Model conversions of uncertain linear systems via the interval Pade approximation method

This paper presents a new interval Pade approximation method to convert a continuous-time (discrete-time) uncertain linear system to an equivalent discrete-time (continuous-time) uncertain model via interval arithmetic operations. Based on the inclusion theorem related to the interval arithmetic, the interval Pade's approximants and their associated interval error matrices with interval arguments are obtained via the Pade's approximants and their associated error matrices with degenerate (real) arguments, respectively. Tighter error bounds of various approximate uncertain models with respect to their exact uncertain models are determined and used to modify the obtained Pade's approximants, so that the resulting approximate uncertain models are able to tightly enclose the original uncertain systems. Thus, the analysis and design of the original uncertain systems can be indirectly carried out using the converted uncertain models in either the continuous-time or the discrete-time domain.This work was supported in part by the U.S. Army Research Office under contract DAAH-04-94-G-0227 and the NASA-Johnson Space Center under Grant NAG-9-746.     

Global analyticity of a geometric decomposition for linear singularly perturbed systems

A geometric decomposition is developed for linear, time-invariant singularly perturbed systems of a general form. The decomposition is shown to be determined by a mappingd between two real analytic manifolds, the range ofd being a manifold of canonical forms. Our main result establishes analyticity ofd over its entire domain.     

Model reduction of uncertain FIR discrete-time systems

Model reduction of high-order polynomial systems is considered. The main novelty of the paper is that the polynomial coefficients are assumed to be known only within given intervals. The resulted reduced system is characterized by a fixed-coefficients polynomial. First, the meaning of such a model reduction is defined. Then, applying a novel approach, the maximal "distance" (error) between the polygon in the complex plane which represents, at each frequency, the original uncertain system and the point which represents the resulted reduced-order fixed-coefficients system, is minimized. By a smart definition of this "distance" and by a formulation of the "closest" distance to the polygon as a "maximum" in some sense, the problem is formulated as linear semi-infinite programming with linear constraints, thus reducing significantly the computational complexity. A numerical example is provided.     

Brachytherapy seed localization using geometric and linear programming techniques

We propose an optimization algorithm to solve the brachytherapy seed localization problem in prostate brachytherapy. Our algorithm is based on novel geometric approaches to exploit the special structure of the problem and relies on a number of key observations which help us formulate the optimization problem as a minimization integer program (IP). Our IP model precisely defines the feasibility polyhedron for this problem using a polynomial number of half-spaces; the solution to its corresponding linear program is rounded to yield an integral solution to our task of determining correspondences between seeds in multiple projection images. The algorithm is efficient in theory as well as in practice and performs well on simulation data (approximately 98% accuracy) and real X-ray images (approximately 95% accuracy). We present in detail the underlying ideas and an extensive set of performance evaluations based on our implementation.     

Semi-global stabilization of a class of uncertain nonlinear systems by linear output feedback

This brief deals with the problem of semi-global stabilization by output feedback for a class of uncertain nonlinear systems. Due to the presence of mismatched uncertainties and the lack of triangularity condition, the systems under consideration are not uniformly completely observable. In addition, the uncertain nonlinear dynamics of the systems are higher order, rather than linearly growing, in the unmeasurable states. All these make the systems not semi-globally stabilizable by the existing output feedback design schemes. In this brief, by extending the feedback domination design techniques proposed by Qian and Lin, a systematic design scheme is developed to construct linear output feedback controllers that semi-globally stabilize a general class of uncertain nonlinear systems under less restrictive conditions.     

Direct method of reducing order of linear systems using koenig's theorem

Linear-system reduction is achieved by a simple and direct method based on Koenig's theorem, to approximate the stability equations of the given system. Thus the proposed technique is superior, for very high-order systems, to other methods which, yielding almost identical results, factorise the stability equations.     

Robust stability and stabilizability of uncertain linear hybrid systems with state delays

In this brief, we consider a class of uncertain linear discrete-time switched systems with state delays. By solving certain matrix and Riccati-like inequalities, sufficient conditions for the robust stability and stabilizability of the system are given.     

Automatic geometric dimension measurements of single-mode fiberpreforms using a novel shadow method

A method is described in which a test preform is immersed in an index-matching liquid so as to detect optical signals from the core/cladding and cladding/index-matching liquid interfaces simultaneously. A light-beam sweeper with a mirror is used to sweep a He-Ne laser beam across a fiber preform, and the time intervals during which the preform intercepts the beam and casts a composite shadow on a photodetector are measured. The method is simple and accurate and has sufficient spatial resolution (better than 10 μm) to obtain detailed measurements of core eccentricity, core and cladding diameters and their ratio, and ellipticity in a step-index single-mode fiber preform for a subscriber line. On the basis of this principle, an automated geometry measurement system has been developed. The system is attractive for quality control applications in mass-production lines of single-mode fibers     

Identification of linear continuous-time multivariable systems using linear multistep methods

It is shown that linear multistep methods, commonly used to integrate ordinary differential equations numerically, can be used for the identification of linear continuous-time multivariable systems from samples of input/output data. An example problem is given to illustrate the use of multistep methods in system identification, and the results are compared with those obtained by the use of a discrete-time model.<>     

Identification of linear systems using correlation data

Powerful algorithms exist for identifying linear systems given input/output data. In many cases, however, it is convenient to obtain the data in the form of correlation functions. The data in this form are often more condensed. An extension of ?str?m's identification algorithm for making it able to use correlation functions in the place of an input/output record is described.     

Extended power method and stability of linear discrete-time systems

A computationally simple and efficient method is proposed to determine the stability of linear discrete-time systems. The method directly utilises the system (state-transition) matrix and avoids the evaluation of the characteristic polynomial. Another interesting feature of this approach is that it can be extended to extract the eigenvalues of matrices, in a recursive fashion.     

Energy optimization of pipelined digital systems using circuit sizing and supply scaling

We present a systematic method for minimizing the energy of pipelined digital systems, through joint optimization of each pipeline stage and the system. A pipeline stage with a constant load can either be optimized for delay at a given input size, minimized for energy at a fixed delay, or have delay traded off for energy at a fixed input size. The results of these optimizations are combined to yield the design region for energy and delay. At the system level with a fixed throughput constraint, the sensitivities to input size and output load of all pipeline stages form the optimal energy criteria that provide a systematic method to minimize the total system energy. This method is applied to a media datapath, where we show up to 37% energy saving for a fixed performance. The minimal energy-delay curve of the system obtained through application of this method demonstrates similar characteristics as that of a single pipeline stage. With voltage scaling, the optimal solution displays a strong dependency between delay, energy, and supply voltage. The proper tradeoff between these entities makes a fundamental impact on efficient digital design.     

Analysis of singular systems using Taylor series approach

The Taylor series approach to the analysis of singular systems is considered. An example is given to demonstrate the use of this method.     

Comments on "Robust stability and stabilizability of uncertain linear hybrid systems with state Delay"

This paper points out some technical errors of matrix dimension mismatch in the above paper, and presents the corrections in the form of Ricatti-like inequalities.     

Model reduction of 2-D systems via orthogonal series

In this article, the problem of model reduction of 2-D systems is studied via orthogonal series. The algorithm proposed reduces the problem to an overdetermined linear algebraic system of equations, which may readily be solved to yield the simplified model. When this model approximates adequately the original system, it has many important advantages, e.g., it simplifies the analysis and simulation of the original system, it reduces the computational effort in design procedures, it reduces the hardware complexity of the system, etc. Several examples are included which illustrate the efficiency of the proposed method and gives some comparison with other model reduction techniques.     

Spectral analysis of linear digital systems using BIFORE

A spectral analysis of linear digital systems using BIFORE is carried out. Expressions for power and amplitude spectra of the input and output signals are developed. The frequency-sequency structure of the power spectra, which are invariant to cyclic shift of the sampled data, is analysed.     

Asymptotic stability of the MMSE linear filter for systems with uncertain observations (Corresp.)

Sufficient conditions for uniform asymptotic stability in the large of the optimal minimum mean-square error (MMSE) linear filter are developed for discrete linear systems whose observations may contain noise alone and where only the probability of occurrence of such cases is known to the estimator. Conditions for existence, uniqueness, and stability of the steady-state optimal filter are also considered for the case when the system is time-invariant.     

Eigenvalue sensitivity method for optimal stabilisation of linear systems

Using properties of eigenvalue sensitivity matrices a procedure is presented for designing state feedback controllers that give the closed loop system a prescribed set of preassigned eigenvalues, minimising a quadratic cost functional.     

利用混合规则几何面的MMS激光扫描仪检校方法

提出了一种利用混合规则几何面进行车载移动测量系统(MMS)激光扫描仪外参数检校的方法。该方法利用现实环境中普遍存在的平面和圆柱面地物,结合平面和柱面可公式化的几何特征对激光点进行严密的数学方程式约束,通过非线性优化的方法精确求解激光扫描仪相对于MMS定位测姿POS系统的相对位置和姿态参数。实验结果表明:相对于只采用平面地物约束进行检校的方法,采用混合规则几何面联合约束检校的方法结果精度更高,距离残差中误差达到了0.006 m;同一车载平台、两套不同激光扫描仪系统检校后,点云叠合效果较好。该检校方法具有精度高、简便、快速、实用等优点,具有较强的工程应用价值。     

Blind and complete modeling of linear systems using third order cumulants

This paper presents a novel approach to structure determination of linear systems along with the choice of system orders and parameters.AutoRegressive (AR),Moving Average (MA) or AutoRegressive-Moving Average (ARMA) model structure can be extracted blindly from the Third Order Cumulants (TOC) of the system output measurements,where the unknown system is driven by an unobservable stationary independent identically distributed (i.i.d.) non-Gaussian signal.By means of the system order recursion,whether the system has an AR structure or has AR part of an ARMA structure is firstly investigated.MA features in the TOC domain is then applied as a threshold to decide if the system is an MA model or has MA part of an ARMA model.Numerical simulations illustrate the generality of the proposed blind structure identification methodology that may serve as a guideline for blind linear system modeling.