Spl Lscr Research Articles

A Generalized Local Time-Step Scheme for Efficient FVTD Simulations in Strongly Inhomogeneous Meshes

A new generalized local time-step scheme is introduced to improve the computational efficiency of the finite-volume time-domain (FVTD) method. The flexibility of unstructured FVTD meshes is fully exploited by avoiding the disadvantage of a single short time step in the entire mesh. The great potential of this scheme is fully revealed in the FVTD simulation of electromagnetic (EM) problems with both large and fine structures in close proximity. The scheme is based on an automatic partition of the computational domain in subdomains where local time steps of the type 2/sup /spl lscr/-1//spl Delta/t(/spl lscr/=1,2,3,...) can be applied without violating the stability condition. Interfaces between subdomains are reduced to a generic two-level system which requires a very limited number of time interpolations during the FVTD iteration, therefore resulting in a very simple and robust technique. The application of local time stepping to three-dimensional EM problems demonstrates a significant speed-up of the computation without compromising the accuracy of the results.

An Efficient Analysis of Shielded Single and Multiple Coupled Microstrip Lines With the Nonuniform Fast Fourier Transform (NUFFT) Technique

A nonuniform fast Fourier transform (NUFFT) technique is incorporated into the spectral-domain approach for the analysis of shielded single and multiple coupled microstrip lines. Each of the spectral-domain Green's functions is decomposed into an asymptotic part and a remaining part. At the interface of layered dielectrics with conducting strips, the product of a basis function and an associated Green's function constitutes an expansion E-field. The inverse Fourier transform (IFT) of the expansion E-field is its spatial distribution all over the interface. We take this advantage to match the final boundary conditions on all the conducting strips simultaneously. As a result, if all the strips are at one interface, the number of operations required in this method is proportional to N/sub /spl lscr//, but not to N/sub /spl lscr///sup 2/, where N/sub /spl lscr// is the number of the strips. The IFT of the asymptotic part of each expansion E-field can be obtained analytically, and that of the remaining part can be quickly processed by the NUFFT. The Gauss-Chebyshev quadrature is used to accelerate the computations of the integrals resulted from the Galerkin's procedure. The proposed method is also applied to investigate the dispersion characteristics of coupled lines with finite metallization thickness and of coupled lines at different levels. A convergence analysis of the results is presented and a comparison of used CPU time is discussed.

Sparse representations in unions of bases

The purpose of this correspondence is to generalize a result by Donoho and Huo and Elad and Bruckstein on sparse representations of signals in a union of two orthonormal bases for R/sup N/. We consider general (redundant) dictionaries for R/sup N/, and derive sufficient conditions for having unique sparse representations of signals in such dictionaries. The special case where the dictionary is given by the union of L/spl ges/2 orthonormal bases for R/sup N/ is studied in more detail. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of the /spl lscr//sup 0/ optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may be highly redundant.

An orthonormal class of exact and simple DFT eigenvectors with a high degree of symmetry

The paper presents a novel orthonormal class of eigenvectors of the discrete Fourier transform (DFT) whose order N is factored as N=rM/sup 2/. The DFT eigenvectors have the form e=E/spl alpha/, where /spl alpha/ are eigenvectors of some /spl lscr/ /spl times//spl lscr/ matrices, given by, or related to, the DFT matrix of order r, with /spl lscr/ = r, 2r, or 4r, and the matrix E expands /spl alpha/ to the full DFT size N=rM/sup 2/. In particular, when N is an arbitrarily large power of 2, r may be 1 or 2. The resulting eigenvectors are expressed exactly with simple exponential expressions, have a considerable number of elements constrained to 0, and show a high degree of symmetry. The derivation of such a class is based on a partition of the N-dimensional linear space into subspaces of very small dimension (r, 2r or 4r).

Cubic self-dual binary codes

We study binary self-dual codes with a fixed point free automorphism of order three. All binary codes of that type can be obtained by a cubic construction that generalizes Turyn's. We regard such "cubic" codes of length 3/spl lscr/ as codes of length /spl lscr/ over the ring F/sub 2//spl times/F/sub 4/. Classical notions of Type II codes, shadow codes, and weight enumerators are adapted to that ring. Two infinite families of cubic codes are introduced. New extremal binary codes in lengths /spl les/ 66 are constructed by a randomized algorithm. Necessary conditions for the existence of a cubic [72,36,16] Type II code are derived.

Λ∞-multipliers for robust performance analysis

Linear systems subject to nonlinear time-varying sector-bounded uncertainties are considered. Robust performance is measured in terms of the worst-case ratio between the /spl Lscr//sub /spl infin//-norms of the output and input signals. A new class of multipliers is introduced and characterized. The characterization can be used to compute an upper bound for robust performance, which tightens the bound obtained by the scaled small gain theorem. While the standard Popov multipliers and their extensions have been developed within the /spl Lscr//sub 2/ framework, our multipliers are adapted to /spl Lscr//sub /spl infin//.

Thinned coincident arrays for the direct measurement of the principal solution in radio astronomy

A new technique is described for the design of a thinned, linear, multiplicative array which directly measures the principal solution of a radio source distribution. The original filled multiplicative array with uniform element spacing /spl lscr/ is first generalized to an array of N/sub 1/+1 subarrays each with M/sub 1/+1 elements. A thinning factor of 1/2 is shown to be possible if M/sub 1/=N/sub 1/. Finally, if each subarray is further divided into smaller subarrays until the smallest are simply two element interferometers, then the principal solution can be directly measured but with far fewer elements. Significant thinning factors are achieved when the array is very large. The method can also be used to measure the principal solution with planar arrays, with very strong thinning occurring for large arrays.

Algebraic theory of optimal filterbanks

We introduce an optimality theory for finite impulse response (FIR) filterbanks using a general algebraic point of view. We consider an admissible set /spl Lscr/ of FIR filterbanks and use scalability as the main notion based on which performance of the elements in /spl Lscr/are compared. We show that quantification of scalability leads naturally to a partial ordering on the set /spl Lscr/. An optimal solution is, therefore, represented by the greatest element in /spl Lscr/. It turns out that a greatest element does not necessarily exist in /spl Lscr/. Hence, one has to settle with one of the maximal elements that exist in /spl Lscr/. We provide a systematic way of finding a maximal element by embedding the partial ordering at hand in a total ordering. This is done by using a special class of order-preserving functions known as Schur-convex. There is, however, a price to pay for achieving a total ordering: there are infinitely many possible choices for Schur-convex functions, and the optimal solution specified in /spl Lscr/ depends on this (subjective) choice. An interesting aspect of the presented algebraic theory is that the connection between several concepts, namely, principal component filterbanks (PCFBs), filterbanks with maximum coding gain, and filterbanks with good scalability, is clearly revealed. We show that these are simply associated with different extremal elements of the partial ordering induced on /spl Lscr/ by scalability.

Computing the error linear complexity spectrum of a binary sequence of period 2/sup n/

Binary sequences with high linear complexity are of interest in cryptography. The linear complexity should remain high even when a small number of changes are made to the sequence. The error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed. We present an algorithm which computes the error linear complexity for binary sequences of period /spl lscr/=2/sup n/ using O(/spl lscr/(log/spl lscr/)/sup 2/) bit operations. The algorithm generalizes both the Games-Chan (1983) and Stamp-Martin (1993) algorithms, which compute the linear complexity and the k-error linear complexity of a binary sequence of period /spl lscr/=2/sup n/, respectively. We also discuss an application of an extension of our algorithm to decoding a class of linear subcodes of Reed-Muller codes.

Robust iterative learning control design is straightforward for uncertain LTI systems satisfying the robust performance condition

This note demonstrates that the design of a robust iterative learning control is straightforward for uncertain linear time-invariant systems satisfying the robust performance condition. It is shown that once a controller is designed to satisfy the well-known robust performance condition, a convergent updating rule involving the performance weighting function can be directly obtained. It is also shown that for a particular choice of this weighting function, one can achieve a perfect tracking. In the case where this choice is not allowable, a sufficient condition ensuring that the least upper bound of the /spl Lscr//sub 2/-norm of the final tracking error is less than the least upper bound of the /spl Lscr//sub 2/-norm of the initial tracking error is provided. This sufficient condition also guarantees that the infinity-norm of the final tracking error is less than the infinity-norm of the initial tracking error.

On optimal sequential prediction for general processes

This paper considers several aspects of the sequential prediction problem for unbounded, nonstationary processes under pth power loss /spl lscr//sub p/(u,v)=|u-v|/sup p/, 1<p</spl infin/. In the first part, it is shown that Bayes prediction schemes are Cesaro optimal under general conditions, that Cesaro optimal prediction schemes are unique in a natural sense, and that Cesaro optimality is equivalent to a form of weak calibration. Connections between calibration and stronger forms of optimality are considered. Extensions of the existence and uniqueness results to generalized prediction, and prediction from observations with additive noise, are established. For binary processes, it is shown that thresholding an optimal prediction scheme for the squared loss yields an optimal binary prediction scheme for the Hamming loss. In the second part of the paper, it is shown how to construct, from a countable family of prediction schemes, a single composite scheme whose asymptotic performance on any suitable process dominates the performance of each member of the family. The construction is based on aggregating methods for individual binary sequences. Using the construction, some results of Algoet (1994, 1995) on the existence of Cesaro optimal schemes for families of ergodic processes are rederived in a direct way and extended to unbounded processes.

Stability of nonconvolutional n-D linear discrete systems

Stability of linear discrete shift-invariant n-D systems is often discussed in terms of best-in best-out stability and/or in terms of zeros of certain polynomials. This approach assumes that there exists a sequence h, such that for any input sequence x, the output y can be expressed as y=h/sup */x. The condition h/spl isin//spl lscr/ /sup 1/ then easily yields the desired result. Many linear discrete systems with n>1 (even some of the shift-invariant ones) do not satisfy this basic assumption. Here, such systems are called nonconvolutional. Among others, all systems described by difference equations with variable coefficients belong to this class together with many difference equations with constant coefficients. This paper establishes some sufficient conditions of stability for these nonconvolutional systems. It also yields methods to establish growth estimates of solutions of n-D difference equations.

Optimal wire-sizing function under the Elmore delay model with bounded wire sizes

In this brief, we develop the optimal wire-sizing functions under the Elmore delay model with bounded wire sizes. Given a wire segment of length /spl Lscr/, let f(x) be the width of the wire at position x, 0/spl les/x/spl les//spl Lscr/. We show that the optimal wire-sizing function that minimizes the Elmore delay through the wire is f(x)=ae/sup -bx/, where a>0 and b>0 are constants that can be computed in O(1) time. In the case where lower bound (L>0) and upper bound (U>0) of the wire widths are given, we show that the optimal wire-sizing function f(x) is a truncated version of ae/sup -bx/ that can also be determined in O(1) time. Our wire-sizing formula can be iteratively applied to optimally size the wire segments in a routing tree.

Linear parameter varying controller for automated lane guidance: experimental study on tractor-trailers

Proposes a linear parameter-varying (LPV) controller design for automated lane keeping for vehicles. The lane keeping objective is to keep the vehicle centered with respect to the lane boundaries by applying appropriate steering action. Most current implementation of lane keeping controllers were based on linear synthesis techniques because linear techniques offer a direct tradeoff between steering action, passenger comfort, robustness, and tracking performance. However, linear methods assume constant longitudinal velocity of the vehicle for controller synthesis. It is known that the position response of the vehicle to the steering input varies significantly with the longitudinal velocity of the vehicle. The LPV design technique deals with this issue by synthesizing a velocity dependent controller. The controller minimizes the induced /spl Lscr//sub 2/ norm of the closed loop from the road curvature to the tracking error. The design has been successfully implemented on a tractor-trailer vehicle and experiments conducted up to longitudinal velocity of 60 mi/h are presented.

On stability margins of the Fiat Dedra engine model

We evaluate the stability margin of a Fiat Dedra engine model to explore possible applications of theoretical achievements in the parametric approach to robust control problems. The study is based on two versions of the model with uncertainties. One is the original model, which has a multilinear characteristic polynomial, while the other is an affine-linearized model which is obtained by the affine linearization technique proposed in the paper. By applying some newly developed theoretical tools in the literature, the stability margins of the affine-linearized model in terms of the /spl lscr//sub /spl infin// norm and the /spl lscr//sub 2/ norm and the stability margin of the original model in terms of the /spl lscr//sub /spl infin// norm are obtained.

Input-to-state dynamical stability and its Lyapunov function characterization

We present a new variant of the input-to-state stability (ISS) property which is based on using a one-dimensional dynamical system for building the class /spl Kscr//spl Lscr/ function for the decay estimate and for describing the influence of the perturbation. We show the relation to the original ISS formulation and describe characterizations by means of suitable Lyapunov functions. As applications, we derive quantitative results on stability margins for nonlinear systems and a quantitative version of a small gain theorem for nonlinear systems.

Integrated system identification and PID controller tuning by frequency loop-shaping

A systematic design methodology for proportional-integral-derivative (PID) controllers is presented. Starting from data sets, a model of the system and its uncertainty bounds are obtained. The parameters of the controller are tuned by a convex optimization algorithm, minimizing a weighted difference between the actual loop transfer function and a target in an /spl Lscr//sub 2///spl Lscr//sub /spl infin// sense. The target selection is guided by the identified model and its uncertainty. The problem of disjoint data sets and/or different models for the same system is also addressed. The method has proved successful in numerous practical cases showing both expediency in controller design and implementation and improved performance over existing controllers.

Two-dimensional weight-constrained codes through enumeration bounds

For a rational /spl alpha//spl isin/(0,1), let /spl Ascr//sub n/spl times/m,/spl alpha// be the set of binary n/spl times/m arrays in which each row has Hamming weight /spl alpha/m and each column has Hamming weight /spl alpha/n, where /spl alpha/m and /spl alpha/n are integers. (The special case of two-dimensional balanced arrays corresponds to /spl alpha/=1/2 and even values for n and m.) The redundancy of /spl Ascr//sub n/spl times/m,/spl alpha// is defined by /spl rho//sub n/spl times/m,/spl alpha//=nmH(/spl alpha/)-log/sub 2/|/spl Ascr//sub n/spl times/m,/spl alpha//| where H(x)=-xlog/sub 2/x-(1-x)log/sub 2/(1-x). Bounds on /spl rho//sub n/spl times/m,/spl alpha// are obtained in terms of the redundancies of the sets /spl Ascr//sub /spl Lscr/,/spl alpha// of all binary /spl Lscr/-vectors with Hamming weight /spl alpha//spl Lscr/, /spl Lscr//spl isin/{n,m}. Specifically, it is shown that /spl rho//sub n/spl times/m,/spl alpha///spl les/n/spl rho//sub m,/spl alpha//+m/spl rho//sub n,/spl alpha// where /spl rho//sub /spl Lscr/,/spl alpha//=/spl Lscr/H(/spl alpha/)-log/sub 2/|/spl Ascr//sub /spl Lscr/,/spl alpha//| and that this bound is tight up to an additive term O(n+log m). A polynomial-time coding algorithm is presented that maps unconstrained input sequences into /spl Ascr//sub n/spl times/m,/spl alpha// at a rate H(/spl alpha/)-(/spl rho//sub m,/spl alpha///m).

Rational suboptimal continuous-time controller design

We obtain rational suboptimal continuous-time solutions to some optimal control problems specified via time domain performance criteria. These include /spl Lscr//sub 1/ and /spl Lscr//sub /spl infin// norms and peak overshoot. The approach uses linear semi-infinite programming to compute weights for a given finite set of rational basis functions and makes the best possible use of the basis. The closed-loop transfer functions obtained satisfy appropriate interpolation constraints for internal stability and the formulation allows additional linear constraints to be incorporated.

PID controller tuning by frequency loop-shaping: application to diffusion furnace temperature control

A frequency loop-shaping technique for tuning proportional-integral-derivative controllers is applied to temperature control of a three-zone industrial diffusion furnace used in semiconductor manufacturing. In this tuning method the controller parameters are tuned so as to minimize the difference between the actual and a target loop transfer function, in an /spl Lscr//sub /spl infin// sense. The problem is formulated in the frequency domain as a convex optimization which can be solved numerically in a reliable way. This method, combined with a system identification step, has produced very satisfactory controllers for the furnace temperature control application.