Unmodeled Components Research Articles

Accurate Parameter Estimation for Safety-Critical Systems with Unmodeled Dynamics (Abstract Reprint)

Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. Much of feedback control design is parametric in nature and as such, accurate and fast estimation of the parameters in the modeled part of the dynamic system is a crucial property for designing risk-aware autonomous systems. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unmodeled components of the dynamic system as sub-Gaussian noise and proposed parameter estimation using Gaussian noise-based exogenous signals. In contrast, we allow the unmodeled part to have deterministic unmodeled dynamics, which are almost always present in physical systems, in addition to sub-Gaussian noise. In addition, we propose a deterministic construction of the exogenous signal in order to carry out parameter estimation. We introduce a new tool kit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. Unlike the existing stochastic approach, these bounds are tunable through an optimal choice of the spectrum of the exogenous signal leading to accurate parameter estimation. We also show that this estimation is robust to unmodeled dynamics, a property that is not assured by the existing approach. Finally, we show that under ideal conditions with no deterministic unmodeled dynamics, the proposed approach can ensure a Õ(√t) Regret, matching existing literature. Experiments are provided to support all theoretical derivations, which show that the spectral lines-based approach outperforms the Gaussian noise-based method when unmodeled dynamics are present, in terms of both parameter estimation error and Regret obtained using the parameter estimates with a Linear Quadratic Regulator in feedback.

A Computational Comparison of Three Nature-Inspired, Population-Based Metaheuristic Algorithms for Modelling-to-Generate Alternatives

In “real life” decision-making situations, inevitably, there are numerous unmodelled components, not incorporated into the underlying mathematical programming models, that hold substantial influence on the overall acceptability of the solutions calculated. Under such circumstances, it is frequently beneficial to produce a set of dissimilar–yet “good”–alternatives that contribute very different perspectives to the original problems. The approach for creating maximally different solutions is known as modelling-to-generate alternatives (MGA). Recently, a data structure that permits MGA using any population-based solution procedure has been formulated that can efficiently construct sets of maximally different solution alternatives. This new approach permits the production of an overall best solution together with n locally optimal, maximally different alternatives in a single computational run. The efficacy of this novel computational approach is tested on four benchmark optimization problems.

Accurate parameter estimation for safety-critical systems with unmodeled dynamics

Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. Much of feedback control design is parametric in nature and as such, accurate and fast estimation of the parameters in the modeled part of the dynamic system is a crucial property for designing risk-aware autonomous systems. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unmodeled components of the dynamic system as sub-Gaussian noise and proposed parameter estimation using Gaussian noise-based exogenous signals. In contrast, we allow the unmodeled part to have deterministic unmodeled dynamics, which are almost always present in physical systems, in addition to sub-Gaussian noise. In addition, we propose a deterministic construction of the exogenous signal in order to carry out parameter estimation. We introduce a new tool kit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. Unlike the existing stochastic approach, these bounds are tunable through an optimal choice of the spectrum of the exogenous signal leading to accurate parameter estimation. We also show that this estimation is robust to unmodeled dynamics, a property that is not assured by the existing approach. Finally, we show that under ideal conditions with no deterministic unmodeled dynamics, the proposed approach can ensure a O˜(T) Regret, matching existing literature. Experiments are provided to support all theoretical derivations, which show that the spectral lines-based approach outperforms the Gaussian noise-based method when unmodeled dynamics are present, in terms of both parameter estimation error and Regret obtained using the parameter estimates with a Linear Quadratic Regulator in feedback.

Regularization for Distributionally Robust State Estimation and Prediction

The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns often do not fulfill the assumptions of existing approaches. We provide a direct method using samples of the noise to create a moving horizon observer for linear time-varying and nonlinear systems, which is optimal under the empirical noise distribution. Moreover, we show how to enhance the observer with distributional robustness properties in order to handle unmodeled components in the noise profile, as well as different noise realizations. We prove that, even though the design of distributionally robust estimators is a complex minmax problem over an infinite-dimensional space, it can be transformed into a regularized linear program using a system level synthesis approach. Numerical experiments with the Van der Pol oscillator show the benefits of not only using empirical samples of the noise to design the state estimator, but also of adding distributional robustness. We show that our method can significantly outperform state-of-the-art approaches under challenging noise distributions, including multi-modal and deterministic components.

Prescribed Performance Rotating Formation Control of Multi-Spacecraft Systems with Uncertainties

This paper investigates the problem of rotating formation control for multi-spacecraft systems with prescribed performance in the presence of model uncertainties. Firstly, The spacecraft dynamics containing unmodelled parts is described in a polar coordinate system, which is to solve the problem of the controllable angular velocity of rotating formation. Then, the prescribed performance control method is improved by developing new prescribed performance functions. Based on the improved prescribed performance control method, the distributed controller is designed for multi-spacecraft systems to achieve rotating formations with prescribed performance, i.e., the formations error converges to a predefined arbitrarily small residual set, with convergence time no less than a prespecified value. And an RBF neural network is used to fit the unmodelled components of the spacecraft dynamics. Compared with the existing works of literature, this paper not only solves the robust prescribed performance rotating formation control of multi-spacecraft system, but also acheives rotating formation with adjustable angular velocity. Finally, the Lyapunov approach is employed for convergence analysis, and simulation results are provided to illustrate the effectiveness of the theoretical results.

Safe learning-based observers for unknown nonlinear systems using Bayesian optimization

In this paper, a modular observer design methodology is formulated for nonlinear systems with partial model knowledge. Our design consists of three phases: (i) an initial robust observer design that enables one to learn the dynamics without allowing the state estimation error to diverge (hence, safe); (ii) a learning phase wherein the unmodeled components are estimated using Gaussian process-based Bayesian optimization; and, (iii) a re-design phase that leverages the learned dynamics to improve convergence rate of the state estimation error. The potential of our proposed learning-based observer is demonstrated on a benchmark nonlinear system. Additionally, certificates of guaranteed estimation performance are provided.

A Control Approach to Web Speed and Tension Regulation of Web Transport Systems Based on Dynamic Surface Control

This paper proposes an approach to deal with control problems of unmodeled components of the web transport system. It is commonly challenging to construct model-based controllers to guarantee tracking quality due to the unknown terms in the mathematical model. Hence, our main contribution is to design a robust controller for the uncertain model of the web transport system based on Dynamic Surface Control (DSC) technique to ensure high accuracy in the tracking process of the web speed and tension. The proposed controller is designed in the face of the mathematical model of the web transport system that is adversely affected by bounded uncertainties. The stability of the controlled system is proved using the Lyapunov standard. The simulation results show the validity and the effectiveness of the proposed control law when the system is lack of system model’s information.

Adaptive Control for Uncertain Model of Omni-directional Mobile Robot Based on Radial Basis Function Neural Network

The paper proposes the method to deal with control problems of unmodeled components of the four-wheeled Omni-directional mobile robot. It is commonly challenging to design a model-based control scheme to achieve smooth movement in the tracking process due to the unknown elements in the mathematical model of the robot or external disturbances. Our main contribution focuses on designing an adaptive controller based on neural networks with online weight updating laws and Fuzzy logic to guarantee the high accuracy of the robot’s movement when the unknown factors adversely affect the robot control. At the initial step, a Dynamic Surface Control plays a role as a core of the controller for the robot system. Then, with the ability to estimate the appropriate value for uncertain nonlinear parts, a Radial Basis Function Neural Network is designed. Finally, a Fuzzy law is to utilize control parameters in each period to increase the adaptive behavior of the system. The stability and convergence of the system are proven by the Lyapunov’s stability theory. The simulation results illustrate the validity and the efficiency of the proposed control algorithm when the system is lack of robot model’s information.

Unbiased Least-Squares Modelling

In this paper we analyze the bias in a general linear least-squares parameter estimation problem, when it is caused by deterministic variables that have not been included in the model. We propose a method to substantially reduce this bias, under the hypothesis that some a-priori information on the magnitude of the modelled and unmodelled components of the model is known. We call this method Unbiased Least-Squares (ULS) parameter estimation and present here its essential properties and some numerical results on an applied example.

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

SummaryThe problem of output stabilization and disturbance rejection for input‐delayed systems is tackled in this work. First, a suitable transformation is introduced to translate mismatched disturbances into an equivalent input disturbance. Then, an extended state observer is combined with a predictive observer structure to obtain a future estimation of both the state and the disturbance. A disturbance model is assumed to be known but attenuation of unmodeled components is also considered. The stabilization is proved via Lyapunov‐Krasovskii functionals, leading to sufficient conditions in terms of linear matrix inequalities for the closed‐loop analysis and parameter tuning. The proposed strategy is illustrated through a numerical example.

Simultaneous multi-residue determination of twenty one veterinary drugs in poultry litter by modeling three-way liquid chromatography with fluorescence and absorption detection data

A method for the simultaneous investigation of twenty one veterinary active ingredients in poultry litter based on MCR-ALS modeling of three-way liquid chromatography with fluorescence and UV detection data is presented. The chromatographic procedure was optimized in terms of both the nature of the organic solvent and the pH of the mobile phase to maximize the resolution of the analytes. In order to improve the simultaneous extraction efficiency of the twenty one veterinary drugs, a simplex-centroid design with combinations of the three components of the extracting mixture, i.e. MeOH, ACN and sodium phosphate buffer 10mmolL–1 pH =3.50, was carried out. The second-order advantage was exploited in the analysis of highly complex samples containing unmodeled components. The qualitative and quantitative results showed that the application of MCR-ALS was appropriate to resolve highly overlapped peaks in the presence of unknown matrix compounds. Limits of quantification, relative errors of prediction (REP) and average recoveries ranging from 0.02 to 0.61µgg–1, 3.09–9.35% and 91.0–105.6%, respectively, were obtained. Eventually, the method was successfully applied to the determination of active ingredients in five poultry litter samples collected from different poultry livestock in Argentina.

Seasonal crustal vertical deformation induced by environmental mass loading in mainland China derived from GPS, GRACE and surface loading models

Obvious seasonal crustal vertical deformation largely related to mass redistribution on the Earth’s surface can be captured by Gravity Recovery and Climate Experiment (GRACE), simulated by surface loading models (SLMs), and recorded by continuous Global Positioning System (GPS). Vertical deformation time series at 224 GPS stations with more than four-year continuous observations are compared with time series obtained by GRACE and SLMs with the aim of investigating the consistency of the seasonal crustal vertical deformation obtained by different techniques in mainland China. Results of these techniques show obvious seasonal vertical deformation with high consistency at almost all stations. The GPS-derived seasonal vertical deformation can be explained, to some content, by the environmental mass redistribution effect represented by GRACE and SLMs. Though the mean weighted root mean square reduction is 34% after removing the environmental mass loading from the monthly GPS height time series (up to 47% for the mean annual signals), systematic signals are still evident in the residual time series. The systematic residuals are probably attributed to GPS related errors, such as draconitic errors, while the leakage errors in the GRACE data processing and unmodeled components in land water storage should be considered in some regions. Additionally, the obvious seasonal residual perturbations in Southwest China may be related to the leakage errors in the GRACE data processing and large uncertainty in the land water storage in SLMs, indicating that GPS observations may provide more realistic mass transport estimates in Southwest China.

Automatic generation of photochemically induced excitation-emission-kinetic four-way data for the highly selective determination of azinphos-methyl in fruit juices

An application of four-way multivariate calibration for the quantitation of azinphos-methyl (AZM) in fruits is presented. The known photochemically induced degradation of AZM into a highly fluorescent product was exploited for the generation of third-order data with quantitative purpose. The data generation consisted in the measurement of excitation-emission fluorescence matrices at different times after UV-light irradiation. For this purpose, a reactor was built connecting an external UV-light source through an optical fiber to the sample holder. The data were modelled with two algorithms, PARAFAC and U-PLS/RTL. The second-order advantage was exploited in the analysis of samples containing un-modelled components and an improvement in the analytical figures of merit was observed as long as the data dimensions were increased. The method was successfully applied to the quantitation of AZM in apple, pear and peach juice samples with and without spiked analyte. The limits of detection were of 3.6μgL−1 in aqueous solution and 21–66μgL−1 in fruit juice samples.

Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds.

An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS.

A State-Space Modeling Approach for Localization of Focal Current Sources From MEG

State-space modeling is a promising approach for current source reconstruction from magnetoencephalography (MEG) because it constrains the spatiotemporal behavior of inverse solutions in a flexible manner. However, state-space model-based source localization research remains underdeveloped; extraction of spatially focal current sources and handling of the high dimensionality of the distributed source model remain problematic. In this study, we propose a novel state-space model-based method that resolves these problems, extending our previous source localization method to include a temporal constraint by state-space modeling. To enable focal current reconstruction, we account for spatially inhomogeneous temporal dynamics by introducing dynamics model parameters that differ for each cortical position. The model parameters and the intensity of the current sources are jointly estimated according to a bayesian framework. We circumvent the high dimensionality of the problem by assuming prior distributions of the model parameters to reduce the sensitivity to unmodeled components, and by adopting variational bayesian inference to reduce the computational cost. Through simulation experiments and application to real MEG data, we have confirmed that our proposed method successfully reconstructs focal current activities, which evolve with their temporal dynamics.

Robustification as a tool in modeling biochemical reaction networks

Biological functions have evolved to become robust against a multitude of perturbations such as gene mutations, intracellular noise and changes in the physical and chemical environment. This robustness should be reflected in models of the underlying biochemical networks, and robustness analysis has consequently been established as an important tool for model validation in systems biology. However, while robustness analysis can be used to invalidate a given model, it does not support the postulation of model modifications that can serve to improve the robustness. Herein we propose a method for this purpose, based on computing the sensitivity of the robustness with respect to generic dynamic perturbations applied to the individual network edges. To quantify robustness we compute the smallest simultaneous change in the activity of the network nodes that induces a bifurcation in the network, resulting in a qualitative change in the network behavior. The proposed method can be used to identify network interactions with the most significant impact on the overall robustness of a given function. By considering the impact of adding new nodes and edges, the method can also be used to postulate the presence of important unmodeled components and interactions. The focus here is on biological functions related to bistable switches and sustained oscillations, and the proposed methodology is demonstrated through application to metabolic oscillations in white blood cells and bistable switching in MAPK signal transduction. The classical Goodwin model of oscillations in a simple gene regulatory network is used for illustration throughout the paper.

A Robust Approach to Misspecifications and Non Linearities for Hedge Fund Replication and Alternative Beta

This paper explores a linear hedge fund replication and alternative beta methodology that is robust to the presence of non linearities and the possibility of model mis-specification. In a fashion similar to Roncalli and Weisang (2009a), the problem is cast as a tracking problem in order to allow for a dynamic treatment of the replication problem. In a quasi-experiment, using simulations, I explore the robustness of the methodology, and develop a statistic that helps in detecting the introduction of unmodeled components in hedge fund portfolios. Finally, the methodology is applied to a set of hedge fund indices.

Testing the capability of the chemistry transport model LOTOS-EUROS to forecast PM10 levels in the Netherlands

Since particulate matter has a direct and adverse impact on public health, a good air quality forecast is important. Several European countries presently use statistical forecasting models, which have their limitations, especially for PM10. An alternative approach is to use a chemistry transport model. Here, the ability of the chemical transport model LOTOS-EUROS to forecast PM10 concentrations in the Netherlands was investigated. LOTOS-EUROS models several PM10 components individually. For sulphate, nitrate and ammonium aerosol the evaluation against observations shows that the modelled annual mean concentrations are within 20% of the measured concentration and that the temporal correlation is reasonably good ( R > 0.6). For sea salt the model tended to overestimate the measured concentrations. For elemental carbon the correspondence with black smoke observations was reasonable. However, total PM10 is seriously underestimated, due to unmodelled components (secondary organic aerosols, mineral dust) and missing sources. Therefore, a simple bias correction for four seasons was derived based on the years 2004–2006. The model was compared with the Dutch operational statistical model PROPART and ground-level observations. With bias correction, LOTOS-EUROS performed better than PROPART regarding the timing of events. The major flaw of LOTOS-EUROS was that high values (>50 μg m −3) were still underestimated. Another advantage of LOTOS-EUROS over the statistical model was the more detailed information in space and time, which facilitates communication of the forecast to the general public.

Parallel Performance Modeling using a Genetic Programming-based Error Correction Procedure

Performance models of high performance computing (HPC) applications are important for several reasons. First, they provide insight to designers of HPC systems on the role of subsystems such as the processor or the network in determining application performance. Second, they allow HPC centers more accurately to target procurements to resource requirements. Third, they can be used to identify application performance bottlenecks and to provide insights about scalability issues. The suitability of a performance model, however, for a particular performance investigation is a function of both the accuracy and the cost of the model. A semi-empirical model previously published by the authors for an astrophysics application was shown to be inaccurate when predicting communication cost for large numbers of processors. It is hypothesized that this deficiency is due to the inability of the model adequately to capture communication contention (threshold effects) as well as other unmodeled components such as noise and I/O contention. In this paper we present a new approach to capture these unknown features to improve the predictive capabilities of the model. This approach uses a systematic model error-correction procedure that uses evolutionary algorithms to find an error correction term to augment the eXisting model. Four variations of this procedure were investigated and all were shown to produce better results than the original model. Successful cross-platform application of this approach showed that it adequately captures machine dependent characteristics. This approach was then successfully demonstrated for a second application, further showing its versatility.

Concentration Residual Augmented Classical Least Squares (CRACLS): A Multivariate Calibration Method with Advantages over Partial Least Squares

A significant extension to the classical least-squares (CLS) algorithm called concentration residual augmented CLS (CRACLS) has been developed. Previously, unmodeled sources of spectral variation have rendered CLS models ineffective for most types of problems, but with the new CRACLS algorithm, CLS-type models can be applied to a significantly wider range of applications. This new quantitative multivariate spectral analysis algorithm iteratively augments the calibration matrix of reference concentrations with concentration residuals estimated during CLS prediction. Because these residuals represent linear combinations of the unmodeled spectrally active component concentrations, the effects of these components are removed from the calibration of the analytes of interest. This iterative process allows the development of a CLS-type calibration model comparable in prediction ability to implicit multivariate calibration methods such as partial least squares (PLS) even when unmodeled spectrally active components are present in the calibration sample spectra. In addition, CRACLS retains the improved qualitative spectral information of the CLS algorithm relative to PLS. More importantly, CRACLS provides a model compatible with the recently presented prediction-augmented CLS (PACLS) method. The CRACLS/PACLS combination generates an adaptable model that can achieve excellent prediction ability for samples of unknown composition that contain unmodeled sources of spectral variation. The CRACLS algorithm is demonstrated with both simulated and real data derived from a system of dilute aqueous solutions containing glucose, ethanol, and urea. The simulated data demonstrate the effectiveness of the new algorithm and help elucidate the principles behind the method. Using experimental data, we compare the prediction abilities of CRACLS and PLS during cross-validated calibration. In combination with PACLS, the CRACLS predictions are comparable to PLS for the prediction of the glucose, ethanol, and urea components for validation samples collected when significant instrument drift was present. However, the PLS predictions required recalibration using nonstandard cross-validated rotations while CRACLS/PACLS was rapidly updated during prediction without the need for time-consuming cross-validated recalibration. The CRACLS/PACLS algorithm provides a more general approach to removing the detrimental effects of unmodeled components.