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This article considers the distributed adaptive fault-tolerant control problem for heterogeneous linear multiagent systems with actuator faults and nonuniform time-varying communication delays. First, novel distributed switching observers are proposed to estimate the system matrix and the state of the exosystem. The observers allow each agent to share its information with its underlying neighbors only at sampled instants of time, thus making a distinct difference from the existing results that require the exosystem matrix to be accessible to all agents at every continuous instant of time. Second, a sufficient condition is derived such that the observer error systems are exponentially stable under the influence of communication delays among interacting agents. Third, new distributed adaptive fault-tolerant controllers, which promise fewer adaptive parameters, are presented to compensate for the actuator faults. It is shown that the developed controllers are capable to effectively and efficiently solve the cooperative fault-tolerant output regulation problem with reduced computational complexity. Finally, three illustrative examples, including an inverted pendulum system, an electronic double-integrator circuit system, and an AC microgrid system, are presented to show the validity and efficiency of the developed method.

Unmixing is an important issue of hyperspectral images. Most unmixing methods adopt linear mixing models for simplicity. However, multiple scattering usually occurs between vegetation and soil in a bilinear scene. Thus, nonlinear mixing problems which are difficult to be solved should be taken into consideration under this circumstance. In practice, both linear and nonlinear spectral mixtures exist in hyperspectral scenes. Considering the characteristics of different regions in images, we propose a hybrid unmixing algorithm for hyperspectral images based on region adaptive segmentation. Our method uses a standard K-means clustering algorithm to obtain different regions, including homogeneous regions and detailed regions. The model of the homogeneous regions is assumed to be linear, which will be pursued using the method of sparse-constrained nonnegative matrix factorization (NMF), and the mixing in the detailed regions is assumed to be based on a nonlinear model. We also propose a new nonlinear unmixing method, called graph-regularized semi-NMF, which considers the manifold structure of hyperspectral data as the unmixing method to deal with the detailed regions. Finally, by combining the two regions, we obtain the abundance of the whole hyperspectral image. The proposed method can not only achieve more precise abundance but also be good at keeping the edge information of the bilinear abundance. The experimental results on both synthetic and real data also show that the proposed method is effective for improving the unmixing accuracy of hyperspectral remote-sensing images.

A fast far-field approximation (FAFFA), which is simple to use, is applied to groundwave propagation modeling from a nonpenetrable surface with both soft and hard boundaries. The results are validated against available reference models as well as compared to other numerical methods such as split step parabolic equation model and the method of moments.

The separate absorption and multiplication (SAM) GaN/AlGaN solar-blind avalanche photodiodes (APDs) integrated with the specific design of 1-D dual-periodic photonic crystal on the back of the sapphire substrate are investigated numerically. The calculated results show that the proposed APDs can increase significantly the avalanche gain compared with the conventional SAM AlGaN solar-blind APDs using GaN instead of AlGaN as the multiplication layer. The enhanced performance can be explained by the larger hole ionization coefficient in the multiplication layer, the higher hole injection efficiency, and the reduced total dark current in this APDs. Meanwhile, the cutoff wavelength of 282 nm is achieved due to the optical filter effect of 1-D dual-periodic photonic crystal.

The volume integral equation method is applied in electromagnetic scattering from arbitrarily shaped three-dimensional inhomogeneous objects. The properties of the volume electric and magnetic field integral equations (VEFIE and VMFIE) are investigated. Numerical experiments show that if the Galerkin's method with the lowest mixed-order basis functions is used to discretize the equations the accuracy of the VMFIE can be significantly poorer than the accuracy of the VEFIE, in particular, for high-contrast objects at high frequencies. The accuracy of the VMFIE can be essentially improved with full first order (linear) basis functions. The linear basis functions are found to be useful also when a single volume integral equation is used to model a general scatterer where both permittivity and permeability differ from the background.

The hybrid volume and surface integral equation approach is applied to solve electromagnetic scattering and radiation problems involving conducting and/or dielectric objects. To flexibly and accurately model the complex structures and reduce the number of unknowns, mixed mesh scheme is developed to discretize the object. In this scheme, the triangles and quadrangles are used to discretize the conducting part of the object, and the tetrahedrons, hexahedrons, prisms and pyramids are used to model the dielectric volumes of the scatterer. Numerical results showed the solution accuracies from the mixed element meshes are of the same level compared with the single element meshes, but uses much less number of unknowns. This leads to flexibility for mesh generating and reduces the use of computing resources.

A high-order locally corrected Nystro/spl uml/m (LCN) method employing the mixed-order basis functions proposed by C$80al/spl iota/s$80kan and Peterson is presented for the electromagnetic scattering by targets composed of both dielectric and conducting bodies. An integral operator based on a combined field formulation for conducting surfaces and a Mu/spl uml/ller formulation for dielectric surfaces is used. It is found that for general scattering objects, mixed-order basis functions accelerate the convergence of the LCN solution, can eliminate spurious charges, and can significantly reduce the condition number of the impedance matrix.

In computational electromagnetics, the multilevel fast multipole algorithm (MLFMA) is used to reduce the computational complexity of the matrix vector product operations. In iteratively solving the dense linear systems arising from discretized hybrid integral equations, the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the Krylov iterations. We show that a good quality SAI preconditioner can be constructed by using the near part matrix numerically generated in the MLFMA. The main purpose of this study is to show that this class of the SAI preconditioners are effective with the MLFMA and can reduce the number of Krylov iterations substantially. Our experimental results indicate that the SAI preconditioned MLFMA maintains the computational complexity of the MLFMA, but converges a lot faster, thus effectively reduces the overall simulation time.

The input impedances of a microstrip antenna with finite and curved substrates are calculated using the hybrid volume surface integral equation approach. The results for flat and large substrate cases are compared with the measurement as well as the method of moment solution based on the spectral domain Green's function for infinitely large ground plane. Numerical results show that the input impedance can be significantly influenced when the substrate of a patch antenna is reduced in size or curved in shape.

The volume integral equation (VIE) combined with the multilevel fast multipole algorithm (MLFMA) is applied to analyze antenna radiation in the presence of dielectric radomes. In solving the VIE, the radome is modeled by small volume cells of tetrahedron or hexahedron shape so that three-dimensional (3-D) complex radomes can be modeled accurately. When the induced volume current is determined by the method of moments, the total radiation is calculated by adding the induced current radiation to that of the antenna in the absence of the radome. The application of MLFMA reduced the computational complexity to a lower order and hence electrically large-sized radomes are analyzed. Numerical results are compared with the analytical solution for spherical shells with dipole array as excitations. The radiation patterns of dipole arrays in the presence of ogive, cone, and hemisphere radomes are also presented.

Compared to the TM case, the inverse scattering problem for the TE incident field is more complicated due to its stronger nonlinearity. This work provides an effective method for the reconstruction of two-dimensional (2-D) inhomogeneous dielectric objects from TE scattering data. The algorithm applies the distorted Born iterative method to the integral equation of strong permittivity fluctuation to reconstruct scatterers with high-permittivity contrast. Numerical simulations are performed and the results show that the distorted Born iterative method (DBIM) for strong permittivity fluctuation (SPF-DBIM) converges faster and can obtain better reconstructions for objects with larger dimensions and higher contrasts in comparison with ordinary DBIM. A frequency hopping technique is also applied to further increase the contrast.

A combined solution of an electromagnetic (EM)-wave equation and head transfer equation is presented to analyze the microwave rewarming process of cryopreserved tissues. The solution process starts with an initial temperature of the tissue. The EM-field distribution inside the tissue is determined first by solving hybrid surface-volume integral equations. This solution provides a thermal source term for the heat-transfer equation. A finite-difference scheme is then applied to solve the heat-transfer equation, which determines the temperature distribution inside the tissue for the next time step. Since the tissue's electrical characteristics (/spl epsiv/ and /spl sigma/) are functions of temperature, their values are then updated based on the new temperature distribution. The iteration continues until a termination condition is satisfied. This combined iterative solution of wave equation and heat-transfer equation allows one to model the complex rewarming process. Numerical results are presented to demonstrate the application of the combined analysis approach.

FISC (Fast Illinois solver code), co-developed by the Center for Computational Electromagnetics, University of Illinois, and DEMACO, is designed to compute the RCS of a target described by a triangular-facet file. The problem is formulated using the method of moments (MoM), where the Rao, Wilton, and Glisson (1982) basis functions are used. The resultant matrix equation is solved iteratively by the conjugate gradient (CG) method. The multilevel fast multipole algorithm (MLFMA) is used to speed up the matrix-vector multiplication in the CG method. The complexities for both the CPU time per iteration and the memory requirements are of O(Nlog N), where N is the number of unknowns. A 2.4-million unknown problem is solved in a few hours on the SGI GRAY origin 2000 at NCSA of the University of Illinois at Urbana-Champaign.

An accurate and efficient technique called the thin-stratified medium fast-multipole algorithm (TSM-FMA) is presented for solving integral equations pertinent to electromagnetic analysis of microstrip structures, which consists of the full-wave analysis method and the application of the multilevel fast multipole algorithm (MLFMA) to thin stratified structures. In this approach, a new form of the electric-field spatial-domain Green's function is developed in a symmetrical form which simplifies the discretization of the integral equation using the method of moments (MoM). The patch may be of arbitrary shape since their equivalent electric currents are modeled with subdomain triangular patch basis functions. TSM-FMA is introduced to speed up the matrix-vector multiplication which constitutes the major computational cost in the application of the conjugate gradient (CG) method. TSM-FMA reduces the central processing unit (CPU) time per iteration to O(N log N) for sparse structures and to O(N) for dense structures, from O(N/sup 3/) for the Gaussian elimination method and O(N/sup 2/) per iteration for the CG method. The memory requirement for TSM-FMA also scales as O(N log N) for sparse structures and as O(N) for dense structures. Therefore, this approach is suitable for solving large-scale problems on a small computer.

This paper studies, in detail, a variety of formulations for the hybrid finite-element and boundary-integral (FE-BI) method for three-dimensional (3-D) electromagnetic scattering by inhomogeneous objects. It is shown that the efficiency and accuracy of the FE-BI method depends highly on the formulation and discretization of the boundary-integral equation (BIE) used. A simple analysis of the matrix condition number identifies the efficiency of the different FE-BI formulations and an analysis of weighting functions shows that the traditional FE-BI formulations cannot produce accurate solutions. A new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance. Finally, the multilevel fast multipole algorithm (MLFMA) is employed to significantly reduce the memory requirement and computational complexity of the proposed FE-BI method.

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects.

Various methods for efficiently solving electromagnetic problems are presented. Electromagnetic scattering problems can be roughly classified into surface and volume problems, while fast methods are either differential or integral equation based. The resultant systems of linear equations are either solved directly or iteratively. A review of various differential equation solvers, their complexities, and memory requirements is given. The issues of grid dispersion and hybridization with integral equation solvers are discussed. Several fast integral equation solvers for surface and volume scatterers are presented. These solvers have reduced computational complexities and memory requirements.

The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer.

The generalized network formulation is applied in combination with the method of moments to calculate the electromagnetic scattering from conducting objects containing near-resonant open-ended cavities. The presence of the cavity increases the iteration number in conjugate gradient iterations due to the near-resonant modes and the multiple wave bounces inside the cavity. The equivalence principle is used to separate the cavity region from the rest of the object, allowing an independent solution of the cavity problem by a direct inversion algorithm using a connection scheme. The solution of the cavity is then represented by a generalized admittance matrix. Numerical results for two-dimensional (2-D) composite targets show that the iteration number can be reduced significantly for objects containing long cavities. This algorithm can also be applied to three-dimensional problems.

The recursive aggregate interaction matrix algorithm (RAIMA) for calculating a wave scattering solution is developed. This algorithm combines the strength of both the recursive aggregate T matrix algorithm (RATMA) and the recursive interaction matrix algorithm (RIMA) that have been previously developed. The resultant algorithm is robust for scattering problems involving highly singular Green's functions by avoiding the violation of the addition theorem. It also has reduced computational complexity for inverting the volume integral equation of scattering. The computational complexity of RAIMA is O(N/sup 7/3/) in three dimensions and O(N/sup 2/) in two dimensions.

A three-dimensional (3-D) version of the nested equivalent principle algorithm (NEPAL) is presented. In 3-D, a scatterer is first decomposed into N subscatterers. Then, spherical wave functions are used to represent the scattered field of the subscatterers. Subscatterers are divided into different levels of groups in a nested manner. For example, each group consists of eight subgroups, and each subgroup contains eight sub-subgroups, and so on. For each subgroup, the scattering solution is first solved and the number of subscatterers of the subgroup is then reduced by replacing the interior subscatterers with boundary subscatterers using Huygens' equivalence principle. As a result, when the subgroups are combined to form a higher level group, the group will have a smaller number of subscatterers. This process is repeated for each level, and in the last level, the number of subscatterers is proportional to that of boundary size of the scatterers. This algorithm has a computational complexity of O(N/sup 2/) in three dimensions for all excitations and has the advantage of solving large scattering problems for multiple excitations. This is in contrast to Gaussian elimination which has a computational complexity of O(N/sup 3/). >

A feast recursive algorithm is used to compute the scattering properties of a finite array of strip gratings on a dielectric slab. this algorithm has a computational complexity of O(N log/sup 2/ N) for one incident angle and O(N/sup 2/ log N) for N incident angles. It uses plane wave basis for expanding the incident wave and the scattered wave. The scattered wave is expanded in terms of a Sommerfeld-type integral with spectral distribution along a vertical branch cut, rendering its expansion very efficient. To validate the scattering solution obtained using the recursive algorithm, comparisons with the method of moments are illustrated. The current distributions on the strips and scattering patterns are both presented. Since this algorithm has reduced computational complexity and is fast compared to other conventional methods, it can be used to analyze very large strip arrays. Scattering solution of a 50-wavelength wide strip is illustrated. >

The first three-dimensional analysis of a short backfire antenna (SBA) is described using the vector-mode-matching method. The computation is efficient for a model that uses only the first harmonic, cos phi , and that deforms the path of numerical integration. This model is useful for SBA computer-aided designs. A larger directivity than previously reported is obtained with the aid of this model. The theoretical predictions of the radiation pattern yield better agreement than previous methods when compared with measurements performed on a prototype. >

A coupled surface-volume integral equation approach is presented fur the calculation of electromagnetic scattering from conducting objects coated with materials. Free-space Green's function is used in the formulation of both integral equations. In the method of moments (MoM) solution to the integral equations, the target is discretized using triangular patches for conducting surfaces and tetrahedral cells for dielectric volume. General roof-top basis functions are used to expand the surface and volume currents, respectively. This approach is applicable to inhomogeneous material coating, and, because of the use of free-space Green's function, it can be easily accelerated using fast solvers such as the multilevel fast multipole algorithm.

The Born-iterative method (BIM) and the distorted-Born-iterative method (DBIM) have been proposed and verified as methods of solving the nonlinear inverse scattering problem for dielectric scatterers. The continuous-wave (CW) implementation of the DBIM was recently used to process microwave scattering data. Previously, diffraction tomography was used to process the data (a microwave image of human arm), resulting in an image with a small dynamic range due to the high contrasts present in the human body. Using the DBIM, the processed image was significantly improved. It is seen that upon iterating with DBIM, the contrast of the image is drastically enhanced.