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Lithium-ion batteries possess high power, energy, and long cycle life. They are best candidates for applications on hybrid and electric vehicles. To ensure reliable operation, one of the functions in a battery management system is health monitoring in terms of fault diagnosis and estimation. The purpose of this brief is to provide a fault-diagnostic scheme that can achieve single fault isolation and estimation for a three-cell battery string subject to uncertainties. Detecting and isolating faults in systems subject to uncertainties is a challenging task due to the difficulty in distinguishing the effects of faults from uncertainties. To facilitate fault isolation, a bank of systems, each corresponding to a particular fault, are formulated by reorganizing the considered system. Each system in the bank is first transformed into two subsystems. Then, a classical Luenberger observer is designed for the first subsystem to generate a fault-detection residual. In this manner, a bank of reduced-order Luenberger observers are designed to locate a specific fault source, and thus fault isolation is achieved. Parallel to the bank of reduced-order Luenberger observers, a bank of learning observers (LOs) are also constructed to provide an estimate of the isolated fault. As a result, the synthesized design of Luenberger observers and LOs can realize simultaneous fault isolation and estimation. Parameters of an A123 battery cell are extracted via experiments, and effectiveness of the proposed design is demonstrated through simulation studies on the model of a three-cell battery string.

Purpose To optimize acquisition parameters for three-dimensional fast spin-echo (3D FSE) imaging of the knee.

Purpose To develop a robust sequence that combines T1ρ and T2 quantifications and to examine the in-vivo repeatability and diurnal variation of T1ρ and T2 quantifications in knee cartilage.

This paper studies the zero properties of blocked linear systems resulting from blocking of linear time-invariant systems. The main idea is to establish a relation between the zero properties of blocked systems and the zero properties of their corresponding unblocked systems. In particular, it is shown that the blocked system has a zero if and only if the associated unblocked system has a zero. Furthermore, the zero properties of blocked systems under a generic setting i.e. a setting which parameter matrices A , B , C , D assume generic values, are examined. It is demonstrated that nonsquare blocked systems i.e. blocked systems with number of outputs unequal to the number of inputs, generically have no zeros; however, square blocked systems i.e. blocked systems with equal number of inputs and outputs, generically have only finite zeros and these finite zeros have geometric multiplicity one.

Summary Objective Changes in T1ρ and T2 magnetic resonance relaxation times have been associated with articular cartilage degeneration, but similar relationships for meniscal tissue have not been extensively investigated. This work examined relationships between T1ρ and T2 measurements and biochemical and mechanical properties across regions of degenerate human menisci. Design Average T1ρ and T2 relaxation times were determined for nine regions each of seven medial and 13 lateral menisci from 14 total knee replacement patients. Sulfated glycosaminoglycan (sGAG), collagen and water contents were measured for each region. Biomechanical measurements of equilibrium compressive, dynamic compressive and dynamic shear moduli were made for anterior, central and posterior regions. Results T1ρ and T2 times showed similar regional patterns, with longer relaxation times in the (radially) middle region compared to the inner and outer regions. Pooled over all regions, T1ρ and T2 times showed strong correlations both with one another and with water content. Correlations with biochemical content varied depending on normalization to wet or dry mass, and both imaging parameters showed stronger correlations with collagen compared to sGAG content. Mechanical properties displayed moderate inverse correlations with increasing T1ρ and T2 times and water content. Conclusion Both T1ρ and T2 relaxation times correlated strongly with water content and moderately with mechanical properties in osteoarthritic menisci, but not as strongly with sGAG or collagen contents alone. While the ability of magnetic resonance imaging (MRI) to detect early osteoarthritic changes remains the subject of investigation, these results suggest that T1ρ and T2 relaxation times have limited ability to detect compositional variations in degenerate menisci.

SUMMARY In iterative identification and control, one needs to determine the closed-loop performance of a new controller designed with the current model so that a decision can be made on whether a new iteration of plant identification and controller design is necessary. In multiple model adaptive control, at times, a decision to connect a different controller is made. It is desirable to check the closed-loop performance with a new controller before it is switched in. Consider a feedback interconnection of an unknown linear plant and a known linear stabilizing controller, and assume that some knowledge of the closed-loop system is available. We aim to develop theory and tools for experimentally verifying the closed-loop performance with a prospective stabilizing controller in advance. The simulation results demonstrate efficacy and versatility of our results.Copyright © 2013 John Wiley & Sons, Ltd.

To investigate normative value and age-related change of brain magnetic resonance T1ρ relaxation at 1.5T.This study was approved by the local ethical committee with participants' written consent obtained. There were 42 adults healthy volunteers, including 20 males (age: 41±16 (mean±standard deviation) years, range: 22-68years,) and 22 females (age: 39±15years, range: 21-62years). MRI was performed at 1.5T using 3D fluid suppressed turbo spin echo sequence. Regions-of-interests (ROIs) were obtained by atlas-based tissue segmentation and T1ρ was calculated by fitting the mean value to mono-exponential model. Correlation between T1ρ relaxation of brain gray matter regions and age was investigated.A regional difference among individual gray matter areas was noted; the highest values were observed in the hippocampus (98.37±5.37ms, median: 97.88ms) and amygdala (94.95±4.34ms, median: 94.73ms), while the lowest values were observed in the pallidum (83.81±5.49ms, median: 83.77ms) and putamen (83.93±4.76ms, median: 83.99ms). Gray matter T1ρ values decreased slowly (mean slope: -0.256) and significantly (p0.05) with age in gray matter for subjects younger than 40years old, while for subjects older than 40years old there was no apparent correlation between T1ρ relaxation and age. Global white matter measured T1ρ value of 88.65±3.47ms (median: 87.86ms), and the correlation with age was not significant (p=0.18).Gray matter T1ρ relaxation demonstrates a bi-phase change with age in adults of 22-68years.

This paper presents a systematic study on the properties of blocked linear systems that are resulted from blocking discrete-time linear time invariant systems. The main idea is to explore the relationship between the blocked and the unblocked systems. Existing results are reviewed and a number of important new results are derived. Focus is given particularly on the zero properties of the blocked system as no such a study has been found in the literature.

A combined multiple model adaptive control (CMMAC) scheme, which is a proper combination of the estimator-based MMAC scheme and the unfalsified MMAC scheme, has been proposed with the aim of taking advantage of the strength of each scheme while avoiding their weaknesses. The major novelty of the CMMAC scheme lies in the fact that it monitors not only the adequacy of candidate models in terms of their estimation performances but also the performance of the active candidate controller. As an application of the CMMAC scheme and one example of such new multiple model adaptive controllers, a CMMAC based controller has been designed for a class of nonlinear systems with nonlinear parameterization. Under some sufficient conditions, a strong finite time switching result (which provides a characterization on the maximum number of switching) and the closed-loop stability have been established. A constructive design based on back-stepping is provided for the adaptive control problem of a special class of nonlinearly parameterized systems, which can satisfy all the sufficient conditions to ensure closed-loop stability.

In this paper, an actuator fault diagnosis scheme is proposed for a class of affine nonlinear systems with both known and unknown inputs. The scheme is based on a novel input/output relation derived from the considered nonlinear systems and the use of the recently developed high-order sliding-mode robust differentiators. The main advantages of the proposed approach are that it does not require a design of nonlinear observer and applies to systems not necessarily detectable. Conditions are provided to characterize the feasibility of fault detection and isolation using the proposed scheme and the maximum number of isolatable actuator faults. The efficacy of the proposed actuator fault diagnosis approach is tested through experiments on a laboratory 3D Crane, and the experimental results show that the proposed actuator fault diagnosis approach is promising and can achieve fault detection and isolation satisfactorily.

A study is presented on solutions of the Yule-Walker equations for singular AR processes that are stationary outputs of a given AR system. If the Yule-Walker equations admit more than one solution and the order of the AR system is no less than two, the solution set includes solutions which define unstable AR systems. The solution set also includes one solution, the minimal norm solution, which defines an AR system whose characteristic polynomial has either only stable zeros (implying that only one stationary output exists for this system and it is linearly regular) or has stable zeros as well as zeros of unit modulus, (implying that stationary solutions of this system are a sum of a linearly regular process and a linearly singular process). The numbers of stable and unit circle zeros of the characteristic polynomial of the defined AR system can be characterized in terms of the ranks of certain matrices, and the characteristic polynomial of the AR system defined by the minimal norm solution has the least number of unit circle zeros and the most number of stable zeros over all possible solutions.

Although many iterative algorithms have been proposed for solving Hamilton-Jacobi-Bellman equation arising from nonlinear optimal control, it remains open how fast those algorithms can converge. The convergence rate of those algorithms is of great importance in concluding whether they offer practical benefit. This paper presents a study on how fast the well-known Leake-Liu algorithm in Leake and Liu (1967) can converge. The relationship between the sequence of approximate solutions to the HLB equation and the corresponding sequence of control laws is first established. Based on this relation, several results are provided on the convergence rate of the Leake-Liu algorithm. These results demonstrate that the convergence rate of the Leake-Liu algorithm can be quadratic in the domain of interest under favorable conditions. Further, they include the well known quadratic convergence results in Kleinman (1968) and in Reid (1972) as special cases, which have been established for linear time-invariant and time-varying systems (with quadratic performance index) respectively. Under weaker conditions, the convergence rate of the Leake-Liu algorithm is shown to be quadratic locally i.e. in the neighborhood of the origin.

An approach for nonlinear unknown input observer (NUIO) design is proposed for a class of nonlinear systems representable by a Takagi—Sugeno (TS) fuzzy system. The proposed NUIO design for TS fuzzy systems is carried out for two cases: (1) the premise variables do not depend on the unmeasured state variables; and (2) the premise variables depend on the unmeasured state variables. Sufficient conditions for the existence of NUIOs are derived, and a linear matrix inequality (LMI)-based design strategy is presented for NUIO design purposes. The proposed NUIO design approach is then applied to solve actuator fault detection and isolation problems for nonlinear systems described by TS fuzzy systems. To this end, a system structure with two groups of inputs where one group of inputs is treated as unknown inputs is developed. Based on the system structure, a bank of NUIOs are then designed using the developed NUIO design approach in order to investigate the following fault diagnosis problems. (1) How can the NUIOs be used for detecting faults? (2) Under what conditions is it possible to isolate single and/or multiple faults? (3) What is the maximum number of faults that can be isolated simultaneously? (4) How can multiple fault isolation be achieved? In this article we present a NUIO-based fault-detection scheme for problem (1), give sufficient conditions for problem (2), determine the maximum number of faults that can be isolated for problem (3), and propose a fault-diagnosis scheme using a bank of NUIOs to solve problem (4). As an illustrative example, Lorenz’s chaotic system with multi-inputs is chosen to show the effect of the designed NUIOs and the proposed fault detection and isolation scheme. Simulation results show that accurate state estimation is achieved and actuator faults can be detected and isolated successfully.

Actuator fault diagnosis problem is studied for a class of nonlinear systems with relative degrees from the inputs to the outputs higher than one. This type of nonlinear systems include many mechanical systems, and their actuator fault diagnosis problem can be very challenging because of nonlinearities and high relative degrees. In this paper, in order to solve the actuator fault diagnosis problem for the considered nonlinear systems, 2nd-order and 3rd-order sliding mode differentiators are used and actuator fault diagnosis schemes are proposed to achieve fault detection and isolation. Computer simulations are carried out to compare the efficacy of the proposed fault diagnosis schemes on a laboratory 3D Crane model with noisy measurements. The fault diagnosis schemes are further tested through experiments on a laboratory 3D Crane in terms of actuator fault detection and isolation.

Many observer-based fault diagnosis strategies proposed for linear systems, subject to unknown inputs, operate based on three assumptions. The first assumption is that the system under consideration is at least detectable. The second one is that the unknown inputs satisfy certain matching conditions. The third one, which is often implicit, is that the relative degrees from the generalized input vector, including both known and unknown inputs, to the outputs are no larger than one. If none of these assumptions are met, little result exists on how to carry out fault diagnosis. The purpose of this paper is to develop a novel actuator fault diagnosis scheme for a general class of linear systems subject to unknown inputs that can work without the mentioned three assumptions. Four actuator fault diagnosis problems related to fault detection, isolation, and estimation are formulated and studied. In order to solve these problems, an input–output relation, which involves only the outputs and their higher-order derivatives, is derived. The posed problems are solved based on this relation via utilizing both the outputs and their higher-order derivatives. Because only the outputs are measured, higher-order output derivatives are estimated using the recently developed high-order sliding-mode robust differentiators (HOSMRDs). The first two fault detection and isolation problems are answered in terms of a concept called Generalized Actuator Fault Isolation IndeX (GAFIX), and it is proved that, under the condition that the derived input–output relation is used for fault diagnosis, actuator faults are detectable if and only if GAFIX⩾1, and l actuator faults can be isolated if and only if GAFIX⩾l+1. A method which can be used to estimate the faults is proposed for the fault estimation problem. To solve the last problem, an actuator fault diagnosis scheme is designed using both the measured outputs and their estimated derivatives obtained by HOSMRDs, and is presented in steps. Finally, an example is provided to show the effectiveness of our fault diagnosis scheme in terms of fault detection, isolation, and estimation. Copyright © 2007 John Wiley & Sons, Ltd.

Spiral scanning is a promising MRI method, but one limitation is that off-resonance effects can cause image blurring. Most current off-resonance correction methods for spiral imaging require an accurate field map, which is difficult to obtain in many applications. Automatic methods can perform off-resonance correction without acquiring a field map. However, these methods are computationally inefficient and relatively prone to estimation error. This study describes a new semiautomatic off-resonance correction method that combines an automatic method with a low resolution field map acquisition for off-resonance correction in spiral scanning. Experiments demonstrate that this method is more robust than conventional automatic off-resonance correction and can provide more accurate off-resonance correction than conventional field map based methods. The proposed method is also computationally efficient and has been implemented for online reconstruction. Magn Reson Med 59:1212–1219, 2008. © 2008 Wiley-Liss, Inc.

This article investigates the design and application of a sliding mode observer (SMO) strategy for actuator as well as sensor fault detection, isolation, and estimation (FDIE) problem for a class of uncertain Lipschitz nonlinear systems. Actuator FDIE is addressed by regrouping the system's inputs into a structure suitable for SMO design. Similarly, by filtering the regrouped outputs, a similar system structure can be developed for sensor FDIE problem. Once in the suitable form and under certain assumptions, nonlinear SMOs are proposed for actuator and sensor FDIE. A systematic LMI-based design approach for the proposed SMO is presented. Additionally, the article addresses four problems, namely: (P1) What are the conditions for isolating single and/or multiple faults? (P2) What is the maximum number of faults that can be isolated simultaneously? (P3) How should one design SMO-based FDI approach in order to achieve multiple fault isolation using as few observers as possible? (P4) How can one estimate the shape of the faults? To solve the above problems, a new concept called fault isolation index (FIX) is proposed for actuator and sensor FDIE. It is proved that fault isolation can only be achieved if FIX ≠ 0, and also that the maximum number of faults that can be isolated is equal to FIX. Using the proposed fault isolation strategy and by treating some healthy inputs or outputs as unknown inputs, a systematic FDIE design scheme using a bank of nonlinear SMOs, which provides a solution for the four problems is provided. An example is used to illustrate the proposed ideas. The simulation results show that the proposed FDIE scheme can successfully detect and isolate both slowly and fast-changing actuator faults. It is also shown that accurate estimation of actuator faults can be achieved.

Adaptive actuator fault detection, isolation, and accommodation problems for linear multi-input single-output (MISO) systems with unknown system parameters are investigated. To solve the detection problem, we construct an adaptive estimate of the output signal. By comparing it with the output of the system, any type of actuator faults can be detected. However, the fault isolation problem is much more complicated. In order to solve it using an adaptive approach, the article considers constant actuator faults, which arise when the actuator output (such as a valve) is stuck at some fixed value. A novel idea which entails controller design for fault isolation is proposed. Thus, the controller in this case is not only designed to meet the control objective, but also to help with fault isolation, in case of an actuator failure. To accomplish this, assuming that there are m inputs, a group of additive functions, called fault isolation design functions in m − 1 inputs, solely used for fault isolation, are introdu...

To optimize acquisition parameters for three dimensional fast spin-echo (3D FSE) imaging of the knee.The knees of eight healthy volunteers were imaged in a 3 Tesla MRI scanner using an eight-channel knee coil. A total of 146 intermediate weighted isotropic resolution 3D FSE (3D-FSE-Cube)images with varied acquisition parameter settings were acquired with an additional reference scan performed for subjective image quality assessment. Images were graded for overall quality, parallel imaging artifact severity and blurring. Cartilage, muscle, and fluid signal-to-noise ratios and fluid-cartilage contrast-to-noise ratios were quantified by acquiring scans without radio frequency excitation and custom-reconstructing the k-space data.Mixed effects regression modeling was used to determine statistically significant effects of different parameters on image quality.Changes in receiver bandwidth, repetition time and echo train length significantly affected all measurements of image quality (P0.05). Reducing band width improved all metrics of image quality with the exception of blurring. Reader agreement was slight to fair for subjective metrics, but overall trends in quality ratings were apparent.We used a systematic approach to optimize 3D-FSE-Cube parameters for knee imaging. Image quality was overall improved using a receiver bandwidth of 631.25 kHz, and blurring increased with lower band width and longer echo trains.

To compare T2 relaxation time measurements between MR pulse sequences at 3 Tesla in agar phantoms and in vivo patellar, femoral, and tibial articular cartilage.T2 relaxation times were quantified in phantoms and knee articular cartilage of eight healthy individuals using a single echo spin echo (SE) as a reference standard and five other pulse sequences: multi-echo SE (MESE), fast SE (2D-FSE), magnetization-prepared spoiled gradient echo (3D-MAPSS), three-dimensional (3D) 3D-FSE with variable refocusing flip angle schedules (3D vfl-FSE), and quantitative double echo steady state (qDESS). Cartilage was manually segmented and average regional T2 relaxation times were obtained for each sequence. A regression analysis was carried out between each sequence and the reference standard, and root-mean-square error (RMSE) was calculated.Phantom measurements from all sequences demonstrated strong fits (R(2) 0.8; P 0.05). For in vivo cartilage measurements, R(2) values, slope, and RMSE were: MESE: 0.25/0.42/5.0 ms, 2D-FSE: 0.64/1.31/9.3 ms, 3D-MAPSS: 0.51/0.66/3.8 ms, 3D vfl-FSE: 0.30/0.414.2 ms, qDESS: 0.60/0.90/4.6 ms.2D-FSE, qDESS, and 3D-MAPSS demonstrated the best fits with SE measurements as well as the greatest dynamic ranges. The 3D-MAPSS, 3D vfl-FSE, and qDESS demonstrated the closest average measurements to SE. Discrepancies in T2 relaxation time quantitation between sequences suggest that care should be taken when comparing results between studies.

Summary Objective To measure the variability of T 1ρ relaxation times using CubeQuant, T 2 relaxation times using quantitative double echo in steady state (DESS), and normalized sodium signals using 3D cones sodium magnetic resonance imaging (MRI) of knee cartilage in vivo at 3 T. Design Eight healthy subjects were scanned at 3 T at baseline, 1 day, 5 months, and 1 year. Ten regions of interest (ROIs) of knee cartilage were segmented in the medial and lateral compartments of each subject's knee. T 1ρ and T 2 relaxation times and normalized sodium signals were measured and the root-mean-square coefficient of variation (CV RMS ) was calculated. Intra-subject variability was measured over short, moderate and long-term, as well as intra-observer and inter-observer variability. Results The average intra-subject CV RMS measurements over short, moderate, and long-term time periods were 4.6%, 6.1%, and 6.0% for the T 1ρ measurements, 6.4%, 9.3%, and 10.7% for the T 2 measurements and 11.3%, 11.6%, and 12.9% for the sodium measurements, respectively. The average CV RMS measurements for intra-observer and inter-observer segmentation were 3.8% and 5.7% for the T 1ρ measurements, 4.7% and 6.7% for the T 2 measurements, and 8.1% and 11.4% for the sodium measurements, respectively. Conclusions These CV RMS measurements are substantially lower than previously measured changes expected in patients with advanced osteoarthritis compared to healthy volunteers, suggesting that CubeQuant T 1ρ , quantitative DESS T 2 and 3D cones sodium measurements are sufficiently sensitive for in vivo cartilage studies.

Three-dimensional (3D) multispectral magnetic resonance imaging (MRI) techniques can significantly reduce image artifacts commonly encountered near embedded metal hardware. These artifact reductions are enabled by applying alternative spectral and spatial encoding schemes to conventional spin-echo imaging techniques. Here, the multi-acquisition with variable resonance image combination (MAVRIC) and slice-encoding for metal artifact correction (SEMAC) multispectral imaging techniques are connected and discussed. The development of a hybrid technique that utilizes the strengths of both methods is then described. This optimized 3D multispectral imaging approach is shown to be capable of producing minimal-artifact, high-resolution images near total joint replacements in a clinical setting.

A robust output-feedback controller is designed by using an observer plus backstepping procedure to solve the tracking problems of a class of uncertain nonlinear systems. In the design procedure, three techniques are applied: a) a single filter whose dynamic order is the same as the system order is constructed; b) a normalization signal is introduced; c) positive nonlinear functions that are used to generate the normalization signal and to construct nonlinear damping terms can be chosen freely. The designed controller has a very simple structure and can be applied to track much broader classes of reference signals. It can guarantee the global boundness of all closed-loop signals and make the output tracking error arbitrarily small. Technique c) may provide the designer with the possibility to find a better choice of positive nonlinear functions for our controller to achieve similar tracking performance with less control effort.

In order to reduce the large control effort needed by the adaptive controller proposed in [1] in the transient period, the regulation problem of parametric-strict-feedback system is restudied and resolved by reformulating it as a tracking problem which aims to asymptotically track the output of a chosen linear stable model. By choosing the model properly, the control effort needed by the adaptive controller proposed in [1] can be greatly reduced while similar or better performance can be achieved. This can be seen clearly in our simulations.

This paper is concerned with identifiability of an underlying high frequency multivariate AR system from mixed frequency observations. Such problems arise for instance in economics when some variables are observed monthly whereas others are observed quarterly. If we have identifiability, the system and noise parameters and thus all second moments of the output process can be estimated consistently from mixed frequency data. Then linear least squares methods for forecasting and interpolating nonobserved output variables can be applied. Two ways for guaranteeing generic identifiability are discussed.

Purpose: To evaluate two magnetic resonance imaging (MRI) techniques, slice encoding for metal artifact correction (SEMAC) and multiacquisition variable-resonance image combination (MAVRIC), for their ability to correct for artifacts in postoperative knees with metal. Materials and Methods: A total of 25 knees were imaged in this study. Fourteen total knee replacements (TKRs) in volunteers were scanned with SEMAC, MAVRIC, and 2D fast spin-echo (FSE) to measure artifact extent and implant rotation. The ability of the sequences to measure implant rotation and dimensions was compared in a TKR knee model. Eleven patients with a variety of metallic hardware were imaged with SEMAC and FSE to compare artifact extent and subsequent patient management was recorded. Results: SEMAC and MAVRIC significantly reduced artifact extent compared to FSE (P < 0.0001) and were similar to each other (P = 0.58), allowing accurate measurement of implant dimensions and rotation. The TKRs were properly aligned in the volunteers. Clinical imaging with SEMAC in symptomatic knees significantly reduced artifact (P < 0.05) and showed findings that were on the majority confirmed by subsequent noninvasive or invasive patient studies. Conclusion: SEMAC and MAVRIC correct for metal artifact, noninvasively providing high-resolution images with superb bone and soft tissue contrast. J. Magn. Reson. Imaging 2011;33:1121–1127. © 2011 Wiley-Liss, Inc.

T(1)(ρ) imaging is useful in a number of clinical applications. T(1)(ρ) preparation methods, however, are sensitive to non-uniformities of the B0 magnetic field and the B1 RF field. These common system imperfections can result in image artifacts and quantification errors in T(1)(ρ) imaging. We report on a phase-cycling method which can eliminate B1 RF inhomogeneity effects in T(1)(ρ) imaging. This method does not only correct for image artifacts but also for T(2)(ρ) contamination caused by B1 RF inhomogeneity. The presence of B0 magnetic field inhomogeneity can compromise the effectiveness of this method for B1 RF inhomogeneity correction. We demonstrate that, by combining the spin-locking scheme reported by Dixon et al. (Myocardial suppression in vivo by spin locking with composite pulses. Magn Reson Med 1996; 36:90-94) with phase cycling, we can simultaneously correct B0 magnetic field inhomogeneity effects and B1 RF inhomogeneity effects in T(1)(ρ) imaging. Phantom and in vivo data sets are used to demonstrate the proposed methods and to compare them with other existing T(1)(ρ) preparation methods.

We consider Generalized Linear Dynamic Factor Models in a stationary context, where the latent variables and thus the static and dynamic factors are the sum of a linearly regular and a linearly singular stationary process and the noise process is linearly regular. The linearly singular component may be useful for modeling e.g. business cycles or seasonal fluctuations in the observed variables. We present a structure theory for this case. The emphasis is laid on the autoregressive case. In general the stationary solutions of the autoregressive models considered here consist of a linearly regular and a linearly singular part. The linearly singular part corresponds to the homogeneous solution of a system having stable roots as well as roots of modulus one. We discuss the solutions of the Yule Walker equations for this case.

The desire to apply magnetic resonance imaging (MRI) techniques in the vicinity of embedded metallic hardware is increasing. The soft-tissue contrast available with MR techniques is advantageous in diagnosing complications near an increasing variety of MR-safe metallic hardware. Near such hardware, the spatial encoding mechanisms utilized in conventional MRI methods are often severely compromised. Mitigating these encoding difficulties has been the focus of numerous research investigations over the past two decades. Such approaches include view-angle tilting, short echo-time projection reconstruction acquisitions, single-point imaging, prepolarized MRI, and postprocessing image correction. Various technical advances have also enabled the recent development of two alternative approaches that have shown promising clinical potential. Here, the physical principals and proposed solutions to the problem of MRI near embedded metal are discussed. J. Magn. Reson. Imaging 2010;32:773–787. © 2010 Wiley-Liss, Inc.

A dwell-time-switching based MMAC scheme is proposed for the adaptive output feedback control problem of nonlinear systems with nonlinear parameterization. As in [1], the novel idea of combining the monitoring of the adequacy of candidate models (in terms of their estimation performances) in most MMAC schemes with the monitoring of the performance of the active candidate controller is employed and emphasis has been put on the design of candidate controllers, multiple estimators and monitoring signals so that they possess desirable properties. With the candidate controllers, multiple estimators and monitoring signals being carefully designed, a finite time switching result has been obtained, a characterization on the maximum number of switchings is provided, and sufficient conditions are derived to guarantee closed-loop stability. As an application of the dwell-time-switching based MMAC scheme, a constructive design based on back-stepping is provided for the adaptive output feedback control problem of a special class of nonlinearly parameterized systems, which can satisfy all those sufficient conditions to ensure closed-loop stability.

Purpose: To demonstrate accelerated imaging with both artifact reduction and different contrast mechanisms near metallic implants. Materials and Methods: Slice-encoding for metal artifact correction (SEMAC) is a modified spin echo sequence that uses view-angle tilting and slice-direction phase encoding to correct both in-plane and through-plane artifacts. Standard spin echo trains and short-TI inversion recovery (STIR) allow efficient PD-weighted imaging with optional fat suppression. A completely linear reconstruction allows incorporation of parallel imaging and partial Fourier imaging. The signal-to-noise ratio (SNR) effects of all reconstructions were quantified in one subject. Ten subjects with different metallic implants were scanned using SEMAC protocols, all with scan times below 11 minutes, as well as with standard spin echo methods. Results: The SNR using standard acceleration techniques is unaffected by the linear SEMAC reconstruction. In all cases with implants, accelerated SEMAC significantly reduced artifacts compared with standard imaging techniques, with no additional artifacts from acceleration techniques. The use of different contrast mechanisms allowed differentiation of fluid from other structures in several subjects. Conclusion: SEMAC imaging can be combined with standard echo-train imaging, parallel imaging, partial-Fourier imaging, and inversion recovery techniques to offer flexible image contrast with a dramatic reduction of metal-induced artifacts in scan times under 11 minutes. J. Magn. Reson. Imaging 2010;31:987–996. ©2010 Wiley-Liss, Inc.

In this chapter, we propose a new algorithm to solve Riccati equations and certain Hamilton—Jacobi—Bellman—Isaacs (HJBI) equations arising in \(H_{\infty}\) control. The need for the algorithm is motivated by the existence of \(H_{\infty}\) problems for which standard Riccati solvers break down, but which can be handled by the algorithm. By using our algorithm, we replace the problem of solving \(H_{\infty}\) Riccati equations or HJBI equations by the problem of solving a sequence of H 2 Riccati equations or Hamilton—Jacobi—Bellman (HJB) equations. The algorithms have some advantages such as a simple initialization, local quadratic rate of convergence, and a natural game theoretic interpretation. Some numerical examples are given to demonstrate advantages of our algorithm.

This paper deals with autoregressive models of singular spectra. The starting point is the assumption that there is available a transfer function matrix W(q) expressible in the form D−1(q)B for some tall constant matrix B of full column rank and with the determinantal zeros of D(q) all stable. It is shown that, even if this matrix fraction representation of W(q) is not coprime, W(q) has a coprime matrix fraction description of the form D−1(q)[I m 0]T . It is also shown how to characterize the equivalence class of all autoregressive matrix fraction descriptions of W(q), and how canonical representatives can be obtained. A canonical representative can be obtained with a minimal set of row degrees for the submatrix of D(q) obtained by deleting the first m rows. The paper also considers singular autoregressive descriptions of nested sequences of W p (q), p = p0, p0+1, …, where p denotes the number of rows, and shows that these canonical descriptions are nested, and contain a number of parameters growing linearly with p.

A novel dwell-time-switching based multiple model adaptive control (MMAC) scheme is proposed for the state feedback stabilization problem of a class of general nonlinear systems with nonlinear parameterization. One major contribution is that it has advanced Morse's dwell-time-switching from linear systems to a class of nonlinear systems. Another significant contribution is that it combines the idea of monitoring the adequacy of candidate models (in terms of their estimation performances) in most MMAC schemes with the idea of monitoring the performance of candidate controllers in unfalsified control. Moreover, sufficient conditions for closed-loop stability are established for the proposed dwell-time-switching based MMAC scheme when applied to the considered class of nonlinear systems. To fulfil those sufficient conditions, emphasis has been put on the design of multiple estimators, candidate controllers and monitoring signals. The carefully designed estimators, candidate controllers, and monitoring signals enable us to derive a finite time switching result and provide a characterization on the maximum number of switchings for the dwell-time-switching algorithm proposed. In order to show how the general design of our dwell-time-switching based MMAC scheme can be applied to a particular nonlinear system, a constructive design based on back-stepping is provided for the adaptive control problem for a special class of nonlinearly parameterized systems, which can satisfy all the sufficient conditions to ensure closed-loop stability.

In this paper, an iterative algorithm is proposed to solve discrete time algebraic Riccati equations (DARE) with a sign indefinite quadratic term, which arise from linear discrete time H ∞ control. By constructing two positive semidefinite matrix sequences, we obtain the stabilizing solution of the given DARE. The algorithm has a global convergence property.

Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method.

Health monitoring and timely fault diagnosis capabilities are essential requirements of many modern control engineering systems. Traditionally, these features have been of utmost importance in safety critical systems such as chemical industrials, civil/military aviation, or nuclear power plants, etc. However, in recent years, other factors have been playing a major role in recognizing the need for these capabilities in other complex systems. Generally speaking, the term fault is referred to any disturbances, errors, malfunctions or failures in the functional units that can lead to undesirable or intolerable behavior of a system. Some factors that have contributed to automatic fault detection, isolation, and accommodation (FDIA) problem to become an active area for research are: 1) the increasingly sophisticated industrial and consumer goods as a result of advances in electronics and computer technologies; 2) more interests in FDIA in manufacturing and process industries mainly due to economics and safety reasons; and 3) greater concerns over the air pollution and the environment in general.

An actuator fault diagnosis approach for affine nonlinear systems with unknown inputs is presented. The proposed approach is based on an input/output relation involving not only the inputs and the outputs but also the higher derivatives of the outputs. It employs the recently developed high-order sliding-mode robust differentiators (HOSMRDs) to estimate the higher derivatives of the outputs. Under certain conditions, the proposed actuator fault diagnosis approach can be used to detect, isolate, and estimate actuator faults. A nonlinear system with an unknown input is used as an example, and simulation results show that the proposed actuator fault diagnosis approach works well in terms of fault detection, isolation and estimation.

Introduction It was shown that MRI T1ρ images could be used to assess proteoglycan loss; therefore, it can be employed as a quantitative measure of intervertebral discs (IVD) degeneration, especially in early stages. To use T1ρ as a diagnostic or prognostic tool, however, one needs to assess the reproducibility of these measurements. Moreover, earlier studies showed diurnal changes in the IVDs during rest and loading conditions. Therefore, the goal of this work was to assess the reproducibility and diurnal changes in T1ρ measurements in the IVDs. Material and Methods This study was approved by the IRB and written consents were obtained from 12 adults (Age: Median [min–max]: 28.5 [20–41] years; F: 5, M: 7). Images were acquired using 3T MRI with CTL-spine coil. 3D MAPSS pulse sequence with spin-lock times (TSL) = [0, 20, 40, 60] ms, spin-lock amplitude = 400 Hz, and TR/TE = 6.5/1.6 ms, FOV = 310 mm and 3 mm/16-sagittal slices was used. T1ρ values were calculated using monoexponential fitting. For reproducibility analysis, the follow-up scans were acquired with a median delay of 112 days and at a different time of day (ToD). For analysis, an operator drew regions of interest (ROI) for nucleus pulposus (NP) and calculated the average ( Fig. 1 ). Data from 59 lumbar discs were used (one disc excluded due to a local artifact). Diurnal changes in T1ρ measurements in the NPs were analyzed using SPSSv21 with α = 0.05. Two variables were defined for analysis: (1) ToD difference between the two scans in hours (Median [min, max]: 2.2 [−3.6, 6.0] h). (2) T1ρ difference between two scans in milliseconds (mean ± SD: −0.093 ± 6.83 ms). Generalized estimating equations (GEE) were employed. To account for the day difference between the repeated scans, it was included in the model. To investigate reproducibility: (1) Bland–Altman plot was generated, (2) repeatability coefficient, RC (1.96·sqrt[2· σ2]); coefficient of variation, CV (σ/µ); and intraclass correlation coefficient, ICC (τ2/[τ2 + σ2]) were calculated. σ2 is the variability attributed to measurement error, µ is the grand average of measurements, and τ2 is the between subject disc variability. Results The time of day was a significant factor ( p = 0.035) in T1ρ measurements. However, the number of days between the repeated scans was not significant ( p = 0.852). Fig. 2 shows the difference between the repeated T1ρ measurements plotted against the number of days between the scans. Interestingly, T1ρ values in the NP increased during the day. The Bland–Altman plot is shown in Fig. 3 . Calculated repeatability coefficients are RC = 13.4 ms, CV = 0.057, and ICC = 0.90. Conclusion Diurnal changes were a small but significant factor in T1ρ measurements. Moreover, there were no significant changes in T1ρ measurements in the repeated scans since the intervals between the longitudinal scans were relatively short compared with the typical time scale of typical disc degeneration processes. The CV of Bland–Altman test showed that the standard deviation of repeated T1ρ measurements was approximately 5.7% of the average T1ρ value. Moreover, ICC parameter showed that the variation in repeated T1ρ measurements was small compared with between subject variations. Acknowledgment This study is supported by AOSpine research grant. [Figure: see text][Figure: see text][Figure: see text]

This paper considers fault detection, isolation and estimation problems for a class of systems with unknown inputs which may not satisfy certain matching conditions. Such conditions are often required for existence of sliding mode observers (SMO). In cases when the unmatched unknown inputs are present, no SMO could be designed such that the state estimation error is invariant to all the unknown inputs, and therefore, existing SMO based fault diagnosis schemes can not be employed. In this article we propose a novel approach to design of output estimators using sliding mode technique. The estimators are then used for fault detection, isolation, and estimation. First, a canonical representation of the system which decouples the matched and unmatched unknown inputs is derived. Second, based on this canonical form, output estimators using sliding mode technique are proposed, and their properties are investigated. Third, a fault diagnosis scheme is developed to carry out the fault detection, isolation, and estimation tasks. Finally, an example is given to show the effectiveness of the output estimator based fault diagnosis scheme in terms of fault detection, isolation and estimation.

Field inhomogeneity and susceptibility variations, coupled with a long readout, can result in image blurring in spiral imaging. Many correction methods based on a priori off-resonance information, such as an acquired field map, have been proposed in the literature. Automatic off-resonance correction methods are alternative approaches that estimate a field map from the image data themselves. In this paper we propose a fast automatic off-resonance correction method that performs linear correction without acquiring a field map. The method requires only about two times the total computation time compared to image reconstruction by gridding. It can also be used in combination with a full field map automatic off-resonance correction method to increase the extent of correction. The method is demonstrated by in vivo coronary artery imaging.

In designing variable structure controllers when the upper bounding function for the matched system uncertainty is not known, the controller design remains to be a challenge. The main purpose of this paper is to solve this problem for a class of uncertain systems with matched uncertainties. To this end, a variable structure controller is proposed whose novelty lies in the form of the controller structure and also the mechanism introduced to update the controller's gain. Unlike most existing variable structure controllers, the new design does not require the upper bounding function for the uncertainty to be exactly known (for the bounded uncertainty case, the knowledge of the upper bound is not needed). It is proved that asymptotic stability of closed-loop systems can be guaranteed globally. One drawback for this controller is that the controller gain may go unbounded if the noises or other system uncertainties are not considered and are present. The other drawback is the well known controller chattering problem. To deal with these drawbacks, we modify the controller's gain update law and replace its discontinuous term with a continuous approximation, and hence propose a modified variable structure controller. With the modified variable structure controller, all the closed-loop signals are guaranteed to be bounded and the states can be driven to an arbitrarily small neighborhood of the origin. The price paid for this is the loss of asymptotic stability. Inspired by the equivalent control concept, a method for estimating the uncertainty is also derived when the modified variable structure controller is applied. Simulation examples are given to show the effectiveness of the controller and uncertainty estimation scheme.

This paper investigates the actuator fault isolation problem for a class of linear systems. To isolate the actuator faults amongst all possibilities, we first relate each possibility to a faulty model, then for each possible faulty model, a sliding mode observer (SMO) is designed. It is proved that, for the faulty model corresponds to the faulty actuators, the SMO designed can ensure the related state estimation error and thus the output estimation error goes to zero. It is also shown that, for all other possible faulty models, none of SMOs can make the related output estimation errors be zero. Based on the results proved, we define the residuals as the square of the magnitudes of the output estimation errors resulting from all possible faulty models. If only residual goes to zero, then it corresponds to the faulty actuators, and actuator fault isolation is done. The use of SMOs has two advantages. One is that it can deal with any types of bounded actuator faults (constant and non-constant faults); the other is that it can provide a method to estimate the faults. The actuator fault isolation method is tested on a research civil aircraft model (RCAM), and simulation results show that it can isolate various types of actuator faults effectively

For a class of linear switched control systems (LSCSs) with unknown inputs, we study in this paper the unknown input observer (UIO) design problem. To design a full (reduced) order UIO, we first design for each subsystem a full (reduced) order UIO, and then we construct a full (reduced) order UIO for the whole system via picking the corresponding full (reduced) order UIO of the active subsystem according to the switching rule. Sufficient conditions for the existence of both full order and reduced order UIOs are derived. The design procedures of full order UIOs and reduced order UIOs are presented. Several stability results regarding to the state estimation error dynamics are established. Examples are given to show how to design UIOs for particular switched systems, and simulation results are given to show the effect of the designed UIOs.

Full and reduced order observers for a class of linear switched control systems (LSCS) are studied in this paper. A "sub-observer" is first designed for the i-th subsystem. Then, a switching observer for an LSCS is constructed by simply picking the i-th sub-observer whenever the i-th subsystem is active. In the case of a full order observer, when subsystems are detectable, the state estimation error can coverage to zero if the dwell time is large enough. Under certain conditions, the state estimation error may even converge to zero exponentially for arbitrary switching. Unlike classical linear systems where full order and reduced order observer can be designed under the same conditions, the design of a reduced order observer for an LSCS, besides detectability/observability, requires additional condition that the gains for all reduced order sub-observers need to be chosen the same. In such a case, similar stability results as those of full order observers are obtained for reduced order observers. Finally, examples and simulation results are given to show the effectiveness of the proposed observers.