Feedback diagonal canonical form and its application to stabilization of nonlinear systems

~~Feedback diagonal canonical form and its application to stabilization of nonlinear systems1. Aeyels, D., Stabilization of a class of non-linear systems by a smooth feedback control, Sys. Contr. Lett., 1985, 5: 289-294. 2. Behtash, S., Dastry, D., Stabilization of non-linear systems with uncontrollable linearization, IEEE Trans. Aut. Contr., 1988, 33(6): 585-590. 3. Byrnes, C. I., Isidori, A., Willems, J. C., Passivity, feedback equivalence, and the global stabilization of …     

Parameterization and identification of multivariable state-space systems: A canonical approach

In this paper, the problem of determining a canonical state-space representation for multivariable systems is revisited. A method is derived to build a canonical state-space representation directly from data generated by a linear time-invariant system. Contrary to the classic construction methods of canonical parameterizations, the technique developed in this paper does not assume the availability of any observability or controllability indices. However, it requires the -matrix of any minimal realization of the system to be non-derogatory. A subspace-based identification algorithm is also introduced to estimate such a canonical state-space parameterization directly from input–output data.     

Subspace model identification Part 2. Analysis of the elementary output-error state-space model identification algorithm

The elementary MOESP algorithm presented in the first part of this series of papers is analysed in this paper. This is done in three different ways. First, we study the asymptotic properties of the estimated state-space model when only considering zero-mean white noise perturbations on the output sequence. It is shown that, in this case, the MOESPl implementation yields asymptotically unbiased estimates. An important constraint to this result is that the underlying system must have a finite impulse response and subsequently the size of the Hankel matrices, constructed from the input and output data at the beginning of the computations, depends on the number of non-zero Markov parameters. This analysis, however, leads to a second implementation of the elementary MOESP scheme, namely MOESP2. The latter implementation has the same asymptotic properties without the finite impulse response constraint. Secondly, we compare the MOESP2 algorithm with a classical state space model identification scheme. The latter scheme, referred to as the CLASSIC algorithm, is based on the Ho and Kalman realization scheme and estimated Markov parameters. The comparison is done by a sensitivity study, where the effect is studied of the errors on the data on the calculated column space of the shift-invariant subspace. This study demonstrates that the elementary MOESP2 scheme is more robust with respect to the errors considered than the CLASSIC algorithm. In the third part, the model reduction capabilities of the elementary MOESP schemes are analysed when the observations are error-free. We demonstrate in which sense the reduced order model is optimal when acquired with the MOESP schemes. The optimality is expressed by the difference between the 2-norm of the errors on the state (or output) sequence of the reduced-order model and the 2-norm of the matrix containing the rejected singular values being as small as possible. The insights obtained in these three parts are evaluated in a simulation study, and validated in this paper. They lead to the assertion that the MOESP2 implementation allows identification of a compact, low-dimensional, state-space model accurately describing the input -output behaviour of the system to be identified, while making use of ‘perturbed’ input-output data. This can be done efficiently.     

Transformation of time-variable multi-input systems to a canonical form

The problem of transforming a multi-input time-variable system to a canonical form is considered in this correspondence. The necessary and sufficient condition for the existence of the nonsingular transformation is stated and proved. The canonical form, when restricted to time-invariant systems, is the same as the one given in [3]. The advantages of the present method over [3] are explained.     

Hamming weight pyramid - A new insight into canonical signed digit representation and its applications

Signed-power-of-two terms are widely used in design automation algorithms for digital filter synthesis and optimization, linear transformation and other multiple constant multiplication problems. In these applications, the computation efficiency or solution quality tends to degrade with the number of nonzero digits in the signed digit representation of the a priori fixed coefficients. This paper provides a new perspective to interpret the hamming weights of fixed-point coefficients represented in signed-power-of-two terms with minimal number of nonzero digits, called the minimal signed digit (MSD) representation. A new hamming weight pyramid (HWP) is proposed to succinctly compress the information about the distribution of the hamming weights of canonical signed digit (CSD) representation in a visually appealing manner for analysis and synthesis. CSD is a unique and popularly used subset of the general MSD representation. Many interesting properties of CSD are uncovered in this regularly structured HWP. These properties are exploited to develop a novel and elegant algorithm for the direct conversion of decimal number to CSD representation. We also show that the HWP can also be employed to overcome the limit imposed on the word length of the coefficients for the reduced adder graph (RAG) algorithm and filter coefficient synthesis.     

Preconditioning approaches related to canonical correlation by use of cyclic form

There are many situations in engineering where we need to calculate the eigensystem of a matrix A which is given as a product of matrices, that is, A = A ₁ A ₂···A _p . Since, usually, we first perform the multiplication of the factors, the matrix A often becomes very ill-conditioned. Actually this happens even when A is a symmetric matrix, which will be our concern here. In this article we introduce a new approach to calculate the eigensystem of A without performing the indicated multiplication, or performing only partially the multiplication of the factors.     

Subspace model identification Part 1. The output-error state-space model identification class of algorithms

In this paper, we present two novel algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data. The algorithms have a number of common features. They are classified as one of the subspace model identification schemes, in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input-output data. This structure is then exploited in the calculation of a realization. Another common feature is their algorithmic organization: an RQ factorization followed by a singular value decomposition and the solution of an overdetermined set (or sets) of equations. The schemes assume that the underlying system has an output-error structure and that a measurable input sequence is available. The latter characteristic indicates that both schemes are versions of the MIMO Output-Error State Space model identification (MOESP) approach. The first algorithm is denoted in particular as the (elementary MOESP scheme). The subspace approximation step requires, in addition to input-output data, knowledge of a restricted set of Markov parameters. The second algorithm, referred to as the (ordinary MOESP scheme), solely relies on input-output data. A compact implementation is presented of both schemes. Although we restrict our presentation here to error-free input-output data, a framework is set up in an identification context. The identification aspects of the presented realization schemes are treated in the forthcoming Parts 2 and 3.     

Document representation and its application to page decomposition

Transforming a paper document to its electronic version in a form suitable for efficient storage, retrieval, and interpretation continues to be a challenging problem. An efficient representation scheme for document images is necessary to solve this problem. Document representation involves techniques of thresholding, skew detection, geometric layout analysis, and logical layout analysis. The derived representation can then be used in document storage and retrieval. Page segmentation is an important stage in representing document images obtained by scanning journal pages. The performance of a document understanding system greatly depends on the correctness of page segmentation and labeling of different regions such as text, tables, images, drawings, and rulers. We use the traditional bottom-up approach based on the connected component extraction to efficiently implement page segmentation and region identification. A new document model which preserves top-down generation information is proposed based on which a document is logically represented for interactive editing, storage, retrieval, transfer, and logical analysis. Our algorithm has a high accuracy and takes approximately 1.4 seconds on a SGI Indy workstation for model creation, including orientation estimation, segmentation, and labeling (text, table, image, drawing, and ruler) for a 2550×3300 image of a typical journal page scanned at 300 dpi. This method is applicable to documents from various technical journals and can accommodate moderate amounts of skew and noise     

Boosted string representation and its application to video surveillance

This paper presents a new behavior analysis system for analyzing human movements via a boosted string representation. First of all, we propose a triangulation-based method to transform each action sequence into a set of symbols. Then, an action sequence can be interpreted and analyzed using this string representation. To analyze action sequences with this string representation, three practical problems should be tackled. Usually, an action sequence has different temporal scaling changes, different initial states, and symbol converting errors. Traditional methods (like hidden Markov models and finite state machines) have limited abilities to deal with the above problems since many unknown states should be constructed and initialized. To tackle the problems, a novel string hypothesis generator is then proposed for generating a bank of string features from which different invariant features can be learned for classifying behaviors more accurately. To learn the invariant features, the Adaboost algorithm is used and modified to train a strong classifier from the set of string hypotheses so that multiple human action events can be well classified. In addition, a forward classification scheme is proposed to classify all input action sequences more accurately even though they have various scaling changes and coding errors. Experimental results prove that the proposed method is a robust, accurate, and powerful tool for human movement analysis.     

A hierarchical representation of form documents for identification and retrieval

In this paper, we present a logical representation for form documents to be used for identification and retrieval. A hierarchical structure is proposed to represent the structure of a form by using lines and the XY-tree approach. The approach is top-down and no domain knowledge such as the preprinted data or filled-in data is used. Geometrical modifications and slight variations are handled by this representation. Logically identical forms are associated to the same or similar hierarchical structure. Identification and the retrieval of similar forms are performed by computing the edit distances between the generated trees. Received: August 21, 2001 / Accepted: November 5, 2001     

A novel 2D graphical representation of DNA sequences and its application

In this paper, we introduce a novel 2D graphical representation of DNA sequences, the W-curve, which is embedded in two unit circles. We associate the W-curves with the classifications of the nucleotides according to their chemical properties. Then we obtain an 8-component vector with entries being the average sums of the abscissa and y-axis of A+C and T+G (A+T and C+G, A+G and T+C), respectively. The introduced vector results in simpler characterizations and comparisons of DNA sequences. The construction of the W-curve has some important advantages: (1) it avoids loss of information and the W-curve standing for DNA doesn't overlap or intersect itself; (2) the space the W-curve occupied is very small, just two unit circles. The utility of the approach can be illustrated by the examination of similarities/dissimilarities among the coding sequences of the first exon of beta-globin gene of eleven different species in Table 1.     

An algorithm for converting the boundary representation of a CAD model to its octree representation

Present CAD systems store the solid model of an object using a convenient representation. Boundary models and CSG (Constructive Solid Geometry) models are the most frequently used representations. Based on recent research findings, octree representation of an object presents a promising approach in solving problems in the areas of Computer Graphics, Manufacturing and Robotics. The most notable use of octree representations is in CAD-based robotic path planning problems. Octree models have also been used in fast rendering of 3-D solid models using ray tracing methods. This paper presents an algorithm for converting the boundary representation of polyhedral models to its octree representation. Such an algorithm would provide the link between an object generated using a solid modelling system and the application involving an octree representation of an object. The algorithm is demonstrated by converting a polyhedral boundary model of a sample object to its octree representation.     

Exposure to information technology and its relation to burnout

This paper investigates - in a sample of 202 Spanish employees - the hypothesis that the impact of the exposure to technology on burnout is mediated by the appraisal of technology. In addition, the factorial validity of the Maslach Burnout Inventory-General Survey (MGI-GS) is studied. The hypothesized three-factor-model of the MBI-GS (i.e. exhaustion, cynicism and professional efficacy) was not replicated; instead a four-factor model (i.e. exhaustion, cynicism, selfconfidence and goal-attainment) fitted better to the data. Results from Structural Equation Modelling confirmed the hypothesis that the impact on burnout of the exposure to technology (in terms of time and frequency of use of computer aided technology) is mediated by the appraisal of technology. The higher the exposure, the more positive the appraisal and the lower the burnout levels (i.e. less cynicism, more selfconfidence and a greater sense of goal attainment). No such effect was demonstrated for exhaustion. Limitations of the study and future research directions are discussed.     

Exposure to information technology and its relation to burnout

This paper investigates - in a sample of 202 Spanish employees - the hypothesis that the impact of the exposure to technology on burnout is mediated by the appraisal of technology. In addition, the factorial validity of the Maslach Burnout Inventory-General Survey (MGI-GS) is studied. The hypothesized three-factor-model of the MBI-GS (i.e. exhaustion, cynicism and professional efficacy) was not replicated; instead a four-factor model (i.e. exhaustion, cynicism, selfconfidence and goal-attainment) fitted better to the data. Results from Structural Equation Modelling confirmed the hypothesis that the impact on burnout of the exposure to technology (in terms of time and frequency of use of computer aided technology) is mediated by the appraisal of technology. The higher the exposure, the more positive the appraisal and the lower the burnout levels (i.e. less cynicism, more selfconfidence and a greater sense of goal attainment). No such effect was demonstrated for exhaustion. Limitations of the study and future research directions are discussed.