Class Of Uncertainties Research Articles

The impact of unmarried people’s values and perceptions on marriage and fertility intentions: Focusing on latent classes of gender role attitudes and subjective economic uncertainty

The impact of unmarried people’s values and perceptions on marriage and fertility intentions: Focusing on latent classes of gender role attitudes and subjective economic uncertainty

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

In control of aerospace systems with large operating envelopes, it is often necessary to adjust the desired dynamics according to operating conditions. This paper presents a robust adaptive control architecture for linear parameter-varying (LPV) systems that allows for the desired dynamics to be systematically scheduled, while being able to handle a broad class of uncertainties, both matched and unmatched, which can depend on both time and states. The proposed controller adopts an L1 adaptive control architecture for designing the adaptive control law and peak-to-peak gain (PPG) minimization for designing the robust control law to mitigate the effect of unmatched uncertainties. Leveraging the PPG bound of a LPV system, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system with respect to a nominal system. The proposed control architecture is applied to control the longitudinal motion of an F-16 aircraft operating within a large envelope. Simulation results using both LPV and fully nonlinear models validate the efficacy of the proposed method.

Trajectories of illness uncertainty among parents of children with atypical genital appearance due to differences of sex development.

The present study aimed to identify distinct trajectories of parental illness uncertainty among parents of children born with atypical genital appearance due to a difference of sex development over the first year following diagnosis. It was hypothesized that four trajectory classes would emerge, including "low stable," "high stable," "decreasing," and "increasing" classes, and that select demographic, familial, and medical factors would predict these classes. Participants included 56 mothers and 43 fathers of 57 children born with moderate to severe genital atypia. Participants were recruited from eleven specialty clinics across the U.S. Growth mixture modeling (GMM) approaches, controlling for parent dyad clustering, were conducted to examine classes of parental illness uncertainty ratings over time. A three-class GMM was identified as the best-fitting model. The three classes were interpreted as "moderate stable" (56.8%), "low stable" (33.0%), and "declining" (10.3%). Findings suggest possible diagnostic differences across trajectories. Findings highlight the nature of parents' perceptions of ambiguity and uncertainty about their child's diagnosis and treatment the year following their child's birth/diagnosis. Future research is needed to better understand how these trajectories might shift over the course of the child's development. Results support the development of tailored, evidence-based interventions to address coping with uncertainty among families raising a child with chronic health needs.

Differential neural network robust constrained controller using approximate dynamic programming

This study focuses on developing a continuous differential neural network (DNN) approximating min–max robust control by applying dynamic neural programming. The suggested controller is applied to a class of nonlinear perturbed systems providing satisfactory dynamics for a given cost function depending on both the trajectories of the perturbed system and the designed constrained control actions. The min–max formulation for dynamic programming offers reliable control for restricted modeling uncertainties and perturbations. The suggested design considers control norm restrictions in the optimization problem. DNN’s approximation of the worst (with respect to the admissible class of perturbations and uncertainties) value function of the Hamilton–Jacobi–Bellman (HJB) equation enables the estimation of the closed-loop formulation of the controller. The robust version of the HJB partial differential equation is studied to create the learning law class for the time-varying weights in the DNN. The controller employs a time-varying Lyapunov-like differential equation and the solution of the corresponding learning laws. A recurrent algorithm based on the Kiefer–Wolfowitz technique can be used by modifying the weights’ initial conditions to fulfill the specified cost function’s end requirements. A numerical example tests the robust control proposed in this study, validating the robust optimal solution based on the DNN approximation for Bellman’s value function.

Workflow-Induced Uncertainty in Data-Driven Mineral Prospectivity Mapping

The primary goal of mineral prospectivity mapping (MPM) is to narrow the search for mineral resources by producing spatially selective maps. However, in the data-driven domain, MPM products vary depending on the workflow implemented. Although the data science framework is popular to guide the implementation of data-driven MPM tasks, and is intended to create objective and replicable workflows, this does not necessarily mean that maps derived from data science workflows are optimal in a spatial sense. In this study, we explore interactions between key components of a geodata science-based MPM workflow on the geospatial outcome, within the modeling stage by modulating: (1) feature space dimensionality, (2) the choice of machine learning algorithms, and (3) performance metrics that guide hyperparameter tuning. We specifically relate these variations in the data science workflow to the spatial selectivity of resulting maps using uncertainty propagation. Results demonstrate that typical geodata science-based MPM workflows contain substantial local minima, as it is highly probable for an arbitrary combination of workflow choices to produce highly discriminating models. In addition, variable domain metrics, which are key to guide the iterative implementation of the data science framework, exhibit inconsistent relationships with spatial selectivity. We refer to this class of uncertainty as workflow-induced uncertainty. Consequently, we propose that the canonical concept of scientific consensus from the greater experimental science framework should be adhered to, in order to quantify and mitigate against workflow-induced uncertainty as part of data-driven experimentation. Scientific consensus stipulates that the degree of consensus of experimental outcomes is the determinant in the reliability of findings. Indeed, we demonstrate that consensus through purposeful modulations of components of a data-driven MPM workflow is an effective method to understand and quantify workflow-induced uncertainty on MPM products. In other words, enlarging the search space for workflow design and experimenting with workflow components can result in more meaningful reductions in the physical search space for mineral resources.

Life Is Uncertain: Inherent Variability Exhibited by Organisms, and at Higher Levels of Biological Organization.

Organisms act stochastically. A not uncommon view in the ecological literature is that this is mainly due to the observer having insufficient information or a stochastic environment-and not partly because organisms themselves respond with inherent unpredictability. In this study, I compile the evidence that contradicts that view. Organisms generate uncertainty internally, which results in irreducible stochastic responses. I consider why: for instance, stochastic responses are associated with greater adaptability to changing environments and resource availability. Over longer timescales, biologically generated uncertainty influences behavior, evolution, and macroecological processes. Indeed, it could be stated that organisms are systems defined by the internal generation, magnification, and record-keeping of uncertainty as inputs to responses. Important practical implications arise if organisms can indeed be defined by an association with specific classes of inherent uncertainty: not least that isolating those signatures then provides a potential means for detecting life, for considering the forms that life could theoretically take, and for exploring the wider limits to how life might become distributed. These are all fundamental goals in astrobiology.

Structured singular value of a repeated complex full‐block uncertainty

AbstractThe structured singular value (SSV), or , is used to assess the robust stability and performance of an uncertain linear time‐invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that contain repeated (real or complex) scalars and/or nonrepeated complex full‐blocks. This paper presents algorithms to compute bounds on the SSV for the case of repeated complex full‐blocks. This specific class of uncertainty is relevant for the input‐output analysis of many convective systems, such as fluid flows. Specifically, we present a power iteration to compute the SSV lower bound for the case of repeated complex full‐blocks. This generalizes existing power iterations for repeated complex scalars and nonrepeated complex full‐blocks. The upper bound can be formulated as a semi‐definite program (SDP), which we solve using a standard interior‐point method to compute optimal scaling matrices associated with the repeated full‐blocks. Our implementation of the method only requires gradient information, which improves the computational efficiency of the method. Finally, we test our proposed algorithms on an example model of incompressible fluid flow. The proposed methods provide less conservative bounds as compared to prior results, which ignore the repeated full‐block structure.

Scheduling in the High-Uncertainty Heavy Traffic Regime

We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate disturbances that are of order 1 at the usual diffusion scale as opposed to asymptotically vanishing disturbances studied previously in relation to heavy traffic. A main advantage of the approach is that the invariance principle underlying diffusion limits makes it possible to define uncertainty classes in terms of the first two moments only. The model we consider is a single-server queue with multiple job types. The problem is formulated as a zero sum stochastic game played between the system controller, who determines scheduling and attempts to minimize an expected linear holding cost, and an adversary, who dynamically controls the service time distributions of arriving jobs and attempts to maximize the cost. The heavy traffic asymptotics of the game are fully solved. It is shown that an asymptotically optimal policy for the system controller is to prioritize according to an index rule, and for the adversary, it is to select distributions based on the system’s current workload. The workload-to-distribution feedback mapping is determined by a Hamilton–Jacobi–Bellman equation, which also characterizes the game’s limit value. Unlike in the vast majority of results in the heavy traffic theory and as a direct consequence of the diffusive size disturbances, the limiting dynamics under asymptotically optimal play are captured by a stochastic differential equation where both the drift and the diffusion coefficients may be discontinuous. Funding: R. Atar is supported by the Israeli Science Foundation [Grant 1035/20].

Stabilizing model predictive control synthesis using integral quadratic constraints and full‐block multipliers

SummaryIn this paper, we discuss how to synthesize stabilizing model predictive control (MPC) algorithms based on convexly parameterized integral quadratic constraints (IQCs), with the aid of general multipliers. Specifically, we consider Lur'e systems subject to sector‐bounded and slope‐restricted nonlinearities. As the main novelty, we introduce point‐wise IQCs with storage in order to accordingly generate the MPC terminal ingredients, thus enabling closed‐loop stability, strict dissipativity with regard to the nonlinear feedback, and recursive feasibility of the optimization. Specifically, we consider formulations involving both static and dynamic multipliers, and provide corresponding algorithms for the synthesis procedures. The major benefit of the proposed approach resides in the flexibility of the IQC framework, which is capable to deal with many classes of uncertainties and nonlinearities. Moreover, for the considered class of nonlinearities, our method yields larger regions of attraction of the synthesized predictive controllers (with reduced conservatism) if compared to the standard approach to deal with sector constraints from the literature.

Addition of finer scale data and uncertainty analysis increases precision of geospatial suitability model for non-native plants in the US

“Proto3” is a geospatial model used by the United States Department of Agriculture (USDA) Plant Protection and Quarantine to predict the potential distribution of non-native weed species in the continental U.S. as part of routine weed risk assessments (WRA). While performing as well as other methods, this tool has the benefit of being simple to produce, expanding accessibility and reproducibility. However, it has the tendency to overestimate potential distributions. To address this shortcoming, this paper introduces the “Proto4” model and compares it with the established and mechanistically similar “Proto3” model currently used. Both models overlay Plant Hardiness Zones, precipitation, and Köppen-Geiger climate classes with global distribution of a plant species and rely on semi-qualitative assessments of a plant's affinity for each of the climate categories. However, Proto4 uses more detailed layers of the Plant Hardiness Zones and Köppen-Geiger climate classes, adds elevation as a fourth predictive variable to increase the precision of predictive maps. Additionally, we incorporate uncertainty to spatially distinguish regions of different potential suitability. We compared the performance of both models by estimating the predicted distributions of 30 broadly distributed, invasive plants in the U.S. with Proto3 and Proto4. We found that on average, the Proto4 model produces predicted distributions that are nearly 780,000 square kilometers (an area larger than the state of Texas) smaller than the Proto3, while only failing to capture a median of fewer than 0.5% more georeferenced points. Furthermore, the inclusion of uncertainty classes adds to the utility of Proto4 by distinguishing areas with greater and lesser degrees of evidence that a particular area is suitable for an invasive species, providing more information to help select invasive species prevention and management prioritization strategies.

A simulation–optimization approach for a cyclic production scheme in a tablets packaging process

This paper discusses an iterative simulation–optimization approach to estimate high-quality solutions for the capacitated lot-sizing problem with linked lot sizes and backorders (CLSP-L-B) based on probabilistic demands. An uncertainty framework for incorporating the impact of simulated demand scenarios is embedded into the CLSP-L-B. The framework is generalized by a variable neighborhood search (VNS) approach, which accelerates the search for stable and cyclic production schemes. Moreover, an exact mathematical problem formulation is introduced for the generalized model framework. Anonymized real-world data of four tablets packaging robots is used for evaluation. The experimental design covers nine classes of demand uncertainty per packaging robot. Additionally, proposed solutions are evaluated against an established benchmark approach from literature for each uncertainty class in terms of manufacturing costs and customer service levels. Finally, planning rules and managerial insights are given for the packaging robots.

Sensitivity Analysis of Genome-Scale Metabolic Flux Prediction.

TRIMER, Transcription Regulation Integrated with MEtabolic Regulation, is a genome-scale modeling pipeline targeting at metabolic engineering applications. Using TRIMER, regulated metabolic reactions can be effectively predicted by integrative modeling of metabolic reactions with a transcription factor-gene regulatory network (TRN), which is modeled through a Bayesian network (BN). In this article, we focus on sensitivity analysis of metabolic flux prediction for uncertainty quantification of BN structures for TRN modeling in TRIMER. We propose a computational strategy to construct the uncertainty class of TRN models based on the inferred regulatory order uncertainty given transcriptomic expression data. With that, we analyze the prediction sensitivity of the TRIMER pipeline for the metabolite yields of interest. The obtained sensitivity analyses can guide optimal experimental design (OED) to help acquire new data that can enhance TRN modeling and achieve specific metabolic engineering objectives, including metabolite yield alterations. We have performed small- and large-scale simulated experiments, demonstrating the effectiveness of our developed sensitivity analysis strategy for BN structure learning to quantify the edge importance in terms of metabolic flux prediction uncertainty reduction and its potential to effectively guide OED.

Super Twisting Based Lyapunov Redesign for Uncertain Linear Delay Systems

We present a new continuous Lyapunov redesign (LR) methodology for the robust stabilization of a class of uncertain time-delay systems that is based on the so-called super twisting algorithm. The main feature of the proposed approach is that allows one to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneously</i> adjust the chattering effect and achieve asymptotic stabilization of the uncertain system, which is lost when continuous approximation of the unit control is considered. At the basis of the super twisting based LR methodology is a well-known class of Lyapunov–Krasovskii functionals. The particular form of the time derivative of this class of functionals allows one to define a delay-free sliding manifold on which some class of smooth uncertainties are compensated.

Distributed Optimization of Uncertain Multiagent Systems With Disturbances and Actuator Faults via Exosystem Observer-Based Output Regulation

This paper investigates a distributed optimization problem for heterogeneous linear multi-agent systems with uncertain parameters and external disturbances. For each agent, the optimal solution of the global objective functions can be regarded as an unknown constant reference signal. From this angle, the problem is transformed into an output regulation problem for an exosystem whose states and outputs are to be estimated. To ensure the trackability of the estimated signal, a fundamental design condition for the exosystem observer to achieve robust output regulation is given in the context of internal model control. Exact global optimization is then realized by embedding an appropriate distributed optimization algorithm (i.e., the exosystem observer) in each agent to estimate the global optimal solution. The result for exosystem observer design is extended to yield an adaptive fault-tolerant control algorithm to deal with a class of practical actuator fault uncertainties. The exosystem observer-based output regulation method provides a general distributed robust optimization framework for uncertain systems with disturbances and actuator faults, which can directly apply to various consensus problems. Simulations are provided to illustrate the effectiveness of the method.

Robust peak-to-peak gain analysis using integral quadratic constraints

This work provides a framework to compute an upper bound on the robust peak-to-peak gain of discrete-time uncertain linear systems using integral quadratic constraints (IQCs). Such bounds are of particular interest in the computation of reachable sets and the l1-norm, as well as when safety-critical constraints need to be satisfied pointwise in time. The use of p-hard IQCs with a terminal cost enables us to deal with a wide variety of uncertainty classes, for example, we provide p-hard IQCs with a terminal cost for the class of parametric uncertainties. This approach unifies, generalizes, and significantly improves state-of-the-art methods, which is also demonstrated in a numerical example.

Differential Linear Matrix Inequalities in Optimal and Robust Sampled-Data Filtering

This paper tackles the design of a robust filter for sampled-data linear time-invariant systems subject to parameter uncertainties. After the optimal solution is obtained, the two major classes of parameter uncertainty are considered, namely, convex bounded and norm bounded. For each of them, the filter associated to the minimum H2 guaranteed performance is determined. The design conditions are expressed through differential linear matrix inequalities (DLMIs), a mathematical device well adapted to cope with sampled-data systems because it naturally avoids matrix exponential and similar mappings. In this framework, the optimal nominal filter is determined, and it is shown that it exhibits a time-invariant observer-based structure. Illustrative examples are presented and discussed in order to put in clear evidence the theoretical results.

PrISM-Tracker

A user often needs training and guidance while performing several daily life procedures, e.g., cooking, setting up a new appliance, or doing a COVID test. Watch-based human activity recognition (HAR) can track users' actions during these procedures. However, out of the box, state-of-the-art HAR struggles from noisy data and less-expressive actions that are often part of daily life tasks. This paper proposes PrISM-Tracker, a procedure-tracking framework that augments existing HAR models with (1) graph-based procedure representation and (2) a user-interaction module to handle model uncertainty. Specifically, PrISM-Tracker extends a Viterbi algorithm to update state probabilities based on time-series HAR outputs by leveraging the graph representation that embeds time information as prior. Moreover, the model identifies moments or classes of uncertainty and asks the user for guidance to improve tracking accuracy. We tested PrISM-Tracker in two procedures: latte-making in an engineering lab study and wound care for skin cancer patients at a clinic. The results showed the effectiveness of the proposed algorithm utilizing transition graphs in tracking steps and the efficacy of using simulated human input to enhance performance. This work is the first step toward human-in-the-loop intelligent systems for guiding users while performing new and complicated procedural tasks.

Data-driven robust optimization using deep neural networks

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called the uncertainty set. An ongoing challenge in the recent literature is to derive uncertainty sets from given historical data that result in solutions that are robust regarding future scenarios. In this paper we use an unsupervised deep learning method to learn and extract hidden structures and anomalies from data, leading to non-convex uncertainty sets and better robust solutions. We prove that most of the classical uncertainty classes are special cases of our derived sets and that optimizing over them is strongly NP-hard. Nevertheless, we show that the trained neural networks can be integrated into a robust optimization model by formulating the adversarial problem as a convex quadratic mixed-integer program. This allows us to derive robust solutions through an iterative scenario generation process. In our computational experiments, we compare this approach to a similar approach using kernel-based support vector clustering and to other benchmark methods. We find that uncertainty sets derived by the unsupervised deep learning method find a better description of data and lead to robust solutions that often outperform the comparison methods both with respect to objective value and feasibility.

Iterative Learning Control for Output Tracking of Nonlinear Systems With Unavailable State Information.

This work presents a novel design framework of adaptive iterative learning control (ILC) approach for a class of uncertain nonlinear systems. By using the closed-loop reference model that can be viewed as an observer, the proposed adaptive ILC approach can be adapted to deal with the output tracking problem of nonlinear systems with unavailable system states. In the systems considered, two classes of uncertainties are taken into account, including parametric input disturbances and input distribution uncertainties. To facilitate the controller design and convergence analysis, the composite energy function (CEF) methodology is employed. The design framework in this brief is novel and widely applicable, which extends the CEF-based ILC approach to output tracking control of nonlinear systems without requiring full knowledge of state information and complicated observer design process. To show the effectiveness of the proposed design framework and control algorithms, two numerical examples are illustrated.

Robust adaptive orthogonal frequency division multiplexing integrated radar and communications waveform design under clutter circumstances

To improve the target recognition and classification performance of integrated radar and communications system in signal-dependent interference, we propose an innovative robust adaptive orthogonal frequency division multiplexing integrated radar and communications waveform design taking into account the clutter. We set the uncertainty class for clutter and other prior information to solve the problem of system performance degradation caused by inaccurate information in actual environments. Then, we formulate the optimization function to maximize the normalized weighted sum of mutual information and data information rate subject to the constraint of the total transmitted energy. To solve the optimization problem, we propose a maximum marginal allocation algorithm that transforms the original problem into a multi-stage energy distribution problem, and performs optimal energy distribution in each stage according to the optimization criteria. Moreover, by considering a more practical scenario of multiple downlink communication users, a joint scheme for channel allocation and waveform design is presented to ensure the fairness of multiple communication users. Simulation results show the effectiveness and feasibility of the designed waveform and channel allocation method.