heating. We evaluate a full year of operational data from a subset of customer meters in a district heating system in Germany. We consider the peak flow rate reduction that could be achieved with full a posteriori knowledge of this data. Three strategies for reducing the peak flow rate are investigated: A load shifting demand response strategy, an upper limitation in substation return temperatures, and an upper limitation on each substation's volume flow rate. We show that imposing up to to 18 % load flexibility for the customers provides an equal reduction in the peak system flow rate under the load shifting strategy. The limited return temperature strategy is less efficient at curtailing the peak flow rate, but provides an overall reduction of volume flow rates. Finally, the flow rate limitation method can introduce new, higher flow rate peaks, reducing performance.
SIS epidemics on open networks: A replacement-based approximation
Authors: Renato Vizuete, Paolo Frasca, Elena Panteley
Date: 2024-03-25 00:00:00

In this paper we analyze continuous-time SIS epidemics subject to arrivals and departures of agents, by using an approximated process based on replacements. In defining the SIS dynamics in an open network, we consider a stochastic setting in which arrivals and departures take place according to Poisson processes with similar rates, and the new value of the infection probability of an arriving agent is drawn from a continuous distribution. Since the system size changes with time, we define an approximated process, in which replacements take place instead of arrivals and departures, and we focus on the evolution of an aggregate measure of the level of infection. So long as the reproduction number is less than one, the long-term behavior of this function measures the impact of the changes of the set of agents in the epidemic. We derive upper bounds for the expectation and variance of this function and we include a numerical example to show that the approximated process is close to the original SIS process.
HEAL-ViT: Vision Transformers on a spherical mesh for medium-range weather forecasting
Authors: Vivek Ramavajjala
Date: 2024-02-14 00:00:00
Tasks: Weather Forecasting

In recent years, a variety of ML architectures and techniques have seen success in producing skillful medium range weather forecasts. In particular, Vision Transformer (ViT)-based models (e.g. Pangu-Weather, FuXi) have shown strong performance, working nearly "out-of-the-box" by treating weather data as a multi-channel image on a rectilinear grid. While a rectilinear grid is appropriate for 2D images, weather data is inherently spherical and thus heavily distorted at the poles on a rectilinear grid, leading to disproportionate compute being used to model data near the poles. Graph-based methods (e.g. GraphCast) do not suffer from this problem, as they map the longitude-latitude grid to a spherical mesh, but are generally more memory intensive and tend to need more compute resources for training and inference. While spatially homogeneous, the spherical mesh does not lend itself readily to be modeled by ViT-based models that implicitly rely on the rectilinear grid structure. We present HEAL-ViT, a novel architecture that uses ViT models on a spherical mesh, thus benefiting from both the spatial homogeneity enjoyed by graph-based models and efficient attention-based mechanisms exploited by transformers. HEAL-ViT produces weather forecasts that outperform the ECMWF IFS on key metrics, and demonstrate better bias accumulation and blurring than other ML weather prediction models. Further, the lowered compute footprint of HEAL-ViT makes it attractive for operational use as well, where other models in addition to a 6-hourly prediction model may be needed to produce the full set of operational forecasts required.
Assessing the similarity of real matrices with arbitrary shape
Authors: Jasper Albers, Anno C. Kurth, Robin Gutzen, Aitor Morales-Gregorio, Michael Denker, Sonja Grün, Sacha J. van Albada, Markus Diesmann
Date: 2024-03-26 00:00:00
Tasks: Dimensionality Reduction

Assessing the similarity of matrices is valuable for analyzing the extent to which data sets exhibit common features in tasks such as data clustering, dimensionality reduction, pattern recognition, group comparison, and graph analysis. Methods proposed for comparing vectors, such as cosine similarity, can be readily generalized to matrices. However, this approach usually neglects the inherent two-dimensional structure of matrices. Here, we propose singular angle similarity (SAS), a measure for evaluating the structural similarity between two arbitrary, real matrices of the same shape based on singular value decomposition. After introducing the measure, we compare SAS with standard measures for matrix comparison and show that only SAS captures the two-dimensional structure of matrices. Further, we characterize the behavior of SAS in the presence of noise and as a function of matrix dimensionality. Finally, we apply SAS to two use cases: square non-symmetric matrices of probabilistic network connectivity, and non-square matrices representing neural brain activity. For synthetic data of network connectivity, SAS matches intuitive expectations and allows for a robust assessment of similarities and differences. For experimental data of brain activity, SAS captures differences in the structure of high-dimensional responses to different stimuli. We conclude that SAS is a suitable measure for quantifying the shared structure of matrices with arbitrary shape.
Deconvolution from two order statistics
Authors: JoonHwan Cho, Yao Luo, Ruli Xiao
Date: 2024-03-26 00:00:00

Economic data are often contaminated by measurement errors and truncated by ranking. This paper shows that the classical measurement error model with independent and additive measurement errors is identified nonparametrically using only two order statistics of repeated measurements. The identification result confirms a hypothesis by Athey and Haile (2002) for a symmetric ascending auction model with unobserved heterogeneity. Extensions allow for heterogeneous measurement errors, broadening the applicability to additional empirical settings, including asymmetric auctions and wage offer models. We adapt an existing simulated sieve estimator and illustrate its performance in finite samples.
The inclusive Synthetic Control Method
Authors: Roberta Di Stefano, Giovanni Mellace
Date: 2024-03-26 00:00:00

We introduce the inclusive synthetic control method (iSCM), a modification of synthetic control methods that includes units in the donor pool potentially affected, directly or indirectly, by an intervention. This method is ideal for situations where including treated units in the donor pool is essential or where donor units may experience spillover effects. The iSCM is straightforward to implement with most synthetic control estimators. As an empirical illustration, we re-estimate the causal effect of German reunification on GDP per capita, accounting for spillover effects from West Germany to Austria.