Sharif Digital Repository

This paper deals with a refined analysis and modification of existing results on the flocking algorithms proposed for the second order dynamic agents. In the present work, the limiting condition of ever connectivity is removed and it is proved that the flocking can be reached if only the union of the network proximity graphs during nonoverlapping time intervals becomes connected frequently enough. Also, it is proved that including a static virtual leader cannot model the group objective of achieving the desired velocity and it will stop eventually at a predefined point in the space. The convergence rate to this fixed point is determined too. The last contribution of this paper is definition... 

In this work, we study the lossy source coding of a Gaussian source with polar codes. We show through two distributions on discrete alphabet, quantized approach as well as Central Limit Theorem (CLT) approach, when the alphabet size grows to infinity, polar codes can achieve the rate distortion bound for a Gaussian source. By comparing the rate of convergence on two distributions, we show that the quantized approach have a better convergence rate than the CLT approach  

This paper considers flocking to the virtual leader in network of agents with double-integrator. A locally linear algorithm is employed which guarantees exponential flocking to the virtual leader. A lower bound for flocking rate is calculated which is independent of the initial conditions. Simulations are provided to validate the result and it is shown that the calculated rate is not over bound the actual convergence rate. The effect of coefficients of algorithm is investigated and it is shown that the similar results can be inferred from the calculated formula for the convergence rate. Copyright  

The purpose of dictionary learning problem is to learn a dictionary D from a training data matrix Y such that Y ≈ DX and the coefficient matrix X is sparse. Many algorithms have been introduced to this aim, which minimize the representation error subject to a sparseness constraint on X. However, the dictionary learning problem is non-convex with respect to the pair (D,X). In a previous work [Sadeghi et al., 2013], a convex approximation to the non-convex term DX has been introduced which makes the whole DL problem convex. This approach can be almost applied to any existing DL algorithm and obtain better algorithms. In the current paper, it is shown that a simple modification on that approach... 

In the present study, a preconditioned Euler flow solver is developed to accurately and efficiently compute the inviscid flowfield around hovering helicopter rotor. The preconditioning method proposed by Eriksson is applied. The three-dimensional preconditioned Euler equations written in a rotating coordinate frame are solved by using a cell-centered finite volume Roe's method on unstructured meshes. High-order accuracy is achieved via the reconstruction of flow variables using the MUSCL interpolation technique. Calculations are carried out for an isolated rotor in hover for different conditions and the computed surface pressure distributions are compared with the experimental data. The... 

Learning sparsifying dictionaries from a set of training signals has been shown to have much better performance than pre-designed dictionaries in many signal processing tasks, including image enhancement. To this aim, numerous practical dictionary learning (DL) algorithms have been proposed over the last decade. This paper introduces an accelerated DL algorithm based on iterative proximal methods. The new algorithm efficiently utilizes the iterative nature of DL process, and uses accelerated schemes for updating dictionary and coefficient matrix. Our numerical experiments on dictionary recovery show that, compared with some well-known DL algorithms, our proposed one has a better convergence... 

Transferring large models in federated learning (FL) networks is often hindered by clients' limited bandwidth. We propose $ extsf {FedAA}$ , an FL algorithm which achieves fast convergence by exploiting the regularized Anderson acceleration (AA) on the global level. First, we demonstrate that FL can benefit from acceleration methods in numerical analysis. Second, $ extsf {FedAA}$ improves the convergence rate for quadratic losses and improves the empirical performance for smooth and strongly convex objectives, compared to FedAvg, an FL algorithm using gradient descent (GD) local updates. Experimental results demonstrate that employing AA can significantly improve the performance of FedAvg,... 

This paper deals with the consensus problem in an uncertain multi-agent system whose agents communicate with each other through a weighted undirected (primary) graph. The considered multi-agent system is described by an uncertain state-space model in which the involved matrices belong to some matrix boxes. As the main contribution of the paper, a unified optimization-based framework is proposed for simultaneously reducing the weights of the edges of the primary communication graph (optimizing the network topology) and synthesizing a controller such that the consensus in the considered uncertain multi-agent system is ensured with an adjustable convergence rate. Considering the NP-hardness... 

We study the statistical and computational properties of a network Lasso method for local graph clustering. The clusters delivered by nLasso can be characterized elegantly via network flows between cluster boundaries and seed nodes. While spectral clustering methods are guided by a minimization of the graph Laplacian quadratic form, nLasso minimizes the total variation of cluster indicator signals. As demonstrated theoretically and numerically, nLasso methods can handle very sparse clusters (chain-like) which are difficult for spectral clustering. We also verify that a primal-dual method for non-smooth optimization allows to approximate nLasso solutions with optimal worst-case convergence... 

In this part, similar to part I of this paper, a new approach for Goal Coordination is introduced that is more convergent than the previously suggested methods. This is mainly because of using the gradient of interaction errors; difference between the actual interactions and the optimum calculated interaction values, to improve the coordination parameters. The proposed scheme extremely improves the convergence rate of the solution in compare to the classical methods. The significance and applicability of the proposed approach is shown in controlling the excitation voltage of two coupled synchronous machines described by six coupled non-linear differential equations. © 2005 IEEE  

In this paper, a new decomposition-coordination framework is presented for two-level optimal control of large-scale nonlinear systems. In the proposed approach, decomposition is performed by defining an interaction vector, while coordination is based on a new interaction prediction approach. In the first level, sub-problems are solved for nonlinear dynamics using a gradient method, while in the second level, the coordination is done using the gradient of coordination errors. This is in contrast to the conventional gradient-type coordination schemes, where they use the gradient of Lagrangian function. It is shown that the proposed decomposition-coordination framework considerably reduces the... 

This paper considers the problem of high-performance global stabilization of an integrator chain via a bounded control at the presence of input disturbance. While nested saturated feedback (NSF) is known as the most inspiring existing solution in the literature, we shall highlight the inherent shortcomings of this approach which cause a poor performance in terms of convergence rate. Then, a novel dual-mode control scheme combining an improved NSF law with a linear matrix inequality (LMI)-based model predictive controller (MPC) is developed to overcome the weaknesses of pure NSF. By offline calculations, a set of nested robust invariant attraction regions and their attributed feedback gains... 

The presence of the desired signal (DS) in the training snapshots makes the adaptive beamformer sensitive to any steering vector mismatch and dramatically reduces the convergence rate. The objective of the present study is to propose a new adaptive beamformer which is robust against direction-of-arrival (DOA) mismatch and its convergence rate is not sensitive to the presence of the DS. This method is applicable to the arrays with specific structure such as the linear array. Our approach is based on the DS elimination from the training snapshots and the sub-array beamforming technique. To accomplish this goal, a blocking matrix which converts the primary data to the DS-free data is... 

The performance of the adaptive spatial resolution technique is improved by making the resolution function of the coordinate transformation as smooth as possible. To this end, the smoothness of the resolution function is probed and a quantitative criterion is proposed to make the jump points; which were conventionally equidistant from each other, regularized. The here-proposed regularization is applied to two different recent formulations and its effects on the overall convergence rate and on the presence of numerical artifacts in analysis of highly conducting gratings are studied. Dielectric and metallic gratings at optical and microwave frequencies are considered and the helpfulness of the... 

This paper presents a dynamically smooth nonlinear observer for satellite attitude determination. The proposed observer uses a 3-axis gyro and a single vector measurement to estimate the attitude of a satellite. The proposed observer preserves orthogonality of the estimated attitude matrix for all time. Almost global and exponential convergence of the estimated attitude to its true value is proven without persistency of excitation conditions. The convergence rate is shown to depend on properties of certain time varying reference vectors expressed in inertial frame. A procedure for maximizing a lower bound of the convergence rate is also presented. Performance of the proposed observer is... 

In this paper, a new interaction prediction approach for hierarchical control of non-linear large-scale systems is presented. The proposed approach uses a new gradient-type coordination scheme which is robust with respect to the parameters' variation, and also has a good convergence rate. In classical coordination strategies, which can be divided into the gradient-type and substitution-type approaches, it is not possible to improve the robustness and the convergence rate at the same time, since by increasing one the other decreases. The proposed approach has the main advantages of the gradient-type algorithms in being independent of the parameter's variation and also the initial guess of the...