Suboptimal control synthesis for state and input delayed quadratic systems

In this article a suboptimal linear-state feedback controller for multi-delay quadratic system is investigated. Optimal state and input coefficients resulting from the expansion over a hybrid basis of block pulse and Legendre polynomials are first obtained by formulating a nonlinear programming problem. Afterwards, suboptimal control gains are found by solving a least square problem constructed with optimal coefficients of the open loop study. A sufficient condition for the exponential stability of the closed loop is obtained from generalized Grönwall–Bellman lemma. The Van de Vusse chemical reactor case is handled allowing to validate the proposed technique.

Nonconvex Energy Minimization with Unsupervised Line Process Classifier for Efficient Piecewise Constant Signals Reconstruction

In this paper, we focus on the problem of signal smoothing and step-detection for piecewise constant signals. This problem is central to several applications such as human activity analysis, speech or image analysis, and anomaly detection in genetics. We present a two-stage approach to minimize the well-known line process model which arises from the probabilistic representation of the signal and its segmentation. In the first stage, we minimize a TV least square problem to detect the majority of the continuous edges. In the second stage, we apply a combinatorial algorithm to filter all false jumps introduced by the TV solution. The performances of the proposed method were tested on several synthetic examples. In comparison to recent step-preserving denoising algorithms, the acceleration presents a superior speed and competitive step-detection quality.

A novel method to identify DH parameters of the rigid serial-link robot based on a geometry model

Purpose Every geometric model corresponding to a unique feature whose errors of parameters uncorrelated, so the linearization technique can be successfully applied. The solution of a linear least square problem can be applied straightforwardly. This method has advantages especially in calibrate the redundant robot because it’s relatively small. The parameters of kinematics are unique and determined by this algorithm. Design/methodology/approach In this paper, a geometric identification method has been studied to estimate the parameters in the Denavit–Hartenberg (DH) model of the robot. Through studying the robot’s geometric features, specific trajectories are designed for calibrating the DH parameters. On the basis of these geometric features, several fitting methods have been deduced so that the important geometric parameters of robots, such as the actual rotation centers and rotate axes, can be found. Findings By measuring the corresponding motion trajectory at the end-effector, the trajectory feature can be identified by using curve fitting methods, and the trajectory feature will reflect back to the actual value of the DH parameters. Originality/value This method is especially suitable for rigid serial-link robots especially for redundant robots because of its specific calibration trajectory and geometric features. Besides, this method uses geometric features to calibrate the robot which is relatively small especially for the redundant robot comparing to the numerical algorithm.

A Novel Method for Asynchronous Time-of-Arrival-Based Source Localization: Algorithms, Performance and Complexity

In time-of-arrival (TOA)-based source localization, accurate positioning can be achieved only when the correct signal propagation time between the source and the sensors is obtained. In practice, a clock error usually exists between the nodes causing the source and sensors to often be in an asynchronous state. This leads to the asynchronous source localization problem which is then formulated to a least square problem with nonconvex and nonsmooth objective function. The state-of-the-art algorithms need to relax the original problem to convex programming, such as semidefinite programming (SDP), which results in performance loss. In this paper, unlike the existing approaches, we propose a proximal alternating minimization positioning (PAMP) method, which minimizes the original function without relaxation. Utilizing the biconvex property of original asynchronous problem, the method divides it into two subproblems: the clock offset subproblem and the synchronous source localization subproblem. For the former we derive a global solution, whereas the later is solved by a proposed efficient subgradient algorithm extended from the simulated annealing-based Barzilai–Borwein algorithm. The proposed method obtains preferable localization performance with lower computational complexity. The convergence of our method in Lyapunov framework is also established. Simulation results demonstrate that the performance of PAMP method can be close to the optimality benchmark of Cramér–Rao Lower Bound.

Novel Implementation Approach with Enhanced Memory Access Performance of MGS Algorithm for VLIW Architecture

Modified Gram–Schmidt (MGS) algorithm is one of the most-known forms of QR decomposition (QRD) algorithms. It has been used in many signal and image processing applications to solve least square problem and linear equations or to invert matrices. However, QRD is well-thought-out as a computationally expensive technique, and its sequential implementation fails to meet the requirements of many real-time applications. In this paper, we suggest a new parallel version of MGS algorithm that uses VLIW (Very Long Instruction Word) resources in an efficient way to get more performance. The presented parallel MGS is based on compact VLIW kernels that have been designed for each algorithm step taking into account architectural and algorithmic constraints. Based on instruction scheduling and software pipelining techniques, the proposed kernels exploit efficiently data, instruction and loop levels parallelism. Additionally, cache memory properties were used efficiently to enhance parallel memory access and to avoid cache misses. The robustness, accuracy and rapidity of the introduced parallel MGS implementation on VLIW enhance significantly the performance of systems under severe rea-time and low power constraints. Experimental results show great improvements over the optimized vendor QRD implementation and the state of art.

Nonlinear Operators as Concerns Convex Programming and Applied to Signal Processing

Splitting methods have received a lot of attention lately because many nonlinear problems that arise in the areas used, such as signal processing and image restoration, are modeled in mathematics as a nonlinear equation, and this operator is decomposed as the sum of two nonlinear operators. Most investigations about the methods of separation are carried out in the Hilbert spaces. This work develops an iterative scheme in Banach spaces. We prove the convergence theorem of our iterative scheme, applications in common zeros of accretive operators, convexly constrained least square problem, convex minimization problem and signal processing.

Multiple Linear Regression Model of Rice Production using Conjugate Gradient Methods

Regression is one of the basic relationship models in statistics. This paper focuses on the formation of regression models for the rice production in Malaysia by analysing the effects of paddy population, planted area, human population and domestic consumption. In this study, the data were collected from the year 1980 until 2014 from the website of the Department of Statistics Malaysia and Index Mundi. It is well known that the regression model can be solved using the least square method. Since least square problem is an unconstrained optimisation, the Conjugate Gradient (CG) was chosen to generate a solution for regression model and hence to obtain the coefficient value of independent variables. Results show that the CG methods could produce a good regression equation with acceptable Root Mean-Square Error (RMSE) value.

Robust Entangled-Photon Ghost Imaging with Compressive Sensing

This work experimentally demonstrates that the imaging quality of quantum ghost imaging (GI) with entangled photons can be significantly improved by properly handling the errors caused by the imperfection of optical devices. We also consider compressive GI to reduce the number of measurements and thereby the data acquisition time. The image reconstruction is formulated as a sparse total least square problem which is solved with an iterative algorithm. Our experiments show that, compared with existing methods, the new method can achieve a significant performance gain in terms of mean square error and peak signal–noise ratio.