pwc-archive/papers-with-abstracts huggingface dataset:
Frequency Domain Auto-tuning of Structured LPV Controllers for High-Precision Motion Control
Authors: Yorick Broens, Hans Butler, Roland Tóth
Date: 2024-03-09 00:00:00

Motion systems are a vital part of many industrial processes. However, meeting the increasingly stringent demands of these systems, especially concerning precision and throughput, requires novel control design methods that can go beyond the capabilities of traditional solutions. Traditional control methods often struggle with the complexity and position-dependent effects inherent in modern motion systems, leading to compromises in performance and a laborious task of controller design. This paper addresses these challenges by introducing a novel structured feedback control auto-tuning approach for multiple-input multiple-output (MIMO) motion systems. By leveraging frequency response function (FRF) estimates and the linear-parameter-varying (LPV) control framework, the proposed approach automates the controller design, while providing local stability and performance guarantees. Key innovations include norm-based magnitude optimization of the sensitivity functions, an automated stability check through a novel extended factorized Nyquist criterion, a modular structured MIMO LPV controller parameterization, and a controller discretization approach which preserves the continuous-time (CT) controller parameterization. The proposed approach is validated through experiments using a state-of-the-art moving-magnet planar actuator prototype.
On the equivalence of direct and indirect data-driven predictive control approaches
Authors: Per Mattsson, Fabio Bonassi, Valentina Breschi, Thomas B. Schön
Date: 2024-03-09 00:00:00

Recently, several direct Data-Driven Predictive Control (DDPC) methods have been proposed, advocating the possibility of designing predictive controllers from historical input-output trajectories without the need to identify a model. In this work, we show that these approaches are equivalent to an indirect approach. Reformulating the direct methods in terms of estimated parameters and covariance matrices allows us to give new insights into how they work in comparison with, for example, Subspace Predictive Control (SPC). In particular, we show that for unconstrained problems the direct methods are equivalent to SPC with a reduced weight on the tracking cost. Via a numerical experiment, motivated by the reformulation, we also illustrate why the performance of direct DDPC methods with fixed regularization tends to degrade as the number of training samples increases.
On constructive extractability of measurable selectors of set-valued maps
Authors: Pavel Osinenko, Stefan Streif
Date: 2024-03-09 00:00:00

This paper investigates the possibility of constructive extraction of measurable selector from set-valued maps which may commonly arise in viability theory, optimal control, discontinuous systems etc. For instance, existence of solutions to certain differential inclusions, often requires iterative extraction of measurable selectors. Next, optimal controls are in general non-unique which naturally leads to an optimal set-valued function. Finally, a viable control law can be seen, in general, as a selector. It is known that selector theorems are non-constructive and so selectors cannot always be extracted. In this work, we analyze under which particular conditions selectors are constructively extractable. An algorithm is derived from the theorem and applied in a computational study with a three-wheel robot model.
Bounding Stochastic Safety: Leveraging Freedman's Inequality with Discrete-Time Control Barrier Functions
Authors: Ryan K. Cosner, Preston Culbertson, Aaron D. Ames
Date: 2024-03-09 00:00:00

When deployed in the real world, safe control methods must be robust to unstructured uncertainties such as modeling error and external disturbances. Typical robust safety methods achieve their guarantees by always assuming that the worst-case disturbance will occur. In contrast, this paper utilizes Freedman's inequality in the context of discrete-time control barrier functions (DTCBFs) and c-martingales to provide stronger (less conservative) safety guarantees for stochastic systems. Our approach accounts for the underlying disturbance distribution instead of relying exclusively on its worst-case bound and does not require the barrier function to be upper-bounded, which makes the resulting safety probability bounds more directly useful for intuitive safety constraints such as signed distance. We compare our results with existing safety guarantees, such as input-to-state safety (ISSf) and martingale results that rely on Ville's inequality. When the assumptions for all methods hold, we provide a range of parameters for which our guarantee is stronger. Finally, we present simulation examples, including a bipedal walking robot, that demonstrate the utility and tightness of our safety guarantee.
On stochastic string stability with applications to platooning over additive noise channels
Authors: Francisco J. Vargas, Marco A. Gordon, Andrés A. Peters, Alejandro I. Maass
Date: 2024-03-08 00:00:00

This paper addresses the string stabilization of vehicular platooning when stochastic phenomena are inherent in inter-vehicle communication. To achieve this, we first provide two definitions to analytically assess the string stability in stochastic scenarios, considering the mean and variance of tracking errors as the platoon size grows. Subsequently, we analytically derive necessary and sufficient conditions to achieve this notion of string stability in predecessor-following linear platoons that communicate through additive white noise channels. We conclude that the condition ensuring string stability with ideal communication is essentially the same that achieves stochastic string stability when additive noise channels are in place and guarantees that the tracking error means and variances converge.
Economic Capacity Withholding Bounds of Competitive Energy Storage Bidders
Authors: Xin Qin, Ioannis Lestas, Bolun Xu
Date: 2024-03-08 00:00:00

Economic withholding in electricity markets refers to generators bidding higher than their true marginal fuel cost, and is a typical approach to exercising market power. However, existing market designs require storage to design bids strategically based on their own future price predictions, motivating storage to conduct economic withholding without assuming market power. As energy storage takes up more significant roles in wholesale electricity markets, understanding its motivations for economic withholding and the consequent effects on social welfare becomes increasingly vital. This paper derives a theoretical framework to study the economic capacity withholding behavior of storage participating in competitive electricity markets and validate our results in simulations based on the ISO New England system. We demonstrate that storage bids can reach unbounded high levels under conditions where future price predictions show bounded expectations but unbounded deviations. Conversely, in scenarios with peak price limitations, we show the upper bounds of storage bids are grounded in bounded price expectations. Most importantly, we show that storage capacity withholding can potentially lower the overall system cost when price models account for system uncertainties. Our paper reveals energy storage is not a market manipulator but an honest player contributing to the social welfare. It helps electricity market researchers and operators better understand the economic withholding behavior of storage and reform market policies to maximize storage contributing to a cost-efficient decolonization.
Kinetic theories of state- and generation-dependent cell populations
Authors: Mingtao Xia, Tom Chou
Date: 2024-03-08 00:00:00
Tasks: Attribute

We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to track subpopulations associated with each generation. Both intrinsic noise of the cell's internal attribute and randomness in a cell's division times (demographic stochasticity) are fundamental to the development of our model. Based on this general framework, we are able to marginalize the high-dimensional kinetic PDEs in a number of different ways to derive equations that describe the dynamics of marginalized or "macroscopic" quantities such as structured population densities, moments of generation-dependent cellular states, and moments of the total population. We also show how nonlinear "interaction" terms in lower-dimensional integrodifferential equations can arise from high-dimensional linear kinetic models that contain rate parameters of a cell (birth and death rates) that depend on variables associated with other cells, generating couplings in the dynamics. Our analysis provides a general, more complete mathematical framework that resolves the coevolution of cell populations and cell states. The approach may be tailored for studying, e.g., gene expression in developing tissues, or other more general particle systems which exhibit Brownian noise in individual attributes and population-level demographic noise.
Repetitive Infection Spreading and Directed Evolution in the Susceptible-Infected-Recovered-Susceptible Model
Authors: Hidetsugu Sakaguchi, Keito Yamasaki
Date: 2024-03-11 00:00:00

We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the SIRS model including the recruitment and death terms and the SIR model in which the recovered population is assumed to be never infected again. When the decay rate \delta of the immune is sufficiently small, the multiple infection spreading occurs in spikes. The model equation can be reduced to be a map when the decay rate \delta is sufficiently small, and the spike-like multiple infection spreading is reproduced in the mapping. The period-doubling bifurcation and chaos are found in the simplified SIRS model with seasonal variation. The nonlinear phenomena are reproduced by the map. Next, we study coupled SIRS equations for the directed evolution where the mutation is expressed with a diffusion-type term. A kind of reaction-diffusion equation is derived by the continuum approximation for the infected population I. The reaction-diffusion equation with the linear dependence of infection rate on the type space has an exact Gaussian solution with a time-dependent average and variance. The propagation of the Gaussian pulse corresponds to the successive transitions of the dominant variant.
Phase autoencoder for limit-cycle oscillators
Authors: Koichiro Yawata, Kai Fukami, Kunihiko Taira, Hiroya Nakao
Date: 2024-02-28 00:00:00
Tasks: Sensitivity, Time Series

We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.
Minimal cellular automaton model with heterogeneous cell sizes predicts epithelial colony growth
Authors: Steffen Lange, Jannik Schmied, Paul Willam, Anja Voss-Böhme
Date: 2024-03-12 00:00:00

Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes the dramatic slowing of proliferation, cell migration and individual cell growth when multiple cells are in contact with each other. While many physiological, molecular and genetic factors are known, the mechanism of contact inhibition is still not fully understood. In particular, the relevance of cellular signaling due to interfacial contact for contact inhibition is still debated. Cellular automata (CA) have been employed in the past as numerically efficient mathematical models to study the dynamics of cell ensembles, but they are not suitable to explore the origins of contact inhibition as such agent-based models assume fixed cell sizes. We develop a minimal, data-driven model to simulate the dynamics of planar cell cultures by extending a probabilistic CA to incorporate size changes of individual cells during growth and cell division. We successfully apply this model to previous in-vitro experiments on contact inhibition in epithelial tissue: After a systematic calibration of the model parameters to measurements of single-cell dynamics, our CA model quantitatively reproduces independent measurements of emergent, culture-wide features, like colony size, cell density and collective cell migration. In particular, the dynamics of the CA model also exhibit the transition from a low-density confluent regime to a stationary postconfluent regime with a rapid decrease in cell size and motion. This implies that the volume exclusion principle, a mechanical constraint which is the only inter-cellular interaction incorporated in the model, paired with a size-dependent proliferation rate is sufficient to generate the observed contact inhibition.
Introducing First-Principles Calculations: New Approach to Group Dynamics and Bridging Social Phenomena in TeNP-Chain Based Social Dynamics Simulations
Authors: Yasuko Kawahata
Date: 2024-03-06 00:00:00
Tasks: Misinformation

This note considers an innovative interdisciplinary methodology that bridges the gap between the fundamental principles of quantum mechanics applied to the study of materials such as tellurium nanoparticles (TeNPs) and graphene and the complex dynamics of social systems. The basis for this approach lies in the metaphorical parallels drawn between the structural features of TeNPs and graphene and the behavioral patterns of social groups in the face of misinformation. TeNPs exhibit unique properties such as the strengthening of covalent bonds within telluric chains and the disruption of secondary structure leading to the separation of these chains. This is analogous to increased cohesion within social groups and disruption of information flow between different subgroups, respectively. . Similarly, the outstanding properties of graphene, such as high electrical conductivity, strength, and flexibility, provide additional aspects for understanding the resilience and adaptability of social structures in response to external stimuli such as fake news. This research note proposes a novel metaphorical framework for analyzing the spread of fake news within social groups, analogous to the structural features of telluric nanoparticles (TeNPs). We investigate how the strengthening of covalent bonds within TeNPs reflects the strengthening of social cohesion in groups that share common beliefs and values. This paper is partially an attempt to utilize "Generative AI" and was written with educational intent. There are currently no plans for it to become a peer-reviewed paper.
Plasmon Resonance Model: Investigation of Analysis of Fake News Diffusion Model with Third Mover Intervention Using Soliton Solution in Non-Complete Information Game under Repeated Dilemma Condition
Authors: Yasuko Kawahata
Date: 2024-03-03 00:00:00

In this research note, we propose a new approach to model the fake news diffusion process within the framework of incomplete information games. In particular, we use nonlinear partial differential equations to represent the phenomenon of plasmon resonance, in which the diffusion of fake news is rapidly amplified within a particular social group or communication network, and analyze its dynamics through a soliton solution approach. In addition, we consider how first mover, second mover, and third mover strategies interact within this nonlinear system and contribute to the amplification or suppression of fake news diffusion. The model aims to understand the mechanisms of fake news proliferation and provide insights into how to prevent or combat it. By combining concepts from the social sciences and the physical sciences, this study attempts to develop a new theoretical framework for the contemporary problem of fake news.This paper is partially an attempt to utilize "Generative AI" and was written with educational intent. There are currently no plans for it to become a peer-reviewed paper.
Partial Identification of Individual-Level Parameters Using Aggregate Data in a Nonparametric Model
Authors: Sarah Moon
Date: 2024-03-12 00:00:00
Tasks: valid

I develop a methodology to partially identify linear combinations of conditional mean outcomes when the researcher only has access to aggregate data. Unlike the existing literature, I only allow for marginal, not joint, distributions of covariates in my model of aggregate data. Identified sets are very wide in an empirical illustration, suggesting that in order to obtain useful results when only using aggregate data, researchers may have no option other than to impose strong assumptions.
Partially identified heteroskedastic SVARs
Authors: Emanuele Bacchiocchi, Andrea Bastianin, Toru Kitagawa, Elisabetta Mirto
Date: 2024-03-11 00:00:00

This paper studies the identification of Structural Vector Autoregressions (SVARs) exploiting a break in the variances of the structural shocks. Point-identification for this class of models relies on an eigen-decomposition involving the covariance matrices of reduced-form errors and requires that all the eigenvalues are distinct. This point-identification, however, fails in the presence of multiplicity of eigenvalues. This occurs in an empirically relevant scenario where, for instance, only a subset of structural shocks had the break in their variances, or where a group of variables shows a variance shift of the same amount. Together with zero or sign restrictions on the structural parameters and impulse responses, we derive the identified sets for impulse responses and show how to compute them. We perform inference on the impulse response functions, building on the robust Bayesian approach developed for set identified SVARs. To illustrate our proposal, we present an empirical example based on the literature on the global crude oil market where the identification is expected to fail due to multiplicity of eigenvalues.
Data-Driven Tuning Parameter Selection for High-Dimensional Vector Autoregressions
Authors: Anders Bredahl Kock, Rasmus Søndergaard Pedersen, Jesper Riis-Vestergaard Sørensen
Date: 2024-03-11 00:00:00
Tasks: Time Series

Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on unknown population quantities. Furthermore, the resulting estimates and the number of variables retained in the model depend crucially on the chosen penalty level. However, there is currently no theoretically founded guidance for this choice in the context of high-dimensional time series. Instead, one resorts to selecting the penalty level in an ad hoc manner using, e.g., information criteria or cross-validation. We resolve this problem by considering estimation of the perhaps most commonly employed multivariate time series model, the linear vector autoregressive (VAR) model, and propose versions of the Lasso, post-Lasso, and square-root Lasso estimators with penalization chosen in a fully data-driven way. The theoretical guarantees that we establish for the resulting estimation and prediction errors match those currently available for methods based on infeasible choices of penalization. We thus provide a first solution for choosing the penalization in high-dimensional time series models.
Estimating Factor-Based Spot Volatility Matrices with Noisy and Asynchronous High-Frequency Data
Authors: Degui Li, Oliver Linton, Haoxuan Zhang
Date: 2024-03-10 00:00:00

We propose a new estimator of high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure from noisy and asynchronous high-frequency data collected for an ultra-large number of assets. The noise processes are allowed to be temporally correlated, heteroskedastic, asymptotically vanishing and dependent on the efficient prices. We define a kernel-weighted pre-averaging method to jointly tackle the microstructure noise and asynchronicity issues, and we obtain uniformly consistent estimates for latent prices. We impose a continuous-time factor model with time-varying factor loadings on the price processes, and estimate the common factors and loadings via a local principal component analysis. Assuming a uniform sparsity condition on the idiosyncratic volatility structure, we combine the POET and kernel-smoothing techniques to estimate the spot volatility matrices for both the latent prices and idiosyncratic errors. Under some mild restrictions, the estimated spot volatility matrices are shown to be uniformly consistent under various matrix norms. We provide Monte-Carlo simulation and empirical studies to examine the numerical performance of the developed estimation methodology.
Locally Regular and Efficient Tests in Non-Regular Semiparametric Models
Authors: Adam Lee
Date: 2024-03-09 00:00:00

This paper considers hypothesis testing in semiparametric models which may be non-regular. I show that C($\alpha$) style tests are locally regular under mild conditions, including in cases where locally regular estimators do not exist, such as models which are (semiparametrically) weakly identified. I characterise the appropriate limit experiment in which to study local (asymptotic) optimality of tests in the non-regular case and generalise classical power bounds to this case. I give conditions under which these power bounds are attained by the proposed C($\alpha$) style tests. The application of the theory to a single index model and an instrumental variables model is worked out in detail.
Estimating Causal Effects of Discrete and Continuous Treatments with Binary Instruments
Authors: Victor Chernozhukov, Iván Fernández-Val, Sukjin Han, Kaspar Wüthrich
Date: 2024-03-09 00:00:00

We propose an instrumental variable framework for identifying and estimating causal effects of discrete and continuous treatments with binary instruments. The basis of our approach is a local copula representation of the joint distribution of the potential outcomes and unobservables determining treatment assignment. This representation allows us to introduce an identifying assumption, so-called copula invariance, that restricts the local dependence of the copula with respect to the treatment propensity. We show that copula invariance identifies treatment effects for the entire population and other subpopulations such as the treated. The identification results are constructive and lead to practical estimation and inference procedures based on distribution regression. An application to estimating the effect of sleep on well-being uncovers interesting patterns of heterogeneity.