Abstract: Profile hidden Markov models (profile-HMMs) are sensitive tools for remote protein homology detection, but the main scoring algorithms, Viterbi or Forward, require considerable time to search large sequence databases. We have designed a series of database filtering steps, HMMERHEAD, that are applied prior to the scoring algorithms, as implemented in the HMMER package, in an effort to reduce search time. Using this heuristic, we obtain a 20-fold decrease in Forward and a 6-fold decrease in Viterbi search time with a minimal loss in sensitivity relative to the unfiltered approaches. We then implemented an iterative profile-HMM search method, JackHMMER, which employs the HMMERHEAD heuristic. Due to our search heuristic, we eliminated the subdatabase creation that is common in current iterative profile-HMM approaches. On our benchmark, JackHMMER detects 14% more remote protein homologs than SAM's iterative method T2K. Our search heuristic, HMMERHEAD, significantly reduces the time needed to score a profile-HMM against large sequence databases. This search heuristic allowed us to implement an iterative profile-HMM search method, JackHMMER, which detects significantly more remote protein homologs than SAM's T2K and NCBI's PSI-BLAST.

Abstract: The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statistics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a plethora of applications.

Abstract: Array processing is widely used in sensing applications for estimating the locations and waveforms of the sources in a given field. In the absence of a large number of snapshots, which is the case in numerous practical applications, such as underwater array processing, it becomes challenging to estimate the source parameters accurately. This paper presents a nonparametric and hyperparameter, free-weighted, least squares-based iterative adaptive approach for amplitude and phase estimation (IAA-APES) in array processing. IAA-APES can work well with few snapshots (even one), uncorrelated, partially correlated, and coherent sources, and arbitrary array geometries. IAA-APES is extended to give sparse results via a model-order selection tool, the Bayesian information criterion (BIC). Moreover, it is shown that further improvements in resolution and accuracy can be achieved by applying the parametric relaxation-based cyclic approach (RELAX) to refine the IAA-APES&BIC estimates if desired. IAA-APES can also be applied to active sensing applications, including single-input single-output (SISO) radar/sonar range-Doppler imaging and multi-input single-output (MISO) channel estimation for communications. Simulation results are presented to evaluate the performance of IAA-APES for all of these applications, and IAA-APES is shown to outperform a number of existing approaches.

Abstract: In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements [1]. The new algorithms are broadly referred to as AMP, for approximate message passing. This is the first of two conference papers describing the derivation of these algorithms, connection with the related literature, extensions of the original framework, and new empirical evidence. In particular, the present paper outlines the derivation of AMP from standard sum-product belief propagation, and its extension in several directions. We also discuss relations with formal calculations based on statistical mechanics methods.

Abstract: Sparse signal models are used in many signal processing applications. The task of estimating the sparsest coefficient vector in these models is a combinatorial problem and efficient, often suboptimal strategies have to be used. Fortunately, under certain conditions on the model, several algorithms could be shown to efficiently calculate near-optimal solutions. In this paper, we study one of these methods, the so-called Iterative Hard Thresholding algorithm. While this method has strong theoretical performance guarantees whenever certain theoretical properties hold, empirical studies show that the algorithm's performance degrades significantly, whenever the conditions fail. What is more, in this regime, the algorithm also often fails to converge. As we are here interested in the application of the method to real world problems, in which it is not known in general, whether the theoretical conditions are satisfied or not, we suggest a simple modification that guarantees the convergence of the method, even in this regime. With this modification, empirical evidence suggests that the algorithm is faster than many other state-of-the-art approaches while showing similar performance. What is more, the modified algorithm retains theoretical performance guarantees similar to the original algorithm.

Abstract: We describe an iterative algorithm that converges to the maximum likelihood estimate of the position and intensity of a single fluorophore. Our technique efficiently computes and achieves the Cramer-Rao lower bound, an essential tool for parameter estimation. An implementation of the algorithm on graphics processing unit hardware achieved more than 10(5) combined fits and Cramer-Rao lower bound calculations per second, enabling real-time data analysis for super-resolution imaging and other applications.

Abstract: We address covariance estimation in the sense of minimum mean-squared error (MMSE) when the samples are Gaussian distributed. Specifically, we consider shrinkage methods which are suitable for high dimensional problems with a small number of samples (large p small n). First, we improve on the Ledoit-Wolf (LW) method by conditioning on a sufficient statistic. By the Rao-Blackwell theorem, this yields a new estimator called RBLW, whose mean-squared error dominates that of LW for Gaussian variables. Second, to further reduce the estimation error, we propose an iterative approach which approximates the clairvoyant shrinkage estimator. Convergence of this iterative method is established and a closed form expression for the limit is determined, which is referred to as the oracle approximating shrinkage (OAS) estimator. Both RBLW and OAS estimators have simple expressions and are easily implemented. Although the two methods are developed from different perspectives, their structure is identical up to specified constants. The RBLW estimator provably dominates the LW method for Gaussian samples. Numerical simulations demonstrate that the OAS approach can perform even better than RBLW, especially when n is much less than p . We also demonstrate the performance of these techniques in the context of adaptive beamforming.

Abstract: A variety of practical methods have recently been introduced for finding maximally sparse representations from overcomplete dictionaries, a central computational task in compressive sensing applications as well as numerous others. Many of the underlying algorithms rely on iterative reweighting schemes that produce more focal estimates as optimization progresses. Two such variants are iterative reweighted l1 and l2 minimization; however, some properties related to convergence and sparse estimation, as well as possible generalizations, are still not clearly understood or fully exploited. In this paper, we make the distinction between separable and non-separable iterative reweighting algorithms. The vast majority of existing methods are separable, meaning the weighting of a given coefficient at each iteration is only a function of that individual coefficient from the previous iteration (as opposed to dependency on all coefficients). We examine two such separable reweighting schemes: an l2 method from Chartrand and Yin (2008) and an l1 approach from Cande's (2008), elaborating on convergence results and explicit connections between them. We then explore an interesting non-separable alternative that can be implemented via either l2 or l1 reweighting and maintains several desirable properties relevant to sparse recovery despite a highly non-convex underlying cost function. For example, in the context of canonical sparse estimation problems, we prove uniform superiority of this method over the minimum l1 solution in that, 1) it can never do worse when implemented with reweighted l1, and 2) for any dictionary and sparsity profile, there will always exist cases where it does better. These results challenge the prevailing reliance on strictly convex (and separable) penalty functions for finding sparse solutions. We then derive a new non-separable variant with similar properties that exhibits further performance improvements in empirical tests. Finally, we address natural extensions to group sparsity problems and non-negative sparse coding.

Abstract: Recent years have seen significant interest in the paradigm of compressed sensing (CS) which permits, under certain conditions, signals to be sampled at sub-Nyquist rates via linear projection onto a random basis while still enabling exact reconstruction of the original signal. As applied to 2D images, however, CS faces several challenges including a computationally expensive reconstruction process and huge memory required to store the random sampling operator. Recently, several fast algorithms have been developed for CS reconstruction, while the latter challenge was addressed by Gan using a block-based sampling operation as well as projection-based Landweber iterations to accomplish fast CS reconstruction while simultaneously imposing smoothing with the goal of improving the reconstructed-image quality by eliminating blocking artifacts. In this technique, smoothing is achieved by interleaving Wiener filtering with the Landweber iterations, a process facilitated by the relative simple implementation of the Landweber algorithm. In this work, we adopt Gan's basic framework of block-based CS sampling of images coupled with iterative projection-based reconstruction with smoothing. Our contribution lies in that we cast the reconstruction in the domain of recent transforms that feature a highly directional decomposition. These transforms---specifically, contourlets and complex-valued dual-tree wavelets---have shown promise to overcome deficiencies of widely-used wavelet transforms in several application areas. In their application to iterative projection-based CS recovery, we adapt bivariate shrinkage to their directional decomposition structure to provide sparsity-enforcing thresholding, while a Wiener-filter step encourages smoothness of the result. In experimental simulations, we find that the proposed CS reconstruction based on directional transforms outperforms equivalent reconstruction using common wavelet and cosine transforms. Additionally, the proposed technique usually matches or exceeds the quality of total-variation (TV) reconstruction, a popular approach to CS recovery for images whose gradient-based operation also promotes smoothing but runs several orders of magnitude slower than our proposed algorithm.

Abstract: We provide a comprehensive review of five representative l 1 -minimization methods, i.e., gradient projection, homotopy, iterative shrinkage-thresholding, proximal gradient, and augmented Lagrange multiplier. The repository is intended to fill in a gap in the existing literature to systematically benchmark the performance of these algorithms using a consistent experimental setting. The experiment will be focused on the application of face recognition, where a sparse representation framework has recently been developed to recover human identities from facial images that may be affected by illumination change, occlusion, and facial disguise. The paper also provides useful guidelines to practitioners working in similar fields.

Abstract: The split feasibility problem (SFP) (Censor and Elfving 1994 Numer Algorithms 8 221–39) is to find a point x* with the property that x* C and Ax* Q, where C and Q are the nonempty closed convex subsets of the real Hilbert spaces and , respectively, and A is a bounded linear operator from to The SFP models inverse problems arising from phase retrieval problems (Censor and Elfving 1994 Numer Algorithms 8 221–39) and the intensity-modulated radiation therapy (Censor et al 2005 Inverse Problems 21 2071–84) In this paper we discuss iterative methods for solving the SFP in the setting of infinite-dimensional Hilbert spaces The CQ algorithm of Byrne (2002 Inverse Problems 18 441–53, 2004 Inverse Problems 20 103–20) is indeed a special case of the gradient-projection algorithm in convex minimization and has weak convergence in general in infinite-dimensional setting We will mainly use fixed point algorithms to study the SFP A relaxed CQ algorithm is introduced which only involves projections onto half-spaces so that the algorithm is implementable Both regularization and iterative algorithms are also introduced to find the minimum-norm solution of the SFP

Abstract: Sparse, redundant representations offer a powerful emerging model for signals. This model approximates a data source as a linear combination of few atoms from a prespecified and over-complete dictionary. Often such models are fit to data by solving mixed ?1-?2 convex optimization problems. Iterative-shrinkage algorithms constitute a new family of highly effective numerical methods for handling these problems, surpassing traditional optimization techniques. In this article, we give a broad view of this group of methods, derive some of them, show accelerations based on the sequential subspace optimization (SESOP), fast iterative soft-thresholding algorithm (FISTA) and the conjugate gradient (CG) method, present a comparative performance, and discuss their potential in various applications, such as compressed sensing, computed tomography, and deblurring.

Abstract: An algebraic multigrid method is presented to solve large systems of linear equations. The coarsen- ing is obtained by aggregation of the unknowns. The aggregation scheme uses two passes of a pairwise matching algorithm applied to the matrix graph, resulting in most cases in a decrease of the number of variables by a factor slightly less than four. The matching algorithm favors the strongest negative coupling(s), inducing a problem depen- dant coarsening. This aggregation is combined with piecewise constant (unsmoothed) prolongation, ensuring low setup cost and memory requirements. Compared with previous aggregation-based multigrid methods, the scalability is enhanced by using a so-called K-cycle multigrid scheme, providing Krylov subspace acceleration at each level. This paper is the logical continuation of (SIAM J. Sci. Comput., 30 (2008), pp. 1082-1103), where the analysis of a model anisotropic problem shows that aggregation-based two-grid methods may have optimal order convergence, and of (Numer. Lin. Alg. Appl., 15 (2008), pp. 473-487), where it is shown that K-cycle multigrid may provide optimal or near optimal convergence under mild assumptions on the two-grid scheme. Whereas in these papers only model problems with geometric aggregation were considered, here a truly algebraic method is presented and tested on a wide range of discrete second order scalar elliptic PDEs, including nonsymmetric and unstructured problems. Numerical results indicate that the proposed method may be significantly more robust as black box solver than the classical AMG method as implemented in the code AMG1R5 by K. Stuben. The parallel implementation is also discussed. Satisfactory speedups are obtained on a medium size multi-processor cluster that is typical of today com- puter market. A code implemanting the method is freely available for download both as a Fortran program and a Matlab function.

Abstract: In this paper, we introduce and analyze a modification of the Hermitian and skew-Hermitian splitting iteration method for solving a broad class of complex symmetric linear systems. We show that the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method is unconditionally convergent. Each iteration of this method requires the solution of two linear systems with real symmetric positive definite coefficient matrices. These two systems can be solved inexactly. We consider acceleration of the MHSS iteration by Krylov subspace methods. Numerical experiments on a few model problems are used to illustrate the performance of the new method.

Abstract: We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the optimally tuned implementations available at sparselab.stanford.edu; they run ?out of the box? with no user tuning: it is not necessary to select thresholds or know the likely degree of sparsity. Our class of algorithms includes iterative hard and soft thresholding with or without relaxation, as well as CoSaMP, subspace pursuit and some natural extensions. As a result, our optimally tuned algorithms dominate such proposals. Our notion of optimality is defined in terms of phase transitions, i.e., we maximize the number of nonzeros at which the algorithm can successfully operate. We show that the phase transition is a well-defined quantity with our suite of random underdetermined linear systems. Our tuning gives the highest transition possible within each class of algorithms. We verify by extensive computation the robustness of our recommendations to the amplitude distribution of the nonzero coefficients as well as the matrix ensemble defining the underdetermined system. Our findings include the following. 1) For all algorithms, the worst amplitude distribution for nonzeros is generally the constant-amplitude random-sign distribution, where all nonzeros are the same amplitude. 2) Various random matrix ensembles give the same phase transitions; random partial isometries may give different transitions and require different tuning. 3) Optimally tuned subspace pursuit dominates optimally tuned CoSaMP, particularly so when the system is almost square.

Abstract: For the large sparse linear complementarity problems, by reformulating them as implicit fixed-point equations based on splittings of the system matrices, we establish a class of modulus-based matrix splitting iteration methods and prove their convergence when the system matrices are positive-definite matrices and H+-matrices. These results naturally present convergence conditions for the symmetric positive-definite matrices and the M-matrices. Numerical results show that the modulus-based relaxation methods are superior to the projected relaxation methods as well as the modified modulus method in computing efficiency. Copyright © 2009 John Wiley & Sons, Ltd.

Abstract: This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each iteration, and each subspace update can be performed in linear time in the dimension of the subspace. The algorithm is derived by analyzing incremental gradient descent on the Grassmannian manifold of subspaces. With a slight modification, GROUSE can also be used as an online incremental algorithm for the matrix completion problem of imputing missing entries of a low-rank matrix. GROUSE performs exceptionally well in practice both in tracking subspaces and as an online algorithm for matrix completion.

Abstract: Krylov subspace methods (KSMs) are iterative algorithms for solving large, sparse linear systems and eigenvalue problems. Current KSMs rely on sparse matrix-vector multiply (SpMV) and vector-vector operations (like dot products and vector sums). All of these operations are communication-bound. Furthermore, data dependencies between them mean that only a small amount of that communication can be hidden. Many important scientific and engineering computations spend much of their time in Krylov methods, so the performance of many codes could be improved by introducing KSMs that communicate less. Our goal is to take s steps of a KSM for the same communication cost as 1 step, which would be optimal. We call the resulting KSMs "communication-avoiding Krylov methods." This thesis makes the following contributions: (1) We have fast kernels replacing SpMV, that can compute the results of s calls to SpMV for the same communication cost as one call (Section 2.1). (2) We have fast dense kernels as well, such as Tall Skinny QR (TSQR – Section 2.3) and Block Gram-Schmidt (BGS – Section 2.4), which can do the work of Modified Gram-Schmidt applied to s vectors for a factor of Θ(s2) fewer messages in parallel, and a factor of Θ(s/W) fewer words transferred between levels of the memory hierarchy (where W is the fast memory capacity in words). (3) We have new communication-avoiding Block Gram-Schmidt algorithms for orthogonalization in more general inner products (Section 2.5). (4) We have new communication-avoiding versions of the following Krylov subspace methods for solving linear systems: the Generalized Minimum Residual method (GMRES – Section 3.4), both unpreconditioned and preconditioned, and the Method of Conjugate Gradients (CG), both unpreconditioned (Section 5.4) and left-preconditioned (Section 5.5). (5) We have new communication-avoiding versions of the following Krylov subspace methods for solving eigenvalue problems, both standard (Ax = λx, for a nonsingular matrix A) and "generalized" (Ax = λMx, for nonsingular matrices A and M): Arnoldi iteration (Section 3.3), and Lanczos iteration, both for Ax = λx (Section 4.2) and Ax = λMx (Section 4.3). (6) We propose techniques for developing communication-avoiding versions of nonsymmetric Lanczos iteration (for solving nonsymmetric eigenvalue problems Ax = λx) and the Method of Biconjugate Gradients (BiCG) for solving linear systems. (7) We can combine more stable numerical formulations that use different bases of Krylov subspaces with our techniques for avoiding communication. For a discussion of different bases, see Chapter 7. To see an example of how the choice of basis affects the formulation of the Krylov method, see Section 3.2.2. (8) We have faster numerical formulations. For example, in our communication-avoiding version of GMRES, CA-GMRES (see Section 3.4), we can pick the restart length r independently of the s-step basis length s. Experiments in Section 3.5.5 show that this ability improves numerical stability. We show in Section 3.6.3 that it also improves performance in practice, resulting in a 2.23× speedup in the CA-GMRES implementation described below. (9) We combine all of these numerical and performance techniques in a shared-memory parallel implementation of our communication-avoiding version of GMRES, CA-GMRES. Compared to a similarly highly optimized version of standard GMRES, when both are running in parallel on 8 cores of an Intel Clovertown (see Appendix A), CA-GMRES achieves 4.3× speedups over standard GMRES on standard sparse test matrices (described in Appendix B.5). When both are running in parallel on 8 cores of an Intel Nehalem (see Appendix A), CA-GMRES achieves 4.1× speedups. See Section 3.6 for performance results and Section 3.5 for corresponding numerical experiments. We first reported performance results for this implementation on the Intel Clovertown platform in Demmel et al. [78]. (10) We have incorporated preconditioning into our methods. Note that we have not yet developed practical communication-avoiding preconditioners; this is future work. We have accomplished the following: (a) We show (in Sections 2.2 and 4.3) what the s-step basis should compute in the preconditioned case for many different types of Krylov methods and s-step bases. We explain why this is hard in Section 4.3. (b) We have identified two different structures that a preconditioner may have, in order to achieve the desired optimal reduction of communication by a factor of s. See Section 2.2 for details. (Abstract shortened by UMI.)

Abstract: The Kaczmarz method is an iterative algorithm for solving systems of linear equations Ax=b. Theoretical convergence rates for this algorithm were largely unknown until recently when work was done on a randomized version of the algorithm. It was proved that for overdetermined systems, the randomized Kaczmarz method converges with expected exponential rate, independent of the number of equations in the system. Here we analyze the case where the system Ax=b is corrupted by noise, so we consider the system Ax≈b+r where r is an arbitrary error vector. We prove that in this noisy version, the randomized method reaches an error threshold dependent on the matrix A with the same rate as in the error-free case. We provide examples showing our results are sharp in the general context.

Abstract: In a multi-atlas based segmentation procedure, propagated atlas segmentations must be combined in a label fusion process. Some current methods deal with this problem by using atlas selection to construct an atlas set either prior to or after registration. Other methods estimate the performance of propagated segmentations and use this performance as a weight in the label fusion process. This paper proposes a selective and iterative method for performance level estimation (SIMPLE), which combines both strategies in an iterative procedure. In subsequent iterations the method refines both the estimated performance and the set of selected atlases. For a dataset of 100 MR images of prostate cancer patients, we show that the results of SIMPLE are significantly better than those of several existing methods, including the STAPLE method and variants of weighted majority voting.

Abstract: Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another A novel method for deflationary ICA, referred to as RobustICA, is put forward in this paper This simple technique consists of performing exact line search optimization of the kurtosis contrast function The step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth-degree polynomial This polynomial rooting can be performed algebraically, and thus at low cost, at each iteration Among other practical benefits, RobustICA can avoid prewhitening and deals with real- and complex-valued mixtures of possibly noncircular sources alike The absence of prewhitening improves asymptotic performance The algorithm is robust to local extrema and shows a very high convergence speed in terms of the computational cost required to reach a given source extraction quality, particularly for short data records These features are demonstrated by a comparative numerical analysis on synthetic data RobustICA's capabilities in processing real-world data involving noncircular complex strongly super-Gaussian sources are illustrated by the biomedical problem of atrial activity (AA) extraction in atrial fibrillation (AF) electrocardiograms (ECGs), where it outperforms an alternative ICA-based technique

Abstract: Purpose: This article considers the problem of reconstructingcone-beam computed tomography(CBCT)images from a set of undersampled and potentially noisy projection measurements. Methods: The authors cast the reconstruction as a compressed sensing problem based on l 1 norm minimization constrained by statistically weighted least-squares of CBCT projection data. For accurate modeling, the noise characteristics of the CBCT projection data are used to determine the relative importance of each projection measurement. To solve the compressed sensing problem, the authors employ a method minimizing total-variation norm, satisfying a prespecified level of measurement consistency using a first-order method developed by Nesterov. Results: The method converges fast to the optimal solution without excessive memory requirement, thanks to the method of iterative forward and back-projections. The performance of the proposed algorithm is demonstrated through a series of digital and experimental phantom studies. It is found a that high quality CBCTimage can be reconstructed from undersampled and potentially noisy projection data by using the proposed method. Both sparse sampling and decreasing x-ray tube current (i.e., noisy projection data) lead to the reduction of radiationdose in CBCTimaging. Conclusions: It is demonstrated that compressed sensing outperforms the traditional algorithm when dealing with sparse, and potentially noisy, CBCT projection views.

Abstract: Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, particularly in problems of design. The solution of such PDE-constrained optimization problems is usually a major computational task. Here we consider simple problems of this type: distributed control problems in which the 2- and 3-dimensional Poisson problem is the PDE. The large-dimensional linear systems which result from discretization and which need to be solved are of saddle-point type. We introduce two optimal preconditioners for these systems, which lead to convergence of symmetric Krylov subspace iterative methods in a number of iterations which does not increase with the dimension of the discrete problem. These preconditioners are block structured and involve standard multigrid cycles. The optimality of the preconditioned iterative solver is proved theoretically and verified computationally in several test cases. The theoretical proof indicates that these approaches may have much broader applicability for other PDEs.

Abstract: We consider a multi-cell wireless network with universal frequency reuse and treat the problem of co-channel interference mitigation in the downlink channel. Assuming that each base station serves multiple single-antenna mobiles via space-division multiple-access, we jointly optimize the linear beam-vectors across a set of coordinated cells and resource slots: the objective function to be maximized is the instantaneous weighted sum-rate subject to per-base-station power constraints. After deriving the general structure of the optimal beam-vectors, a novel iterative algorithm is presented which attempts to solve the Karush-Kuhn-Tucker conditions of the non-convex problem at hand. The proposed algorithm admits a distributed implementation which we illustrate. Also, various approaches to choose the initial beam-vectors are considered, one of which maximizes the signal-to-leakage-plus-noise ratio. Finally, simulation results are provided to assess the performance of the proposed algorithm.

Abstract: This paper studies linear precoding and decoding schemes for K-user interference channel systems. It was shown by Cadambe and Jafar that the interference alignment (IA) algorithm achieves a theoretical bound on degrees of freedom (DOF) for interference channel systems. Based on this, we first introduce a non-iterative solution for the precoding and decoding scheme. To this end, we determine the orthonormal basis vectors of each user's precoding matrix to achieve the maximum DOF, then we optimize precoding matrices in the IA method according to two different decoding schemes with respect to individual rate. Second, an iterative processing algorithm is proposed which maximizes the weighted sum rate. Deriving the gradient of the weighted sum rate and applying the gradient descent method, the proposed scheme identifies a local-optimal solution iteratively. Simulation results show that the proposed iterative algorithm outperforms other existing methods in terms of sum rate. Also, we exhibit that the proposed non-iterative method approaches a local optimal solution at high signal-to-noise ratio with reduced complexity.

Abstract: In this paper, a new self adaptive iterative learning PD control(ILC-PD) scheme is proposed for trajectory tracking of robot manipulators with unknown parameters and performing repetitive tasks. This proposed control scheme is based upon a proportional-derivative(PD) feedback structure, for which an iterative term is added to cope with the unknown model parameters and disturbances. In contrast to classical iterative learning schemes, ILC-PD method is very simple in the sense that the only requirement on the PD and learning gains are just two iterative variables and the bounds of the robot parameters are not required, which is an interesting fact from a practical point of view. Furthermore, the ILC-PD method possesses both adaptive and learning capabilities with a simple control structure, and the asymptotical convergence is guaranteed based on the Lyapunov theorem. Finally simulations are presented for a planner manipulator with two revolute degrees of freedom. The results are provided to illustrate the effectiveness of the proposed controllers.