Frequency-Domain Analysis of Robust Monotonic Convergence of Norm-Optimal Iterative Learning Control

In this paper, we study MIMO Iterative Learning Control (ILC) and its robustness against model uncertainty. Although it is argued that, so-called, norm optimal ILC controllers have some inherent robustness, not many results are available that can make quantitative statements about the allowable model uncertainty. In this paper, we derive sufficient conditions for robust convergence of the ILC algorithm in presence of an uncertain system with an additive uncertainty bound. These conditions are applied to norm optimal ILC, resulting in guidelines for robust controller design. Theoretical results are illustrated by simulations.

Resource-efficient ILC for LTI/LTV systems through LQ tracking and stable inversion: Enabling large feedforward tasks on a position-dependent printer

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

The error in smoke transport models have mainly been analyzed with qualitative approaches till date. The results make it difficult to perform a quantitative assessment of the model error in fire safety design applications. Even if a model has a substantial model error, it can be a very useful tool, as long as the designer is aware of the errors and the uncertainties in the predictions. This paper presents a methodology to quantify the error in model predictions and the associated uncertainties with a statistical analysis of multiple scenarios. The knowledge of the model error can then be used to adjust future model predictions in order to take the error into account explicitly. This is done with an adjustment model valid for predictions during the whole pre-flashover phase of the fire scenario and not just at a single point in time. The approach taken is based on a quantitative comparison of model predictions and experimental measurements from several fire scenarios which constitute a scenario configuration. The application of the method is presented in a subsequent paper, where the model error in temperature predictions by the two-zone model CFAST 2.0 is analyzed.

The usual model updating method may be considered to be deterministic since it uses measurements from a single test system to correct a nominal finite element model. There may however be variability in seemingly identical test structures and uncertainties in the finite element model. Variability in test structures may arise from many sources including geometric tolerances and the manufacturing process, and modelling uncertainties may result from the use of nominal material properties, ill-defined joint stiffnesses and rigid boundary conditions. In this paper the theory of stochastic model updating using a Monte-Carlo inverse procedure with multiple sets of experimental results is explained and then applied to the case of a simulated three degree-of-freedom system, which is used to fix ideas and also to illustrate some of the practical limitations of the method. In the companion paper, stochastic model updating is applied to a benchmark structure using a contact finite element model that includes common uncertainties in the modelling of the spot welds.

This study aims to quantify suction velocities for hybrid laminar flow control of a vertical fin by taking data and model uncertainties into account. Because suction velocities cannot be measured directly, they are calculated using the Darcy–Forchheimer model, which needs the pressure distribution and porosity characteristics as input. Uncertainties in the pressure distribution are characterized using a novel data fusion method incorporating wind-tunnel and numerical data. Furthermore, geometrical uncertainties of the airfoil that alter the pressure distribution are considered. Two methods are proposed to model the porosity characteristics of the surface: one of which uses a local representation, and the other a global representation. In addition, the modeling error of the Darcy–Forchheimer model is estimated. These input uncertainties are quantified and propagated by Monte Carlo sampling through the Darcy–Forchheimer model. It reveals that local information on the porosity characteristics is essential for accurate suction velocity estimates for this specific application. A sensitivity study shows that the most influential contribution to the variance of suction velocities is the uncertainty in the porosity characteristics, followed by uncertainties in the pressure distribution. The model error and uncertainties in the reference pressure are shown to have a negligible influence.

Chapter Eighteen Uncertainty and Sensitivity Issues in Process-based Models of Carbon and Nitrogen Cycles in Terrestrial Ecosystems

Uncertainties in finite element (FE) model updating arise from two main sources: measurement noise and modeling errors. The latter includes model parameter uncertainty and model uncertainty itself. Among these sources of uncertainty, model uncertainty has been proven to be the most influential source of error in FE model updating, which is particularly important when using the updated model for damage identification (DID) purposes. This paper investigates the effects of model uncertainty when updating mechanics-based nonlinear FE models of building structures subjected to earthquake excitation. To solve the parameter estimation problem, the unscented Kalman filter is used as parameter estimation tool. Numerically simulated response data of two state-of-the-art nonlinear FE models of building structures designed according to modern design codes are used as application examples. A two-dimensional steel building and a three-dimensional reinforced concrete building, both subjected to seismic base excitation, are analyzed for different types and levels of model uncertainty. The results show that model uncertainty may have significant detrimental effects when using the updated FE model for DID, chiefly in the case of large modeling uncertainty. Although a good match between the measured (observed) and FE predicted responses is usually achieved, unobserved responses at global and local levels often show significant errors.

A Bayesian framework for uncertainty quantification of perturbed gamma process based on simulated likelihood

Projected changes in regional seasonal precipitation due to climate change are highly uncertain, with model disagreement on even the sign of change in many regions. Using a 20-member CMIP5 ensemble under the RCP8.5 scenario, the intermodel uncertainty of the spatial patterns of projected end-of-twenty-first-century change in precipitation is found not to be strongly influenced by uncertainty in global mean temperature change. In the tropics, both the ensemble mean and intermodel uncertainty of regional precipitation change are found to be predominantly related to spatial shifts in convection and convergence, associated with processes such as sea surface temperature (SST) pattern change and land–sea thermal contrast change. The authors hypothesize that the zonal-mean seasonal migration of these shifts is driven by 1) the nonlinear spatial response of convection to SST changes and 2) a general movement of convection from land to ocean in response to SST increases. Assessment of tropical precipitation model projections over East Africa highlights the complexity of regional rainfall changes. Thermodynamically driven moisture increases determine the magnitude of the long rains (March–May) ensemble mean precipitation change in this region, whereas model uncertainty in spatial shifts of convection accounts for almost all of the intermodel uncertainty. Moderate correlations are found across models between the long rains precipitation change and patterns of SST change in the Pacific and Indian Oceans. Further analysis of the capability of models to represent present-day SST–rainfall links, and any relationship with model projections, may contribute to constraining the uncertainty in projected East Africa long rains precipitation.

[1] Estimating the current sources and sinks of carbon and projecting future levels of CO2 and climate require biospheric carbon models that cover the landscape. Such models inevitably suffer from deficiencies and uncertainties. This paper addresses how to quantify errors in modeled carbon fluxes and then trace them to specific input variables. To date, few studies have examined uncertainties in biospheric models in a quantitative fashion that are relevant to landscape-scale simulations. In this paper, we introduce a general framework to quantify errors in biospheric carbon models that “unmix” the contributions to the total uncertainty in simulated carbon fluxes and attribute the error to different variables. To illustrate this framework we apply and use a simple biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM), in boreal forests of central Canada, using eddy covariance flux measurement data from two main sites of the Canadian Carbon Program (CCP). We explicitly distinguish between systematic errors (“biases”) and random errors and focus on the impact of errors present in biospheric parameters as well as driver data sets (satellite indices, temperature, solar radiation, and land cover). Biases in downward shortwave radiation accumulated to the most significant amount out of the driver data sets and accounted for a significant percentage of the annually summed carbon uptake. However, the largest cumulative errors were shown to stem from biospheric parameters controlling the light-use efficiency and respiration-temperature relationships. This work represents a step toward a carbon model-data fusion system because in such systems the outcome is determined as much by uncertainties as by the measurements themselves.

Distributed tracking control of unmanned aerial vehicles under wind disturbance and model uncertainty

A methodology is proposed to quantify prediction uncertainty associated with ground water vulnerability models that were developed through an approach that coupled multivariate logistic regression with a geographic information system (GIS). This method uses Latin hypercube sampling (LHS) to illustrate the propagation of input error and estimate uncertainty associated with the logistic regression predictions of ground water vulnerability. Central to the proposed method is the assumption that prediction uncertainty in ground water vulnerability models is a function of input error propagation from uncertainty in the estimated logistic regression model coefficients (model error) and the values of explanatory variables represented in the GIS (data error). Input probability distributions that represent both model and data error sources of uncertainty were simultaneously sampled using a Latin hypercube approach with logistic regression calculations of probability of elevated nonpoint source contaminants in ground water. The resulting probability distribution represents the prediction intervals and associated uncertainty of the ground water vulnerability predictions. The method is illustrated through a ground water vulnerability assessment of the High Plains regional aquifer. Results of the LHS simulations reveal significant prediction uncertainties that vary spatially across the regional aquifer. Additionally, the proposed method enables a spatial deconstruction of the prediction uncertainty that can lead to improved prediction of ground water vulnerability.

WITHDRAWN: Incorporating IMERG satellite precipitation uncertainty into seasonal and peak streamflow predictions using the Hillslope Link hydrological model

SummaryThis paper addresses the iterative learning control problem under random data dropout environments. The recent progress on iterative learning control in the presence of data dropouts is first reviewed from 3 aspects, namely, data dropout model, data dropout position, and convergence meaning. A general framework is then proposed for the convergence analysis of all 3 kinds of data dropout models, namely, the stochastic sequence model, the Bernoulli variable model, and the Markov chain model. Both mean square and almost sure convergence of the input sequence to the desired input are strictly established for noise‐free systems and stochastic systems, respectively, where the measurement output suffers from random data dropouts. Illustrative simulations are provided to verify the theoretical results.