Design of reduced-order scalar functional observers

In the existing literature, the existence conditions and design procedures for scalar functional observers are available for the cases where the observers’ order p is either p=1 or p=(v-1), where v is the observability index of the matrix pair (C,A). Therefore, if an observer with an order p=1 does not exist, the other available option is to use a higher order observer with p=(v-1). This paper shows that there exists another option that can be used to design scalar linear functional observers of the order lower than the well-known upper bound (v-1). The paper provides the existence conditions and a design procedure for scalar functional observers of order 0≤ p ≤2, and demonstrates the presented results with a numerical example.

Design of scalar functional observers of order less than (v-1)

This paper presents a new method of designing scalar functional observers of order less than the well-known upper bound (ν - 1). A condition for the existence of observers of order p where 1 ≤ p ≤ (ν - 1) is given. A simple and effective algorithm for solving the constrained generalized Sylvester equation is proposed. Several numerical examples are given to illustrate the attractiveness of the design algorithm.

Existence and design of reduced-order scalar functional observers

In the existing literature, the existence conditions and design procedures for scalar functional observers are available for the cases where the observers’ order p is either p=1 or p=(v-1), where v is the observability index of the matrix pair (C,A). Therefore, if an observer with an order p=1 does not exist, the other option is to use a high-order observer with p=(v-1). This paper provides the existence conditions and a design procedure for scalar functional observers of order 0≤p≤2, and demonstrates the presented results with a numerical example. where K, M, E, H and G are constant matrices to be designed. The problem of observing a scalar functional or multi functionals (z(t)∈Rk , k>1) of the state vector has been the subject of numerous papers, and different algorithms have been proposed (see, [1]-[13] and references therein). There are also papers that deal with the order reduction of multi-dimensional functional observers [9,10,12,13]. For scalar functional observers, a well-known Luenberger’s classic result [1] provides an upper bound on the order with p=(v-1). It is interesting to note here that, except for a recent result of Darouach [12,13], little results have been reported on the order reduction for scalar functional observers.

New scalar politics : implications for education policy

This paper argues that globalisation has implications for research and theory in the social sciences, demanding that the social no longer be seen as homologous with nation, but also linked to postnational or global fields. This situation has theoretical and methodological implications for comparative education specifically focused on education policy, which traditionally has taken the nation-state as the unit of analysis, and also worked with 'methodological nationalism'. The paper argues that globalisation has witnessed a rescaling of educational politics and policymaking and relocated some political authority to an emergent global education policy field, with implications for the functioning of national political authority and national education policy fields. This rescaling and this reworking of political authority are illustrated through two cases: the first is concerned with the impact of a globalised policy discourse of the ‘knowledge economy’ proselytised by the OECD and its impact in Australian policy developments; the second is concerned explicitly with the constitution of a global education policy field as a commensurate space of equivalence, as evidenced in the OECD’s PISA and educational indicators work and their increasing global coverage. The paper indicatively utilises Bourdieu’s ‘thinking tools’ to understand the emergent global education policy field and suggest these are very useful for doing comparative education policy analysis.

The determination of all syzygies for the dependent polynomial invariants of the Riemann tensor. I. Pure Ricci and pure Weyl invariants

In this paper, we shall consider all pure Ricci and pure Weyl scalar invariants of any degree, in a four-dimensional Lorentzian space. We present a general graph-theoretic based reduction algorithm which decomposes, using syzygies, any pure invariant in terms of the independent base invariants {r₁,r₂,r₃} or {w₁,w₂}

The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor

We continue our analysis of the polynomial invariants of the Riemann tensor in a four-dimensional Lorentzian space. We concentrate on the mixed invariants of even degree in the Ricci spinor Φ_ABȦḂ and show how, using constructive graph-theoretic methods, arbitrary scalar contractions between copies of the Weyl spinor ψ_ABCD, its conjugate ψ_ȦḂĊḊ and an even number of Ricci spinors can be expressed in terms of paired contractions between these spinors. This leads to an algorithm for the explicit expression of dependent invariants as polynomials of members of the complete set. Finally, we rigorously prove that the complete set as given by Sneddon [J. Math. Phys. 39, 1659-1679 (1998)] for this case is both complete and minimal.

Multi-wavelets from B-spline super-functions with approximation order

Approximation order is an important feature of all wavelets. It implies that polynomials up to degree p−1 are in the space spanned by the scaling function(s). In the scalar case, the scalar sum rules determine the approximation order or the left eigenvectors of the infinite down-sampled convolution matrix H determine the combinations of scaling functions required to produce the desired polynomial. For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix H_f; a finite portion of H determines the combinations of scaling functions that produce the desired superfunction from which polynomials of desired degree can be reproduced. The superfunctions in this work are taken to be B-splines. However, any refinable function can serve as the superfunction. The condition of approximation order is derived and new, symmetric, compactly supported and orthogonal multi-wavelets with approximation orders one, two, three and four are constructed.

Disturbance decoupled observers for systems with unknown inputs

This note deals with the design of reduced-order disturbance decoupled scalar functional observers for linear systems with unknown inputs. Based on a parametric approach, existence conditions are derived and a design procedure for finding reduced-order scalar functional observers is given. The derived existence conditions are relaxed and the procedure can find first-order disturbance decoupled scalar functional observers for some cases where the number of unknown inputs is more than the number of outputs. Also, the observer matching condition, which is the necessary requirement for the design of state observers for linear systems with unknown inputs, is not required. Numerical examples are given to illustrate the attractiveness of the proposed design method.

Polar luminance measurements : a direction in qualifying modelling

Through experimentation, it is revealed that the polar luminance method is capable of measuring the modelling of an object effectively in scenarios where the vector/scalar ratio is deficient. It is suggested that polar luminance measurement is a new direction for the measurement of modelling.

The mediatization of the knowledge based economy : an Australian field based account

This paper presents an empirical account of mediatization from a Bourdieuian perspective, based on the development of a number of new concepts, such as cross-field effects and the rescaling of such effects as linked to processes of globalization. Built on an Australian empirical case relating to educational policy and the knowledge based economy, this paper argues that mediatization can be understood in relation to the cross-field effects of different fields of journalism on subsequent fields, which have their genesis in forms of practice that cross different social fields. Specifically, the case analysis details interactions between the field of print journalism and the field of policy over the course of an Australian science capability review, chaired by the then chief scientist, Dr Robin Batterham, which led to Australia adopting a national version of the knowledge economy. The empirical case also leads us to consider the impact of both global and national fields of journalism on fields of educational policy in relation to mediatization.

Guided wave propagation and spectral element method for debonding damage assessment in RC structures

A concrete–steel interface spectral element is developed to study the guided wave propagation along the steel rebar in the concrete. Scalar damage parameters characterizing changes in the interface (debonding damage) are incorporated into the formulation of the spectral finite element that is used for damage detection of reinforced concrete structures. Experimental tests are carried out on a reinforced concrete beam with embedded piezoelectric elements to verify the performance of the proposed model and algorithm. Parametric studies are performed to evaluate the effect of different damage scenarios on wave propagation in the reinforced concrete structures. Numerical simulations and experimental results show that the method is effective to model wave propagation along the steel rebar in concrete and promising to detect damage in the concrete–steel interface.

Construction of wavelets and multiwavelets basis : a generalized method

Multiwavelets are wavelets with multiplicity r, that is r scaling functions and r wavelets, which define multiresolution analysis similar to scalar wavelets. They are advantageous over scalar wavelets since they simultaneously posse symmetry and orthogonality. In this work, a new method for constructing multiwavelets with any approximation order is presented. The method involves the derivation of a matrix equation for the desired approximation order. The condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors give the combinations of scaling functions required to reconstruct the desired spline or super function. The method is demonstrated by constructing a specific class of symmetric and non-symmetric multiwavelets with different approximation orders, which include Geranimo-Hardin-Massopust (GHM), Daubechies and Alperts like multi-wavelets, as parameterized solutions. All multi-wavelets constructed in this work, posses the good properties of orthogonality, approximation order and short support.

Existence conditions for unknown input functional observers

This article presents necessary and sufficient conditions for the existence and design of an unknown input Functional observer. The existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions. The existence of the observer does not require the satisfaction of the observer matching condition (i.e. Equation (16) in Hou and Muller 1992, ‘Design of Observers for Linear Systems with Unknown Inputs’, IEEE Transactions on Automatic Control, 37, 871–875), is not limited to estimating scalar functionals and allows for arbitrary pole placement. The proposed observer always exists when a state observer exists for the unknown input system, and furthermore, the proposed observer can exist even in some instances when an unknown input state observer does not exist.

Cross-cultural adaption of the Health Educaiton Impact Questionnaire: experimental study showed expert committee, not back-translation, added value

Objectives
To assess the contribution of back-translation and expert committee to the content and psychometric properties of a translated multidimensional questionnaire.

Study Design and Setting
Recommendations for questionnaire translation include back-translation and expert committee, but their contribution to measurement properties is unknown. Four English to French translations of the Health Education Impact Questionnaire were generated with and without committee or back-translation. Face validity, acceptability, and structural properties were compared after random assignment to people with rheumatoid arthritis (N = 1,168), chronic renal failure (N = 2,368), and diabetes (N = 538). For face validity, 15 bilingual people compared translations quality with the original. Psychometric properties were examined using confirmatory factor analysis (metric and scalar invariance) and item response theory.

Results
Qualitatively, there were five types of translation errors: style, intensity, frequency/time frame, breadth, and meaning. Bilingual assessors ranked best the translations with committee (P = 0.0026). All translations had good structural properties (root mean square error of approximation <0.05; comparative fit index [CFI], ≥0.899; and Tucker–Lewis index, ≥0.889). Full measurement invariance was observed between translations (ΔCFI ≤ 0.01) with metric invariance between translations and original (lowest ΔCFI = 0.022 between fully constrained models and models with free intercepts). Item characteristic curve analyses revealed no significant differences.

Conclusion
This is the first experimental evidence that back-translation has moderate impact, whereas expert committee helps to ensure accurate content.