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result(s) for
"estimation problem"
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Linear quadratic Gaussian control for linear time-delay systems
This study investigates a separation principle for the H2 control of time-delay systems with partial observations. The authors first consider the linear quadratic regulation problem for time-delay systems. Based on the dynamic programming technique, the solution to the controller is given in terms of a backward partial difference Riccati equation. Then the estimation problem is investigated for linear discrete-time systems in the presence of time-delays. By employing the innovation analysis approach, the linear minimum-mean-square error (LMMSE) estimator is developed in terms of a forward partial difference Riccati equation. The Riccati equation is of the same dimension as the plant. Therefore compared with the conventional augmented approach, the presented approach greatly lessens the computational demand when the delay is large. Finally, they show that the separation principle holds in the following sense: an optimal controller can be obtained from two parts, one associated with the optimal control problem when state variable is available, and the other one associated with the LMMSE estimation problem.
Journal Article
Singular linear parameter-varying observer for composition estimation in a binary distillation column
The aim of this study is to provide a full comprehensive study of the singular linear parameter-varying (LPV) systems and observer synthesis in a real process. The states and unknown inputs estimation problem for a binary distillation column is solved by using an LPV proportional-integral observer (PI-Observer). A singular LPV model of the process is developed. This model facilitates the design of the PI-Observer for singular LPV systems. The observer proposed is tested using experimental data of a distillation column separating an ethanol–water mixture. The results indicate that the observer is able to accurately reconstruct the product composition dynamics and the unknown inputs of the process.
Journal Article
PIVOTAL ESTIMATION VIA SQUARE-ROOT LASSO IN NONPARAMETRIC REGRESSION
We propose a self-tuning $\\sqrt {Lasso} $ Lasso method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic) non-Gaussianity of the noise. In addition, our analysis allows for badly behaved designs, for example, perfectly collinear regressors, and generates sharp bounds even in extreme cases, such as the infinite variance case and the noiseless case, in contrast to Lasso. We establish various nonasymptotic bounds for $\\sqrt {Lasso} $ including prediction norm rate and sparsity. Our analysis is based on new impact factors that are tailored for bounding prediction norm. In order to cover heteroscedastic non-Gaussian noise, we rely on moderate deviation theory for self-normalized sums to achieve Gaussian-like results under weak conditions. Moreover, we derive bounds on the performance of ordinary least square (ols) applied to the model selected by $\\sqrt {Lasso} $ accounting for possible misspecification of the selected model. Under mild conditions, the rate of convergence of ols post $\\sqrt {Lasso} $ is as good as $\\sqrt {Lasso's} $ rate. As an application, we consider the use of $\\sqrt {Lasso} $ and ols post $\\sqrt {Lasso} $ as estimators of nuisance parameters in a generic semiparametric problem (nonlinear moment condition or Z-problem), resulting in a construction of $\\sqrt n - consistent$ and asymptotically normal estimators of the main parameters.
Journal Article
Analytical approach for placement and sizing of distributed generation on distribution systems
An analytical method for placement and sizing of distributed generation on power distribution systems for loss reduction is introduced. The proposed analytical method is developed based on a new formulation for the power flow problem, which is non-iterative, direct, and involves no convergence issues even for systems with high R/X branch ratios. Further, this power flow solution is extremely useful whenever fast and repetitive power flow estimations are required. A priority list based on loss sensitivity factors is developed to determine the optimal locations of the candidate distributed generation units. Sensitivity analysis is performed to estimate the optimal size and power factor of the candidate distributed generation units. Various types of distributed generators (DGs) have been dealt with and viable solutions are proposed to reduce total system loss. The proposed method has been tested on 33-bus and 69-bus distribution systems, which are extensively used as examples in solving the placement and sizing problem of DGs. Exhaustive power flow routines are also performed to verify the sizes obtained by the analytical method. The test results show that the proposed analytical method could lead to optimal or near-optimal solution, while requiring lower computational effort.
Journal Article
Iterative Regularization Methods for Nonlinear Ill-Posed Problems
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
eBook
A Relaxation Approach for Estimating Origin–Destination Trip Tables
The problem of estimating origin-destination travel demands from partial observations of traffic conditions has often been formulated as a network design problem (NDP) with a bi-level structure. The upper level problem in such a formulation minimizes a distance metric between measured and estimated traffic conditions, and the lower level enforces user-equilibrium traffic conditions in the network. Since bi-level problems are usually challenging to solve numerically, especially for large-scale networks, we proposed, in an earlier effort (Nie et al.,
Transp Res
, 39B:497–518, 2005), a decoupling scheme that transforms the O–D estimation problem into a single-level optimization problem. In this paper, a novel formulation is proposed to relax the user equilibrium conditions while taking users’ route choice behavior into account. This relaxation approach allows the development of efficient solution procedures that can handle large-scale problems, and makes the integration of other inputs, such as path travel times and historical O–Ds rather straightforward. An algorithm based on column generation is devised to solve the relaxed formulation and its convergence is proved. Using a benchmark example, we compare the estimation results obtained from bi-level, decoupled and relaxed formulations, and conduct various sensitivity analysis. A large example is also provided to illustrate the efficiency of the relaxation method.
Journal Article
State-of-charge estimation of the lithium-ion battery system with time-varying parameter for hybrid electric vehicles
This study addresses the state-of-charge (SOC) estimation problem for a lithium-ion battery system with time-varying parameter. Although many methods have been proposed for the SOC estimation, the time-varying parameter problem has not been solved perfectly up to now. In this study, by introducing a novel physical meaning for that the battery terminal current is ℒ2-norm bounded and solving one linear matrix inequality, a robust H∞ filter is proposed for the first time to estimate the SOC of the lithium-ion battery of hybrid electric vehicles. The proposed method is evaluated by the sequence of urban dynamometer driving schedule test. The experimental results show that the filter proposed here is more accurate and reliable than that without considering the time-varying parameter.
Journal Article
An inverse analysis of the brain cooling process in neonates using the particle filter method
Purpose
This study deals with the computational simulation and inverse analysis of the cooling treatment of the hypoxic-ischemic encephalopathy in neonates. A reduced-order model is implemented for real-time monitoring of the internal body temperatures. The purpose of this study is to sequentially estimate the transient temperatures of the brain and other body regions with reduced uncertainties.
Design/methodology/approach
Pennes’ model was applied in each body element, and Fiala’s blood pool concept was used for the solution of the forward bioheat transfer problem. A state estimation problem was solved with the Sampling Importance Resampling (SIR) algorithm of the particle filter method.
Findings
The particle filter method was stable and accurate for the estimation of the internal body temperatures, even in situations involving large modeling and measurement uncertainties.
Research limitations/implications
The proposed reduced-order model was verified with the results of a high-fidelity model available in the literature. Validation of the proposed model and of the solution of the state estimation problem shall be pursued in the future.
Practical implications
The solution of the state estimation problem with the reduced-order model presented in this paper has great potential to perform as an observer of the brain temperature of neonates, for the analysis and control of the systemic cooling treatment of neonatal hypoxic-ischemic encephalopathy.
Social implications
The main treatment for hypoxic-ischemic encephalopathy in neonates is the cooling of affected regions. Accurate and fast models might allow the development of individualized protocols, as well as control strategies for the cooling treatment.
Originality/value
This paper presents the application of the SIR algorithm for the solution of a state problem during the systemic cooling of a neonate for the treatment of the hypoxic-ischemic encephalopathy.
Journal Article