pwc-archive/papers-with-abstracts huggingface dataset:
Approximate Dynamic Programming based Model Predictive Control of Nonlinear systems
Authors: Keerthi Chacko, Midhun T. Augustine, S. Janardhanan, Deepak U. Patil, I. N. Kar
Date: 2023-12-10 00:00:00
Tasks: Model Predictive Control

This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the proposed approach, the value function is approximated as a quadratic function for which the parametric matrix is computed using a switched system approximate of the nonlinear system. The approach is modified further using a multi-stage scheme to improve the control accuracy and an extension to incorporate state constraints. The MPC scheme is validated experimentally on a multi-tank system which is modeled as a third-order nonlinear system. The experimental results show the proposed MPC scheme results in significantly lesser online computation compared to the Nonlinear MPC scheme.
Towards targeted exploration for non-stochastic disturbances
Authors: Janani Venkatasubramanian, Johannes Köhler, Mark Cannon, Frank Allgöwer
Date: 2023-12-10 00:00:00

We present a novel targeted exploration strategy for linear time-invariant systems without stochastic assumptions on the noise, i.e., without requiring independence or zero mean, allowing for deterministic model misspecifications. This work utilizes classical data-dependent uncertainty bounds on the least-squares parameter estimates in the presence of energy-bounded noise. We provide a sufficient condition on the exploration data that ensures a desired error bound on the estimated parameter. Using common approximations, we derive a semidefinite program to compute the optimal sinusoidal input excitation. Finally, we highlight the differences and commonalities between the developed non-stochastic targeted exploration strategy and conventional exploration strategies based on classical identification bounds through a numerical example.
Real-time Estimation of DoS Duration and Frequency for Security Control
Authors: Yifan Sun, Jianquan Lu, Daniel W. C. Ho, Lulu Li
Date: 2023-12-10 00:00:00

In this paper, we develop a new denial-of-service (DoS) estimator, enabling defenders to identify duration and frequency parameters of any DoS attacker, except for three edge cases, exclusively using real-time data. The key advantage of the estimator lies in its capability to facilitate security control in a wide range of practical scenarios, even when the attacker's information is previously unknown. We demonstrate the advantage and application of our new estimator in the context of two classical control scenarios, namely consensus of multi-agent systems and impulsive stabilization of nonlinear systems, for illustration.
Data-Driven Robust Covariance Control for Uncertain Linear Systems
Authors: Joshua Pilipovsky, Panagiotis Tsiotras
Date: 2023-12-10 00:00:00
Tasks: Uncertainty Quantification

The theory of covariance control and covariance steering (CS) deals with controlling the dispersion of trajectories of a dynamical system, under the implicit assumption that accurate prior knowledge of the system being controlled is available. In this work, we consider the problem of steering the distribution of a discrete-time, linear system subject to exogenous disturbances under an unknown dynamics model. Leveraging concepts from behavioral systems theory, the trajectories of this unknown, noisy system may be (approximately) represented using system data collected through experimentation. Using this fact, we formulate a direct data-driven covariance control problem using input-state data. We then propose a maximum likelihood uncertainty quantification method to estimate and bound the noise realizations in the data collection process. Lastly, we utilize robust convex optimization techniques to solve the resulting norm-bounded uncertain convex program. We illustrate the proposed end-to-end data-driven CS algorithm on a double integrator example and showcase the efficacy and accuracy of the proposed method compared to that of model-based methods
Synthesis of Temporally-Robust Policies for Signal Temporal Logic Tasks using Reinforcement Learning
Authors: Siqi Wang, ShaoYuan Li, Li Yin, Xiang Yin
Date: 2023-12-10 00:00:00
Tasks: Q-Learning

This paper investigates the problem of designing control policies that satisfy high-level specifications described by signal temporal logic (STL) in unknown, stochastic environments. While many existing works concentrate on optimizing the spatial robustness of a system, our work takes a step further by also considering temporal robustness as a critical metric to quantify the tolerance of time uncertainty in STL. To this end, we formulate two relevant control objectives to enhance the temporal robustness of the synthesized policies. The first objective is to maximize the probability of being temporally robust for a given threshold. The second objective is to maximize the worst-case spatial robustness value within a bounded time shift. We use reinforcement learning to solve both control synthesis problems for unknown systems. Specifically, we approximate both control objectives in a way that enables us to apply the standard Q-learning algorithm. Theoretical bounds in terms of the approximations are also derived. We present case studies to demonstrate the feasibility of our approach.
Cyber-Physical Testbed Integrating RTAC with RTDS for Game-Theoretic Topology Control Under Load Altering Attacks
Authors: Alaa Selim, Junbo Zhao
Date: 2023-12-10 00:00:00

This paper introduces a cyber-physical testbed that integrates the Real-Time Digital Simulator (RTDS) with the Real-Time Automation Controller (RTAC) to enhance cybersecurity in electrical distribution networks. Focused on addressing vulnerabilities to cyber attacks, our testbed employs an advanced control algorithm developed in Python and executed through real-time controllers. Key to our approach is the seamless integration of the host PC machine, RTDS, and RTAC via the Modbus protocol. We present a game theory-based topology control strategy as an effective response to cyber attacks, specifically targeting smart meters. This testbed validates the efficacy of our method in fully eliminating voltage violations due to load altering attacks, showcasing substantial advancements in smart grid cybersecurity via the innovative use of RTDS and RTAC to simulate and counteract complex cyber threats.
Minimum-Time Trajectory Optimization With Data-Based Models: A Linear Programming Approach
Authors: Nan Li, Ehsan Taheri, Ilya Kolmanovsky, Dimitar Filev
Date: 2023-12-10 00:00:00
Tasks: Motion Planning, Trajectory Planning, Trajectory Prediction

In this paper, we develop a computationally-efficient approach to minimum-time trajectory optimization using input-output data-based models, to produce an end-to-end data-to-control solution to time-optimal planning/control of dynamic systems and hence facilitate their autonomous operation. The approach integrates a non-parametric data-based model for trajectory prediction and a continuous optimization formulation based on an exponential weighting scheme for minimum-time trajectory planning. The optimization problem in its final form is a linear program and is easy to solve. We validate the approach and illustrate its application with a spacecraft relative motion planning problem.
Schrödinger's control and estimation paradigm with spatio-temporal distributions on graphs
Authors: Asmaa Eldesoukey, Tryphon T. Georgiou
Date: 2023-12-09 00:00:00

The problem of reconciling a prior probability law on paths with data was introduced by E. Schr\"odinger in 1931/32. It represents an early formulation of a maximum likelihood problem. This specific formulation can also be seen as the control problem to modify the law of a diffusion process so as to match specifications on marginal distributions at given times. Thereby, in recent years, this so-called Schr\"odinger's bridge problem has been at the center of the uncertainty control development. However, an understudied facet of this program has been to address uncertainty in space (state) and time, modeling the effect of tasks being completed contingent on meeting a certain condition at some random time instead of imposing specifications at fixed times. The present work is a study to extend Schr\"odinger's paradigm on such an issue, and herein, it is tackled in the context of random walks on directed graphs. Specifically, we study the case where one marginal is the initial probability distribution on a Markov chain, while others are marginals of stopping (first-arrival) times at absorbing states, signifying completion of tasks. We show when the prior law on paths is Markov, a Markov policy is once again optimal to satisfy those marginal constraints with respect to a likelihood cost following Schr\"odinger's dictum. Based on this, we present the mathematical formulation involving a Sinkhorn-type iteration to construct the optimal probability law on paths matching the spatio-temporal marginals.
Closed-Loop Finite-Time Analysis of Suboptimal Online Control
Authors: Aren Karapetyan, Efe C. Balta, Andrea Iannelli, John Lygeros
Date: 2023-12-09 00:00:00
Tasks: Model Predictive Control

Suboptimal methods in optimal control arise due to a limited computational budget, unknown system dynamics, or a short prediction window among other reasons. Although these methods are ubiquitous, their transient performance remains relatively unstudied. We consider the control of discrete-time, nonlinear time-varying dynamical systems and establish sufficient conditions to analyze the finite-time closed-loop performance of such methods in terms of the additional cost incurred due to suboptimality. Finite-time guarantees allow the control design to distribute a limited computational budget over a time horizon and estimate the on-the-go loss in performance due to suboptimality. We study exponential incremental input-to-state stabilizing policies and show that for nonlinear systems, under some mild conditions, this property is directly implied by exponential stability without further assumptions on global smoothness. The analysis is showcased on a suboptimal model predictive control use case.
Real-time Building Energy Storage Scheduling under Electrical Load Uncertainty: A Dynamic Markov Decision Process Approach with Comprehensive Analysis of Different Pricing Policies
Authors: Hussein Sharadga, Ahmad Dawahdeh, Golbon Zakeri, Abdullah Hayajneh, Geoff Pritchard
Date: 2023-12-09 00:00:00
Tasks: Scheduling

In response to the increasing deployment of battery storage systems for cost reduction and grid stress mitigation, this study presents the development of a new real-time Markov decision process model to efficiently schedule battery systems in buildings under electrical load uncertainty. The proposed model incorporates quantile Fourier regression for load fitting, leading to a large-scale optimization problem with approximately a million decision variables and constraints. To address this complexity, the problem is formulated as a linear program and solved using a commercial solver, ensuring effective navigation and identification of optimal solutions. The model's performance is evaluated by considering different pricing policies and scenarios, including demand peak shaving. Validation of the Markov model is conducted using one year of historical demand data from a school. Findings indicate that MDP performance in adapting to uncertain loads can range from 30 to 99% depending on the pricing policy.
Discrete-time Negative Imaginary Systems from ZOH Sampling
Authors: Kanghong Shi, Ian R. Petersen, Igor G. Vladimirov
Date: 2023-12-09 00:00:00

A new definition of discrete-time negative imaginary (NI) systems is provided. This definition characterizes the dissipative property of a zero-order hold sampled continuous-time NI system. Under some assumptions, asymptotic stability can be guaranteed for the closed-loop interconnection of an NI system and an output strictly negative imaginary system, with one of them having a one step advance. In the case of linear systems, we also provide necessary and sufficient frequency-domain and LMI conditions under which the definition is satisfied. Also provided is a simple DC gain condition for the stability results in the linear case.
Target search on DNA -- effect of coiling
Authors: Michael A. Lomholt, Ralf Metzler
Date: 2023-12-10 00:00:00

Some proteins can find their targets on DNA faster than by pure diffusion in the three-dimensional cytoplasm, through the process of facilitated diffusion: They can loosely bind to DNA and temporarily slide along it, thus being guided by the DNA molecule itself to the target. This chapter examines this process in mathematical detail with a focus on including the effect of DNA coiling on the search process.
Representing stimulus motion with waves in adaptive neural fields
Authors: Sage Shaw, Zachary P Kilpatrick
Date: 2023-12-11 00:00:00

Traveling waves of neural activity emerge in cortical networks both spontaneously and in response to stimuli. The spatiotemporal structure of waves can indicate the information they encode and the physiological processes that sustain them. Here, we investigate the stimulus-response relationships of traveling waves emerging in adaptive neural fields as a model of visual motion processing. Neural field equations model the activity of cortical tissue as a continuum excitable medium, and adaptive processes provide negative feedback, generating localized activity patterns. Synaptic connectivity in our model is described by an integral kernel that weakens dynamically due to activity-dependent synaptic depression, leading to marginally stable traveling fronts (with attenuated backs) or pulses of a fixed speed. Our analysis quantifies how weak stimuli shift the relative position of these waves over time, characterized by a wave response function we obtain perturbatively. Persistent and continuously visible stimuli model moving visual objects. Intermittent flashes that hop across visual space can produce the experience of smooth apparent visual motion. Entrainment of waves to both kinds of moving stimuli are well characterized by our theory and numerical simulations, providing a mechanistic description of the perception of visual motion.
Finding the last bits of positional information
Authors: Lauren McGough, Helena Casademunt, Miloš Nikolić, Mariela D. Petkova, Thomas Gregor, William Bialek
Date: 2023-12-10 00:00:00
Tasks: Position

In a developing embryo, information about the position of cells is encoded in the concentrations of "morphogen" molecules. In the fruit fly, the local concentrations of just a handful of proteins encoded by the gap genes are sufficient to specify position with a precision comparable to the spacing between cells along the anterior--posterior axis. This matches the precision of downstream events such as the striped patterns of expression in the pair-rule genes, but is not quite sufficient to define unique identities for individual cells. We demonstrate theoretically that this information gap can be bridged if positional errors are spatially correlated, with relatively long correlation lengths. We then show experimentally that these correlations are present, with the required strength, in the fluctuating positions of the pair-rule stripes, and this can be traced back to the gap genes. Taking account of these correlations, the available information matches the information needed for unique cellular specification, within error bars of ~2%. These observation support a precisionist view of information flow through the underlying genetic networks, in which accurate signals are available from the start and preserved as they are transformed into the final spatial patterns.
The built environment and induced transport CO2 emissions: A double machine learning approach to account for residential self-selection
Authors: Florian Nachtigall, Felix Wagner, Peter Berrill, Felix Creutzig
Date: 2023-12-07 00:00:00

Understanding why travel behavior differs between residents of urban centers and suburbs is key to sustainable urban planning. Especially in light of rapid urban growth, identifying housing locations that minimize travel demand and induced CO2 emissions is crucial to mitigate climate change. While the built environment plays an important role, the precise impact on travel behavior is obfuscated by residential self-selection. To address this issue, we propose a double machine learning approach to obtain unbiased, spatially-explicit estimates of the effect of the built environment on travel-related CO2 emissions for each neighborhood by controlling for residential self-selection. We examine how socio-demographics and travel-related attitudes moderate the effect and how it decomposes across the 5Ds of the built environment. Based on a case study for Berlin and the travel diaries of 32,000 residents, we find that the built environment causes household travel-related CO2 emissions to differ by a factor of almost two between central and suburban neighborhoods in Berlin. To highlight the practical importance for urban climate mitigation, we evaluate current plans for 64,000 new residential units in terms of total induced transport CO2 emissions. Our findings underscore the significance of spatially differentiated compact development to decarbonize the transport sector.
Structural Analysis of Vector Autoregressive Models
Authors: Christis Katsouris
Date: 2023-12-11 00:00:00

This set of lecture notes discuss key concepts for the Structural Analysis of Vector Autoregressive models for the teaching of a course on Applied Macroeconometrics with Advanced Topics.
Trends in Temperature Data: Micro-foundations of Their Nature
Authors: Maria Dolores Gadea, Jesus Gonzalo, Andrey Ramos
Date: 2023-12-11 00:00:00

Determining whether Global Average Temperature (GAT) is an integrated process of order 1, I(1), or is a stationary process around a trend function is crucial for detection, attribution, impact and forecasting studies of climate change. In this paper, we investigate the nature of trends in GAT building on the analysis of individual temperature grids. Our 'micro-founded' evidence suggests that GAT is stationary around a non-linear deterministic trend in the form of a linear function with a one-period structural break. This break can be attributed to a combination of individual grid breaks and the standard aggregation method under acceleration in global warming. We illustrate our findings using simulations.
Causal inference and policy evaluation without a control group
Authors: Augusto Cerqua, Marco Letta, Fiammetta Menchetti
Date: 2023-12-10 00:00:00
Tasks: Causal Inference, counterfactual

Without a control group, the most widespread methodologies for estimating causal effects cannot be applied. To fill this gap, we propose the Machine Learning Control Method, a new approach for causal panel analysis that estimates causal parameters without relying on untreated units. We formalize identification within the potential outcomes framework and then provide estimation based on machine learning algorithms. To illustrate the practical relevance of our method, we present simulation evidence, a replication study, and an empirical application on the impact of the COVID-19 crisis on educational inequality. We implement the proposed approach in the companion R package MachineControl
Influence Analysis with Panel Data
Authors: Annalivia Polselli
Date: 2023-12-09 00:00:00
Tasks: Diagnostic

The presence of units with extreme values in the dependent and/or independent variables (i.e., vertical outliers, leveraged data) has the potential to severely bias regression coefficients and/or standard errors. This is common with short panel data because the researcher cannot advocate asymptotic theory. Example include cross-country studies, cell-group analyses, and field or laboratory experimental studies, where the researcher is forced to use few cross-sectional observations repeated over time due to the structure of the data or research design. Available diagnostic tools may fail to properly detect these anomalies, because they are not designed for panel data. In this paper, we formalise statistical measures for panel data models with fixed effects to quantify the degree of leverage and outlyingness of units, and the joint and conditional influences of pairs of units. We first develop a method to visually detect anomalous units in a panel data set, and identify their type. Second, we investigate the effect of these units on LS estimates, and on other units' influence on the estimated parameters. To illustrate and validate the proposed method, we use a synthetic data set contaminated with different types of anomalous units. We also provide an empirical example.
Economic Forecasts Using Many Noises
Authors: Yuan Liao, Xinjie Ma, Andreas Neuhierl, Zhentao Shi
Date: 2023-12-09 00:00:00
Tasks: Dimensionality Reduction, Variable Selection

This paper addresses a key question in economic forecasting: does pure noise truly lack predictive power? Economists typically conduct variable selection to eliminate noises from predictors. Yet, we prove a compelling result that in most economic forecasts, the inclusion of noises in predictions yields greater benefits than its exclusion. Furthermore, if the total number of predictors is not sufficiently large, intentionally adding more noises yields superior forecast performance, outperforming benchmark predictors relying on dimension reduction. The intuition lies in economic predictive signals being densely distributed among regression coefficients, maintaining modest forecast bias while diversifying away overall variance, even when a significant proportion of predictors constitute pure noises. One of our empirical demonstrations shows that intentionally adding 300~6,000 pure noises to the Welch and Goyal (2008) dataset achieves a noteworthy 10% out-of-sample R square accuracy in forecasting the annual U.S. equity premium. The performance surpasses the majority of sophisticated machine learning models.
GCov-Based Portmanteau Test
Authors: Joann Jasiak, Aryan Manafi Neyazi
Date: 2023-12-08 00:00:00
Tasks: Diagnostic, Time Series

We study nonlinear serial dependence tests for non-Gaussian time series and residuals of dynamic models based on portmanteau statistics involving nonlinear autocovariances. A new test with an asymptotic $\chi^2$ distribution is introduced for testing nonlinear serial dependence (NLSD) in time series. This test is inspired by the Generalized Covariance (GCov) residual-based specification test, recently proposed as a diagnostic tool for semi-parametric dynamic models with i.i.d. non-Gaussian errors. It has a $\chi^2$ distribution when the model is correctly specified and estimated by the GCov estimator. We derive new asymptotic results under local alternatives for testing hypotheses on the parameters of a semi-parametric model. We extend it by introducing a GCov bootstrap test for residual diagnostics,\color{black} which is also available for models estimated by a different method, such as the maximum likelihood estimator under a parametric assumption on the error distribution. \color{black} A simulation study shows that the tests perform well in applications to mixed causal-noncausal autoregressive models. The GCov specification test is used to assess the fit of a mixed causal-noncausal model of aluminum prices with locally explosive patterns, i.e. bubbles and spikes between 2005 and 2024.