Regularization of Descriptor Systems by Derivative and Proportional State Feedback

For linear multivariable time-invariant continuous or discrete-time singular systems it is customary to use a proportional feedback control in order to achieve a desired closed loop behaviour. Derivative feedback is rarely considered. This paper examines how derivative feedback in descriptor systems can be used to alter the structure of the system pencil under various controllability conditions. It is shown that derivative and proportional feedback controls can be constructed such that the closed loop system has a given form and is also regular and has index at most 1. This property ensures the solvability of the resulting system of dynamic-algebraic equations. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. The problem of pole placement with derivative feedback alone and in combination with proportional state feedback is also investigated. A computational algorithm for improving the “conditioning” of the regularized closed loop system is derived.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Minimum norm regularization of descriptor systems by mixed output feedback

We study the regularization problem for linear, constant coefficient descriptor systems Ex' = Ax+Bu, y1 = Cx, y2 = Γx' by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and E+BGΓ has a desired rank, i.e., there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω 2 u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.

An elastic net orthogonal forward regression algorithm

In this paper we propose an efficient two-level model identification method for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularization parameters in the elastic net are optimized using a particle swarm optimization (PSO) algorithm at the upper level by minimizing the leave one out (LOO) mean square error (LOOMSE). Illustrative examples are included to demonstrate the effectiveness of the new approaches.

On the drivers of inter-annual and decadal rainfall variability in Queensland, Australia

Queensland experiences considerable inter-annual and decadal rainfall variability, which impacts water-resource management, agriculture and infrastructure. To understand the mechanisms by which large-scale atmospheric and coupled air–sea processes drive these variations, empirical orthogonal teleconnection (EOT) analysis is applied to 1900–2010 seasonal Queensland rainfall. Fields from observations and the 20th Century Reanalysis are regressed onto the EOT timeseries to associate the EOTs with large-scale drivers. In winter, spring and summer the leading, state-wide EOTs are highly correlated with the El Nino–Southern Oscillation (ENSO); the Inter-decadal Pacific Oscillation modulates the summer ENSO teleconnection. In autumn, the leading EOT is associated with locally driven, late-season monsoon variations, while ENSO affects only tropical northern Queensland. Examining EOTs beyond the first, southeastern Queensland and the Cape York peninsula emerge as regions of coherent rainfall variability. In the southeast, rainfall anomalies respond to the strength and moisture content of onshore easterlies, controlled by Tasman Sea blocking. The summer EOT associated with onshore flow and blocking has been negative since 1970, consistent with the observed decline in rainfall along the heavily populated coast. The southeastern Queensland EOTs show considerable multi-decadal variability, which is independent of large-scale drivers. Summer rainfall in Cape York is associated with tropical-cyclone activity.

Preferred orientation in an angled intercalation site of a chloro-substituted lambda- [Ru(TAP)2(dppz)]2+ complex bound to d(TCGGCGCCGA)2

The crystal structure of the ruthenium DNA ‘light-switch’ complex -[Ru(TAP)2(11-Cl-dppz)]2+ (TAP = tetraazaphenanthrene, dppz = dipyrido[3,2-a':2',3'-c]phenazine)) bound to the oligonucleotide duplex d(TCGGCGCCGA)2 is reported. The synthesis of the racemic ruthenium complex is described for the first time, and the racemate was used in this study. The crystal structure, at atomic resolution (1.0 Å), shows one ligand as a wedge in the minor groove, resulting in the 51 kinking of the double helix, as with the parent lambda-[Ru(TAP)2(dppz)]2+. Each complex binds to one duplex by intercalation of the dppz ligand and also by semi-intercalation of one of the orthogonal TAP ligands into a second symmetrically equivalent duplex. The 11-Cl substituent binds with the major component (66%) oriented with the 11-chloro substituent on the purine side of the terminal step of the duplex.

Isomap nonlinear dimensionality reduction and bimodality of Asian monsoon convection

It is known that the empirical orthogonal function method is unable to detect possible nonlinear structure in climate data. Here, isometric feature mapping (Isomap), as a tool for nonlinear dimensionality reduction, is applied to 1958–2001 ERA-40 sea-level pressure anomalies to study nonlinearity of the Asian summer monsoon intraseasonal variability. Using the leading two Isomap time series, the probability density function is shown to be bimodal. A two-dimensional bivariate Gaussian mixture model is then applied to identify the monsoon phases, the obtained regimes representing enhanced and suppressed phases, respectively. The relationship with the large-scale seasonal mean monsoon indicates that the frequency of monsoon regime occurrence is significantly perturbed in agreement with conceptual ideas, with preference for enhanced convection on intraseasonal time scales during large-scale strong monsoons. Trend analysis suggests a shift in concentration of monsoon convection, with less emphasis on South Asia and more on the East China Sea.

Influence of the quasi-biennial oscillation on the extratropical winter stratosphere in an atmospheric general circulation model and in reanalysis data

The interannual variability of the stratospheric polar vortex during winter in both hemispheres is observed to correlate strongly with the phase of the quasi-biennial oscillation (QBO) in tropical stratospheric winds. It follows that the lack of a spontaneously generated QBO in most atmospheric general circulation models (AGCMs) adversely affects the nature of polar variability in such models. This study examines QBO–vortex coupling in an AGCM in which a QBO is spontaneously induced by resolved and parameterized waves. The QBO–vortex coupling in the AGCM compares favorably to that seen in reanalysis data [from the 40-yr ECMWF Re-Analysis (ERA-40)], provided that careful attention is given to the definition of QBO phase. A phase angle representation of the QBO is employed that is based on the two leading empirical orthogonal functions of equatorial zonal wind vertical profiles. This yields a QBO phase that serves as a proxy for the vertical structure of equatorial winds over the whole depth of the stratosphere and thus provides a means of subsampling the data to select QBO phases with similar vertical profiles of equatorial zonal wind. Using this subsampling, it is found that the QBO phase that induces the strongest polar vortex response in early winter differs from that which induces the strongest late-winter vortex response. This is true in both hemispheres and for both the AGCM and ERA-40. It follows that the strength and timing of QBO influence on the vortex may be affected by the partial seasonal synchronization of QBO phase transitions that occurs both in observations and in the model. This provides a mechanism by which changes in the strength of QBO–vortex correlations may exhibit variability on decadal time scales. In the model, such behavior occurs in the absence of external forcings or interannual variations in sea surface temperatures.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Analysis and compensation of power amplifier nonlinearity in MIMO transmit diversity systems

The nonlinearity of high-power amplifiers (HPAs) has a crucial effect on the performance of multiple-input-multiple-output (MIMO) systems. In this paper, we investigate the performance of MIMO orthogonal space-time block coding (OSTBC) systems in the presence of nonlinear HPAs. Specifically, we propose a constellation-based compensation method for HPA nonlinearity in the case with knowledge of the HPA parameters at the transmitter and receiver, where the constellation and decision regions of the distorted transmitted signal are derived in advance. Furthermore, in the scenario without knowledge of the HPA parameters, a sequential Monte Carlo (SMC)-based compensation method for the HPA nonlinearity is proposed, which first estimates the channel-gain matrix by means of the SMC method and then uses the SMC-based algorithm to detect the desired signal. The performance of the MIMO-OSTBC system under study is evaluated in terms of average symbol error probability (SEP), total degradation (TD) and system capacity, in uncorrelated Nakagami-m fading channels. Numerical and simulation results are provided and show the effects on performance of several system parameters, such as the parameters of the HPA model, output back-off (OBO) of nonlinear HPA, numbers of transmit and receive antennas, modulation order of quadrature amplitude modulation (QAM), and number of SMC samples. In particular, it is shown that the constellation-based compensation method can efficiently mitigate the effect of HPA nonlinearity with low complexity and that the SMC-based detection scheme is efficient to compensate for HPA nonlinearity in the case without knowledge of the HPA parameters.

Joint compensation of multiple RF impairments in MIMO STBC systems

In this paper, we propose a compensation method for the joint effect of high-power amplifier (HPA) nonlinearity, in-phase/quadrature-phase (I/Q) imbalance and crosstalk in multiple-input multiple-output (MIMO) orthogonal space-time block coding (OSTBC) systems. The performance of the MIMO OSTBC equipped with the proposed compensation mechanism is evaluated in terms of average symbol error probability and system capacity, in Rayleigh fading channels. Numerical results are provided and show the effects on performance of several system parameters, namely, the HPA parameters, image-leakage ratio, crosstalk, numbers of antennas, and phase-shift keying modulation order.

Surface water temperature observations of large lakes by optimal estimation

Optimal estimation (OE) and probabilistic cloud screening were developed to provide lake surface water temperature (LSWT) estimates from the series of (advanced) along-track scanning radiometers (ATSRs). Variations in physical properties such as elevation, salinity, and atmospheric conditions are accounted for through the forward modelling of observed radiances. Therefore, the OE retrieval scheme developed is generic (i.e., applicable to all lakes). LSWTs were obtained for 258 of Earth's largest lakes from ATSR-2 and AATSR imagery from 1995 to 2009. Comparison to in situ observations from several lakes yields satellite in situ differences of −0.2 ± 0.7 K for daytime and −0.1 ± 0.5 K for nighttime observations (mean ± standard deviation). This compares with −0.05 ± 0.8 K for daytime and −0.1 ± 0.9 K for nighttime observations for previous methods based on operational sea surface temperature algorithms. The new approach also increases coverage (reducing misclassification of clear sky as cloud) and exhibits greater consistency between retrievals using different channel–view combinations. Empirical orthogonal function (EOF) techniques were applied to the LSWT retrievals (which contain gaps due to cloud cover) to reconstruct spatially and temporally complete time series of LSWT. The new LSWT observations and the EOF-based reconstructions offer benefits to numerical weather prediction, lake model validation, and improve our knowledge of the climatology of lakes globally. Both observations and reconstructions are publically available from http://hdl.handle.net/10283/88.

A modified PNN algorithm with optimal PD modeling using the orthogonal least squares method

In this paper a modified algorithm is suggested for developing polynomial neural network (PNN) models. Optimal partial description (PD) modeling is introduced at each layer of the PNN expansion, a task accomplished using the orthogonal least squares (OLS) method. Based on the initial PD models determined by the polynomial order and the number of PD inputs, OLS selects the most significant regressor terms reducing the output error variance. The method produces PNN models exhibiting a high level of accuracy and superior generalization capabilities. Additionally, parsimonious models are obtained comprising a considerably smaller number of parameters compared to the ones generated by means of the conventional PNN algorithm. Three benchmark examples are elaborated, including modeling of the gas furnace process as well as the iris and wine classification problems. Extensive simulation results and comparison with other methods in the literature, demonstrate the effectiveness of the suggested modeling approach.

EOF analysis of three records of sea-ice concentration spanning the last 30 years

Several continuous observational datasets of Artic sea-ice concentration are currently available that cover the period since the advent of routine satellite observations. We report on a comparison of three sea-ice concentration datasets. These are the National Ice Center charts, and two passive microwave radiometer datasets derived using different approaches: the NASA team and Bootstrap algorithms. Empirical orthogonal function (EOF) analyses were employed to compare modes of variability and their consistency between the datasets. The analysis was motivated by the need for a reliable, realistic sea ice climatology for use in climate model simulations, for which both the variability and absolute values of extent and concentration are important. We found that, while there are significant discrepancies in absolute concentrations, the major modes of variability derived from all records were essentially the same.