Browsing by Subject "Linear systems"

Now showing 1 - 20 of 37

Open Access
Approximate MLFMA as an efficient preconditioner
(IEEE, 2007) Malas, Tahir; Ergül, Özgür; Gürel, Levent
In this work, we propose a preconditioner that approximates the dense system operator. For this purpose, we develop an approximate multilevel fast multipole algorithm (AMLFMA), which performs a much faster matrix-vector multiplication with some relative error compared to the original MLFMA. We use AMLFMA to solve a closely related system, which makes up the preconditioner. Then, this solution is embedded in the main solution that uses MLFMA. By taking into account the far-field elements wisely, this preconditioner proves to be much more effective compared to the near-field preconditioners.
Open Access
Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams
(Optical Society of America, 2013) Şahin, E.; Onural, L.
We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a twodimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.
Open Access
Capacity bounds for an ultra-wideband channel model
(IEEE, 2004-10) Arıkan, Erdal
There is an ongoing effort by the IEEE 802.15.3a subcommittee to reach a UWB personal area network standard. We estimate the achievable rates for such networks using a channel model specified by the same group. The analysis of this channel model is of interest in light of recent information-theoretic work on multipath fading channels which show that in order to take full advantage of such channels' capacity the transmitted signals have to be "peaky" in a certain sense. The immense bandwidth of the UWB channel also suggests at first that peaky signals should be used. However, unlike the many other wireless systems where the transmitter energy is limited, in the UWB channel only the power spectral density of the transmitted signal is constrained. As a result, the signal power can grow in proportion to the utilized bandwidth and peaky signals are not needed. © 2004 IEEE.
Open Access
Compressive sampling and adaptive multipath estimation
(IEEE, 2010) Pilancı, Mert; Arıkan, Orhan
In many signal processing problems such as channel estimation and equalization, the problem reduces to a linear system of equations. In this proceeding we formulate and investigate linear equations systems with sparse perturbations on the coefficient matrix. In a large class of matrices, it is possible to recover the unknowns exactly even if all the data, including the coefficient matrix and observation vector is corrupted. For this aim, we propose an optimization problem and derive its convex relaxation. The numerical results agree with the previous theoretical findings of the authors. The technique is applied to adaptive multipath estimation in cognitive radios and a significant performance improvement is obtained. The fact that rapidly varying channels are sparse in delay and doppler domain enables our technique to maintain reliable communication even far from the channel training intervals. ©2010 IEEE.
Open Access
Computing moments of first passage times to a subset of states in Markov chains
(SIAM, 2005) Dayar T.; Akar, N.
This paper presents a relatively efficient and accurate method to compute the moments of first passage times to a subset of states in finite ergodic Markov chains. With the proposed method, the moment computation problem is reduced to the solution of a linear system of equations with the right-hand side governed by a novel recurrence for computing the higher-order moments. We propose using a form of the Grassmann-Taksar-Heyman (GTH) algorithm to solve these linear equations. Due to the form of the linear systems involved, the proposed method does not suffer from the drawbacks associated with GTH in a row-wise sparse implementation. © 2005 Society for Industrial and Applied Mathematics.
Open Access
Conditions of well-posedness for planar conewise linear systems
(Sage Publications, 2023-04-24) Namdar, Daniyal; Özgüler, Arif Bülent
A planar (2D) conewise linear system (CLS) is considered. This is a piecewise linear system of two states and multiple modes, where each mode is linear with its state-space constrained into a polyhedral, finitely generated, convex cone. It is allowed to have a discontinuous vector field and sliding modes. Alternative conditions for well-posedness of Caratheodory solutions of this system that have intuitive interpretations with respect to eigenvectors and cone-boundary vectors are derived. It is also shown that a well-known condition for well-posedness of bimodal systems also applies to two adjacent modes of this system without any change.
Open Access
Continuous and discrete fractional fourier domain decomposition
(IEEE, 2000) Yetik, İ. Şamil; Kutay, M. A.; Özaktaş, H.; Özaktaş, Haldun M.
We introduce the fractional Fourier domain decomposition for continuous and discrete signals and systems. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems.
Open Access
Controller redesign for delay margin improvement
(Elsevier, 2020-01) Gündeş, A. N.; Özbay, Hitay
Two important design objectives in feedback control are steady-state error minimization and delaymargin maximization. For many practical systems it is not possible to have infinite delay margin andzero steady state error for unit step reference input. This paper proposes a re-design method forcontrollers initially designed to satisfy the steady-state error requirement. The objective is to makestructural changes in the controller so that a lower bound of the delay margin is improved withoutaffecting the steady-state error. The order of the new controller is (ν+1) higher than the order of theoriginal controller, whereνis the number of unstable poles of the plant.
Open Access
Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations
(IEEE, 1998-05) Kutay, Mehmet Alper; Erden, M. F.; Özaktaş, Haldun M.; Arıkan, Orhan; Candan, Ç.; Güleryüz, Ö.
It is possible to obtain either exact realizations or useful approximations of linear systems or matrix-vector products arising in many different applications, by synthesizing them in the form of repeated or multi-channel filtering operations in fractional Fourier domains, resulting in much more efficient implementations with acceptable decreases in accuracy. By varying the number and configuration of filter blocks, which may take the form of arbitrary flow graphs, it is possible to trade off between accuracy and efficiency in the desired manner. The proposed scheme constitutes a systematic way of exploiting the information inherent in the regularity or structure of a given linear system or matrix, even when that structure is not readily apparent.
Open Access
Delay margin optimization for systems with ınternal delayed feedback
(Elsevier, 2021-07-16) Özbay, Hitay
In this brief paper, controller design for delay margin optimization is considered for systems with internal feedback delays (systems with delays in the state variables). Similar to existing results on delay margin optimization for finite dimensional systems with I/O delays, it is shown that the problem considered can be solved by using Nevanlinna-Pick interpolation involving non-minimum phase zeros of the plant.
Open Access
An effective preconditioner based on schur complement reduction for integral-equation formulations of dielectric problems
(IEEE, 2009) Malas, Tahir; Gürel, Levent
The author consider effective preconditioning of recently proposed two integral-equation formulations for dielectrics; the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). These two formulations are of utmost interest since CTF yields more accurate results and JMCFIE yields better-conditioned systems than other formulations.
Open Access
Electromagnetic modeling of split-ring resonators
(IEEE, 2007) Gürel, Levent; Ünal, Alper; Ergül, Özgür
In this paper, we report our efforts to model splitring resonators (SRRs) and their large arrays accurately and efficiently in a sophisticated simulation environment based on recent advances in the computational electromagnetics. The resulting linear system obtained from the simultaneous discretization of the geometry and Maxwell's equations is solved iteratively with the multilevel fast multipole algorithm. As an example, we present an array of 125 SRRs showing a negative effective permeability about 92 GHz.
Open Access
Ellipsoid genişletmeyle seyrek sinyal geri oluşturma
(IEEE, 2011-04) Gürbüz, A. C.; Pilancı, M.; Arıkan, Orhan
Bu makalede b = Ax + n şeklinde gürültülü A’nın tam rank ve x’in seyrek olduğu doğrusal bir denklem sistemi için seyrek x sinyallerini doğru olarak geri oluşturmaya yönelik yeni bir yöntem sunulmuştur. Önerilen yöntem kullanılan veri sınırını belirleyen ||Ax − b||2 = ellipsoidinin genişletilirken sırayla eksenlerin sıfırlanmasına dayanan yinelemeli bir yöntemdir. Seyrek sinyal oluşturma alanında yinelemeli ve 1 norm minimizasyon tabanlı standard yöntemlere göre benzer problemlerde daha yüksek başarım gösteren metot, eksik belirtilmiş sistemlerde standard metotların oluşturması gereken seyreklik seviyesini de yumuşatmaktadır
Open Access
The fractional Fourier domain decomposition
(Elsevier, 1999) Kutay, M. A.; Özaktaş, H.; Özaktaş, Haldun M.; Arıkan, Orhan
We introduce the fractional Fourier domain decomposition. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems.
Open Access
H∞ filter design for vehicle tracking under delayed and noisy measurements
(IEEE, 2007-06) Ezercan, Sami; Özbay, Hitay
In many intelligent vehicles applications tracking plays an important role. This paper considers tracking of a vehicle under delayed and noisy measurements. For this purpose we design an H∞ optimal filter for linear systems with time delays in the state and output variables. By using the duality between filtering and control, the problem at hand is transformed to a robust controller design for systems with time delays. The skew Toeplitz method developed earlier for the robust control of infinite dimensional systems is used to solve the H∞ filtering problem. The results are illustrated with simulations and effects of the time delay on the tracking performance are demonstrated. ©2007 IEEE.
Open Access
Incomplete LU preconditioning for the electric-field integral equation
(2006) Malas, Tahir; Gürel, Levent
Linear systems resulting from the electric-field integral equation (EFIE) become ill-conditioned, particularly for large-scale problems. Hence, effective preconditioners should be used to obtain the iterative solution with the multilevel fast multipole algorithm in a reasonable time. In this paper, we show that a threshold-based incomplete LU (ILU) preconditioner, i.e., ILUT, can be used safely for such systems, provided that column pivoting is applied for the stability of the incomplete factors. It is observed that the resulting preconditioner ILUTP reduces the solution times by an order of magnitude, compared to simple Jacobi preconditioner. Moreover, we also use the iterative solution of the near-field system as a preconditioner, and use ILUTP as the preconditioner for the near-field system. This way, the effectiveness of the ILUTP is further improved.
Open Access
Inverse optimal control and positive real systems
(1997) Ünal Yılmaz
In this thesis an inverse optimal control problem for constant output feedbacks is investigated. Necessary and sufficient conditions for optimality of an output feedback are derived for single-input, single-output systems. The class of systems with members for which any constant positive output feedback is optimal turns out to be precisely the class of positive real systems. It is also shown that for a class of minimum phase systems all “large” positive gains are optimal.
Open Access
Measurement strategies for input estimation in linear systems
(IEEE, 2007) Özçelikkale, Ayça; Özaktaş, Haldun M.; Arıkan, Erdal
In this work, we present a mathematical approach for some of the measurement problems arising in optics, which is also applicable to other contexts. We see the measurement problem as the problem of determining the best measurement strategy to estimate an unknown stochastic process by noisy measurements. The number of measurement devices, their positions and qualities characterize the measurement strategies. The model we use also includes a cost function based on resolving powers of sensors. We are unable to offer a solution to this problem in such generality; but for the metrical problem in which the number and locations of the measurement devices are fixed, we present an efficient numerical approach.
Open Access
Model based anticontrol of discrete-time systems
(IEEE, 2003) Morgül, Ömer
We will consider a model-based approach for the anticontrol of some discrete-time systems. We first assume the existence of a chaotic model in an appropriate form. Then by using an appropriate control input we try to match the controlled system with the chaotic system model.
Open Access
Nonlinear laser lithography for indefinitely large-area nanostructuring with femtosecond pulses
(Nature publishing group, 2013) Öktem, B.; Pavlov, I.; Ilday, S.; Kalaycıoǧlu, H.; Rybak, A.; Yavaş, S.; Erdoǧan, M.; Ilday F. Ö.
Dynamical systems based on the interplay of nonlinear feedback mechanisms are ubiquitous in nature. Well-understood examples from photonics include mode locking and a broad class of fractal optics, including self-similarity. In addition to the fundamental interest in such systems, fascinating technical functionalities that are difficult or even impossible to achieve with linear systems can emerge naturally from them if the right control tools can be applied. Here, we demonstrate a method that exploits positive nonlocal feedback to initiate, and negative local feedback to regulate, the growth of ultrafast laser-induced metal-oxide nanostructures with unprecedented uniformity, at high speed, low cost and on non-planar or flexible surfaces. The nonlocal nature of the feedback allows us to stitch the nanostructures seamlessly, enabling coverage of indefinitely large areas with subnanometre uniformity in periodicity. We demonstrate our approach through the fabrication of titanium dioxide and tungsten oxide nanostructures, but it can also be extended to a large variety of other materials.