Feedback design for regularizing descriptor systems

This paper surveys numerical techniques for the regularization of descriptor (generalized state-space) systems by proportional and derivative feedback. We review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the Weierstraß canonical form. Three condensed forms display the controllability and observability properties of a descriptor system. The condensed forms are obtained through orthogonal equivalence transformations and rank decisions, so they may be computed by numerically stable algorithms. In addition, the condensed forms display whether a descriptor system is regularizable, i.e., when the system pencil can be made to be regular by derivative and/or proportional output feedback, and, if so, what index can be achieved. Also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Regularization of descriptor systems by output feedback

Conditions are given under which a descriptor, or generalized state-space system can be regularized by output feedback. It is shown that under these conditions, proportional and derivative output feedback controls can be constructed such that the closed-loop system is regular and has index at most one. This property ensures the solvability of the resulting system of dynamic-algebraic equations. A reduced form is given that allows the system properties as well as the feedback to be determined. 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.

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.

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.

Radar scattering from ice aggregates using the horizontally aligned oblate spheroid approximation

The assumed relationship between ice particle mass and size is profoundly important in radar retrievals of ice clouds, but, for millimeter-wave radars, shape and preferred orientation are important as well. In this paper the authors first examine the consequences of the fact that the widely used ‘‘Brown and Francis’’ mass–size relationship has often been applied to maximumparticle dimension observed by aircraftDmax rather than to the mean of the particle dimensions in two orthogonal directions Dmean, which was originally used by Brown and Francis. Analysis of particle images reveals that Dmax ’ 1.25Dmean, and therefore, for clouds for which this mass–size relationship holds, the consequences are overestimates of ice water content by around 53% and of Rayleigh-scattering radar reflectivity factor by 3.7 dB. Simultaneous radar and aircraft measurements demonstrate that much better agreement in reflectivity factor is provided by using this mass–size relationship with Dmean. The authors then examine the importance of particle shape and fall orientation for millimeter-wave radars. Simultaneous radar measurements and aircraft calculations of differential reflectivity and dual-wavelength ratio are presented to demonstrate that ice particles may usually be treated as horizontally aligned oblate spheroids with an axial ratio of 0.6, consistent with them being aggregates. An accurate formula is presented for the backscatter cross section apparent to a vertically pointing millimeter-wave radar on the basis of a modified version of Rayleigh–Gans theory. It is then shown that the consequence of treating ice particles as Mie-scattering spheres is to substantially underestimate millimeter-wave reflectivity factor when millimeter-sized particles are present, which can lead to retrieved ice water content being overestimated by a factor of 4.h

Slideshow by POLLYFIBRE

A live work where digital and analogue media collide. This work uses the Internet as a central point of departure in that the script is taken from the Wikipedia entry for the word 'slideshow'. Words are randomly extracted and transferred onto photographic 35mm slide to be projected with analogue carousel slide projectors taking the audience into a visual wordplay, from Google to PowerPoint presentation. The sound of projectors is manipulated gradually into a clashing, confrontational, digital/analogue crescendo. 'Slideshow' investigates how information is sourced, navigated and considered in a culture of accelerating mediation. It posits the notion of a post-digital era in which we are increasingly faced with challenging questions of authenticity and authority.

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.

A neurofuzzy classifier for two class problems

A neurofuzzy classifier identification algorithm is introduced for two class problems. The initial fuzzy base construction is based on fuzzy clustering utilizing a Gaussian mixture model (GMM) and the analysis of covariance (ANOVA) decomposition. The expectation maximization (EM) algorithm is applied to determine the parameters of the fuzzy membership functions. Then neurofuzzy model is identified via the supervised subspace orthogonal least square (OLS) algorithm. Finally a logistic regression model is applied to produce the class probability. The effectiveness of the proposed neurofuzzy classifier has been demonstrated using a real data set.

A mechanism for Atlantic multidecadal variability in the Kiel Climate Model

Atlantic Multidecadal Variability (AMV) is investigated in a millennial control simulation with the Kiel Climate Model (KCM), a coupled atmosphere–ocean–sea ice model. An oscillatory mode with approximately 60 years period and characteristics similar to observations is identified with the aid of three-dimensional temperature and salinity joint empirical orthogonal function analysis. The mode explains 30 % of variability on centennial and shorter timescales in the upper 2,000 m of the North Atlantic. It is associated with changes in the Atlantic Meridional Overturning Circulation (AMOC) of ±1–2 Sv and Atlantic Sea Surface Temperature (SST) of ±0.2 °C. AMV in KCM results from an out-of-phase interaction between horizontal and vertical ocean circulation, coupled through Irminger Sea convection. Wintertime convection in this region is mainly controlled by salinity anomalies transported by the Subpolar Gyre (SPG). Increased (decreased) dense water formation in this region leads to a stronger (weaker) AMOC after 15 years, and this in turn leads to a weaker (stronger) SPG after another 15 years. The key role of salinity variations in the subpolar North Atlantic for AMV is confirmed in a 1,000 year long simulation with salinity restored to model climatology: No low frequency variations in convection are simulated, and the 60 year mode of variability is absent.

File Transfer Protocol

The discourse surrounding the virtual has moved away from the utopian thinking accompanying the rise of the Internet in the 1990s. The Cyber-gurus of the last decades promised a technotopia removed from materiality and the confines of the flesh and the built environment, a liberation from old institutions and power structures. But since then, the virtual has grown into a distinct yet related sphere of cultural and political production that both parallels and occasionally flows over into the old world of material objects. The strict dichotomy of matter and digital purity has been replaced more recently with a more complex model where both the world of stuff and the world of knowledge support, resist and at the same time contain each other. Online social networks amplify and extend existing ones; other cultural interfaces like youtube have not replaced the communal experience of watching moving images in a semi-public space (the cinema) or the semi-private space (the family living room). Rather the experience of viewing is very much about sharing and communicating, offering interpretations and comments. Many of the web’s strongest entities (Amazon, eBay, Gumtree etc.) sit exactly at this juncture of applying tools taken from the knowledge management industry to organize the chaos of the material world along (post-)Fordist rationality. Since the early 1990s there have been many artistic and curatorial attempts to use the Internet as a platform of producing and exhibiting art, but a lot of these were reluctant to let go of the fantasy of digital freedom. Storage Room collapses the binary opposition of real and virtual space by using online data storage as a conduit for IRL art production. The artworks here will not be available for viewing online in a 'screen' environment but only as part of a downloadable package with the intention that the exhibition could be displayed (in a physical space) by any interested party and realised as ambitiously or minimally as the downloader wishes, based on their means. The artists will therefore also supply a set of instructions for the physical installation of the work alongside the digital files. In response to this curatorial initiative, File Transfer Protocol invites seven UK based artists to produce digital art for a physical environment, addressing the intersection between the virtual and the material. The files range from sound, video, digital prints and net art, blueprints for an action to take place, something to be made, a conceptual text piece, etc. About the works and artists: Polly Fibre is the pseudonym of London-based artist Christine Ellison. Ellison creates live music using domestic devices such as sewing machines, irons and slide projectors. Her costumes and stage sets propose a physical manifestation of the virtual space that is created inside software like Photoshop. For this exhibition, Polly Fibre invites the audience to create a musical composition using a pair of amplified scissors and a turntable. http://www.pollyfibre.com John Russell, a founding member of 1990s art group Bank, is an artist, curator and writer who explores in his work the contemporary political conditions of the work of art. In his digital print, Russell collages together visual representations of abstract philosophical ideas and transforms them into a post apocalyptic landscape that is complex and banal at the same time. www.john-russell.org The work of Bristol based artist Jem Nobel opens up a dialogue between the contemporary and the legacy of 20th century conceptual art around questions of collectivism and participation, authorship and individualism. His print SPACE concretizes the representation of the most common piece of Unicode: the vacant space between words. In this way, the gap itself turns from invisible cipher to sign. www.jemnoble.com Annabel Frearson is rewriting Mary Shelley's Frankenstein using all and only the words from the original text. Frankenstein 2, or the Monster of Main Stream, is read in parts by different performers, embodying the psychotic character of the protagonist, a mongrel hybrid of used language. www.annabelfrearson.com Darren Banks uses fragments of effect laden Holywood films to create an impossible space. The fictitious parts don't add up to a convincing material reality, leaving the viewer with a failed amalgamation of simulations of sophisticated technologies. www.darrenbanks.co.uk FIELDCLUB is collaboration between artist Paul Chaney and researcher Kenna Hernly. Chaney and Hernly developed together a project that critically examines various proposals for the management of sustainable ecological systems. Their FIELDMACHINE invites the public to design an ideal agricultural field. By playing with different types of crops that are found in the south west of England, it is possible for the user, for example, to create a balanced, but protein poor, diet or to simply decide to 'get rid' of half the population. The meeting point of the Platonic field and it physical consequences, generates a geometric abstraction that investigates the relationship between modernist utopianism and contemporary actuality. www.fieldclub.co.uk Pil and Galia Kollectiv, who have also curated the exhibition are London-based artists and run the xero, kline & coma gallery. Here they present a dialogue between two computers. The conversation opens with a simple text book problem in business studies. But gradually the language, mimicking the application of game theory in the business sector, becomes more abstract. The two interlocutors become adversaries trapped forever in a competition without winners. www.kollectiv.co.uk

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.

Elastic-net prefiltering for two-class classification

A two-stage linear-in-the-parameter model construction algorithm is proposed aimed at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage which constructs a sparse linear-in-the-parameter classifier. The prefiltering stage is a two-level process aimed at maximizing a model's generalization capability, in which a new elastic-net model identification algorithm using singular value decomposition is employed at the lower level, and then, two regularization parameters are optimized using a particle-swarm-optimization algorithm at the upper level by minimizing the leave-one-out (LOO) misclassification rate. It is shown that the LOO misclassification rate based on the resultant prefiltered signal can be analytically computed without splitting the data set, and the associated computational cost is minimal due to orthogonality. The second stage of sparse classifier construction is based on orthogonal forward regression with the D-optimality algorithm. Extensive simulations of this approach for noisy data sets illustrate the competitiveness of this approach to classification of noisy data problems.