Minimum Condition Number Research Articles

Performance Improvement of Deception Jamming Against SAR Based on Minimum Condition Number

This paper proposes a new approach to improve the error performance of the synergy netting deception jamming against synthetic aperture radar (SAR). The existing methods cannot tackle the issue of error amplification induced by the linear equations constructed for jamming coefficients calculation. To handle this problem, we develop an optimal layout for radar receivers to minimize the effect of the error by minimizing the condition number, which measures the sensitivity of the synergy deception jamming system to the perturbation. It is revealed that the devised approach relies little on the SAR kinematic parameters. To further improve the error performance of the jamming system, collaborative receivers, which provide more observations of time difference of arrivals, are introduced to perform a linear least-squares estimation. The error reduction level due to the cooperative receivers is analyzed. Simulation results are provided to illustrate the superiority of the proposed method.

Intrinsic coincident full-Stokes polarimeter using stacked organic photovoltaics.

An intrinsic coincident full-Stokes polarimeter is demonstrated by using strain-aligned polymer-based organic photovoltaics (OPVs) that can preferentially absorb certain polarized states of incident light. The photovoltaic-based polarimeter is capable of measuring four Stokes parameters by cascading four semitransparent OPVs in series along the same optical axis. This in-line polarimeter concept potentially ensures high temporal and spatial resolution with higher radiometric efficiency as compared to the existing polarimeter architecture. Two wave plates were incorporated into the system to modulate the S₃ Stokes parameter so as to reduce the condition number of the measurement matrix and maximize the measured signal-to-noise ratio. Radiometric calibration was carried out to determine the measurement matrix. The polarimeter presented in this paper demonstrated an average RMS error of 0.84% for reconstructed Stokes vectors after normalized to S₀. A theoretical analysis of the minimum condition number of the four-cell OPV design showed that for individually optimized OPV cells, a condition number of 2.4 is possible.

On a vectorized version of a generalized Richardson extrapolation process

Let {xm} be a vector sequence that satisfies xm~s+?i=1??igi(m)asm??,$$\boldsymbol{x}_{m}\sim \boldsymbol{s}+\sum\limits^{\infty}_{i=1}\alpha_{i} \boldsymbol{g}_{i}(m)\quad\text{as \(m\to\infty\)}, $$s being the limit or antilimit of {xm} and {gi(m)}i=1?$\{\boldsymbol {g}_{i}(m)\}^{\infty }_{i=1}$ being an asymptotic scale as m ? ?, in the sense that limm???gi+1(m)??gi(m)?=0,i=1,2,?.$$\lim\limits_{m\to\infty}\frac{\|\boldsymbol{g}_{i+1}(m)\|}{\|\boldsymbol{g}_{i}(m)\|}=0,\quad i=1,2,\ldots. $$ The vector sequences {gi(m)}m=0?$\{\boldsymbol {g}_{i}(m)\}^{\infty }_{m=0}$, i = 1, 2,?, are known, as well as {xm}. In this work, we analyze the convergence and convergence acceleration properties of a vectorized version of the generalized Richardson extrapolation process that is defined via the equations ?i=1k?y,Δgi(m)??~i=?y,Δxm?,n≤m≤n+k?1;sn,k=xn+?i=1k?~igi(n),$$\sum\limits^{k}_{i=1}\langle\boldsymbol{y},{\Delta}\boldsymbol{g}_{i}(m)\rangle\widetilde{\alpha}_{i}=\langle\boldsymbol{y},{\Delta}\boldsymbol{x}_{m}\rangle,\quad n\leq m\leq n+k-1;\quad \boldsymbol{s}_{n,k}=\boldsymbol{x}_{n}+\sum\limits^{k}_{i=1}\widetilde{\alpha}_{i}\boldsymbol{g}_{i}(n), $$sn, k being the approximation to s. Here, y is some nonzero vector, ?? ,?? is an inner product, such that ??a,sb?=?¯s?a,b?$\langle \alpha \boldsymbol {a},\beta \boldsymbol {b}\rangle =\overline {\alpha }\beta \langle \boldsymbol {a},\boldsymbol {b}\rangle $, and Δxm = xm + 1? xm and Δgi(m) = gi(m + 1)?gi(m). By imposing a minimal number of reasonable additional conditions on the gi(m), we show that the error sn, k ? s has a full asymptotic expansion as n??. We also show that actual convergence acceleration takes place, and we provide a complete classification of it.

Off-line programming of six-axis robots for optimum five-dimensional tasks

Five-degree-of-freedom (five-dof) tasks are of particular interest in industry, since machining, arc-welding and deburring operations all fall into this category. These tasks, normally conducted with industrial six-dof robots, render the robot functionally redundant. Upon exploiting this redundancy to minimize the condition number of the Jacobian matrix, it is expected that the accuracy of the performed task will be increased. Traditional methods for redundancy-resolution are normally used to solve the more frequent intrinsic redundancy; however, they are not applicable to functional redundancy. Five-dof tasks are formulated using an approach that leads to a system of six velocity-level kinematics relations in six unknowns, with a 6×6 Jacobian matrix, of nullity 1, which reflects the functional redundancy of the problem at hand. To resolve the foregoing redundancy, a method based on sequential quadratic programming (SQP) is proposed. A novel method to compute the gradient of the condition number is also discussed, as it is a key element for finding the posture of minimum condition number using a gradient method. An example then shows how the SQP algorithm can be applied to offline robot trajectory-planning for five-dof tasks. In this example, a comparison is also made between the quasi-Newton and the Newton–Raphson methods to find the posture of minimum condition number for the robot. This is an essential step in finding the trajectory of minimum condition number.

A New Approach for Optimising GNSS Positioning Performance in Harsh Observation Environments

Maintaining good positioning performance has always been a challenging task for Global Navigation Satellite Systems (GNSS) applications in partially obstructed environments. A method that can optimise positioning performance in harsh environments is proposed. Using a carrier double-difference (DD) model, the influence of the satellite-pair geometry on the correlation among different equations has been researched. This addresses the critical relationship between DD equations and its ill-posedness. From analysing the collected multi-constellation observations, a strong correlation between the condition number and the positioning standard deviation is detected as the correlation coefficient is larger than 0·92. Based on this finding, a new method for determining the reference satellites by using the minimum condition number rather than the maximum elevation is proposed. This reduces the ill-posedness of the co-factor matrix, which improves the single-epoch positioning solution with a fixed DD ambiguity. Finally, evaluation trials are carried out by masking some satellites to simulate common satellite obstruction scenarios including azimuth shielding, elevation shielding and strip shielding. Results indicate the proposed approach improves the positioning stability with multi-constellation satellites notably in harsh environments.

Development and evaluation of SYBR Green-I based quantitative PCR assays for herpes simplex virus type 1 whole transcriptome analysis

There is an emerging need for viral gene specific quantitative PCR (qPCR) assays that validate and complement whole transcriptome level technologies, including microarray and next generation sequencing. Therefore, a compilation of qPCR assays that represented the breadth of the entire Herpes simplex virus type 1 (HSV-1) genome were developed and evaluated. SYBR Green-I-based quantitation of each of the 74 HSV-1 lytic genes enabled accurate and reproducible detection of viral genes using a minimal number of reaction conditions. The amplification specificity of these assays for HSV-1 target genes was confirmed by amplicon size and purity determination on agarose gels, melt temperature dissociation curve analysis, and direct DNA sequencing of amplified products. Analysis of representative target genes demonstrated that these assays accurately and reproducibly quantified target gene expression across a wide and linear range of detection. In addition, minimal intra- and inter-assay variability was observed with significant well-to-well and plate-to-plate/assay-to-assay precision. To evaluate the utility of the developed qPCR assay system, kinetic profiles of viral gene expression were determined for an array of representative genes from all HSV-1 transcriptional gene classes. Collectively, these data demonstrate that the compiled optimized qPCR assays is a scalable and cost-effective method to assess HSV-1 gene expression with broad application potential, including investigation of pathogenesis and antiviral therapies. In addition, they can be employed to validate and complement evolving technologies for genome-wide transcriptome analysis.

Numerical aspects of direct quadrature-based moment methods for solving the population balance equation

Direct-quadrature generalized moment based methods were analysed in terms of accuracy, computational cost and robustness for the solution of the population balance problems in the [0,∞) and [0,1] domains. The minimum condition number of the coefficient matrix of their linear system of equations was obtained by global optimization. An heuristic scaling rule from the literature was also evaluated. The results indicate that the methods based on Legendre generalized moments are the most robust for the finite domain problems, while the DQMoM formulation that solves for the abscissas and weights using the heuristic scaling rule is the best for the infinite domain problems.

Analysis of Dynamic Performance for Multiple Dividing Wall Distillation Columns

Dividing wall columns are intensified process equipment with the capacity of reducing both capital and operational costs for a given vapor–liquid separation, when compared with conventional distillation sequences. For some kinds of mixtures, distillation systems with two dividing walls have been theoretically proved to present lower energy requirements and lower total annual costs than systems with a single dividing wall. Nevertheless, the use of an additional wall may lead to operational issues on the column, because of the more complex arrangement of the walls on the trays of the columns, where additional split of the vapor and liquid streams is expected. Thus, in this work the open-loop properties (minimum singular value and condition number) for the double dividing wall column are studied and compared with those of the dividing wall column for a wide range of frequencies, in order to determinate if the use of additional dividing walls may lead to potential control problems. It has been found that both systems show similar dynamic performance, with advantages for the double dividing wall column for mixtures with low composition of the middle-boiling component.

Localization algorithm based on minimum condition number for wireless sensor networks

During range-based self-localization of Wireless Sensor Network (WSN) nodes, the number and placement methods of beacon nodes have a great influence on the accuracy of localization. This paper proves a theorem which describes the relationship between the placement of beacon nodes and whether the node can be located in 3D indoor environment. In fact, as the highest locating accuracy can be acquired when the beacon nodes form one or more equilateral triangles in 2D plane, we generalizes this conclusion to 3D space, and proposes a beacon nodes selection algorithm based on the minimum condition number to get the higher locating accuracy, which can minimize the influence of distance measurement error. Simulation results show that the algorithm is effective and feasible.

MULTI-OBJECTIVE RECONFIGURABLE OUTPUT FEEDBACK CONTROLLER FOR MIMO SYSTEM USING MOEAS

This article deals with the design of a parametric eigenstructure assignment (PEA)-based multi-objective reconfigurable output feedback controller for a multiple-input multiple-output (MIMO) system against partial actuator failure. The significance of the PEA technique is that it provides more design degrees of freedom to obtain multi-objective functions, namely robust stability and improved transient response. Robust stability and transient response are ensured by a minimum condition number of the eigenvector and a minimum norm of controller gain. These two objectives are conflicting in nature, and, hence, the main aim is to minimize both objectives simultaneously by means of a multi-objective evolutionary algorithm (MOEA). In this study, a multi-objective optimization problem is formulated and is solved by non-dominated sorting genetic algorithm-II (NSGA-II) and strength Pareto evolutionary algorithm-II (SPEA-II). Four indicators are used to evaluate each algorithm performance: spacing, error ratio, generational distance, and hypervolume. Then a reconfigurable controller is designed using PEA against actuator failure, which guarantees closed-loop stability. The effectiveness of the proposed controllers is demonstrated by implementing them in an interacting three-tank benchmark system.

Diagonal Scaling of Ill-Conditioned Matrixes by Genetic Algorithm

Diagonal Scaling of Ill-Conditioned Matrixes by Genetic AlgorithmThe purpose of this article is to use genetic algorithm for finding two invertible diagonal matricesD1andD2such that the scaled matrixD1AD2approaches to minimum condition number.

Preparing Projected Entangled Pair States on a Quantum Computer

We present a quantum algorithm to prepare injective projected entangled pair states (PEPS) on a quantum computer, a class of open tensor networks representing quantum states. The run time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS's parent Hamiltonian.

Well-conditioned configurations of fault-tolerant manipulators

Fault-tolerant motion of redundant manipulators can be obtained by joint velocity reconfiguration. For fault-tolerant manipulators, it is beneficial to determine the configurations that can tolerate the locked-joint failures with a minimum relative joint velocity jump, because the manipulator can rapidly reconfigure itself to tolerate the fault. This paper uses the properties of the condition numbers to introduce those optimal configurations for serial manipulators. The relationship between the manipulator’s locked-joint failures and the condition number of the Jacobian matrix is indicated by using a matrix perturbation methodology. Then, it is observed that the condition number provides an upper bound of the required relative joint velocity change for recovering the faults which leads to define the optimal fault-tolerant configuration from the minimization of the condition number. The optimization problem to obtain the minimum condition number is converted to three standard Eigen value optimization problems. A solution is for selected optimization problem is presented. Finally, in order to obtain the optimal fault-tolerant configuration, the proposed method is applied to a 4-DoF planar manipulator.

Optimal placement of PMU and SCADA measurements for security constrained state estimation

This paper presents a method for the use of Supervisory Control and Data Acquisition (SCADA) and synchronized measurements for complete observability of a power system. Under normal operation, both Node Phasor Measurement Unit (NPMU) and SCADA measurements are optimally placed using integer programming and Genetic Algorithm (GA) respectively. The minimum condition number of the Jacobian matrix is used as a criteria in conjunction with GA to obtain a completely determined condition. Next, a triangular factorization approach is used to search for the necessary candidates for single branch outage and single/multiple measurement loss. These candidate measurements are optimized by the binary integer programming method. Numerical results on the IEEE test systems are demonstrated. The results clearly show the robustness of the method to obtain reliable measurements under both normal and contingency conditions.

Multi-objective dynamic state and output feedback controllers for MIMO system using evolutionary algorithm and eigenstructure assignment

Most of the complex industrial plants are generally interacting multi-input multi-output (MIMO) systems. Controller design for such complex plants is a challenging task. In this paper, design of eigenstructure assignment (EA)-based multi-objective dynamic state and output feedback controllers for linear discrete MIMO system are considered. The significance of parametric eigenstructure assignment technique is that it provides more design degrees of freedom to obtain multi-objective functions. Based on parametric eigenstructure assignment, control problem is formulated to achieve conflicting multi-objective functions such as robust stability to parameter perturbation and smaller control gain to improve the transient response of the closed loop system. It is difficult to solve the conflicting objective functions using conventional optimisation techniques. In this paper, fast and elitist multi-objective evolutionary algorithm (MOEA) known as non-dominated sorting genetic algorithm-II (NSGA-II) is successfully applied for solving multi-objective problem. The robust stability and transient response are ensured by minimum condition number of eigenvector and minimum norm of controller gain. The proposed controllers use complex valued chromosomes to represent complex parametric vector. The effectiveness of the proposed controllers is validated by implementing the same in an interacting three-tank benchmark system.

MULTI-OBJECTIVE RECONFIGURABLE CONTROLLER DESIGN FOR THREE-TANK SYSTEM USING PARAMETRIC EIGENSTRUCTURE ASSIGNMENT

The reconfigurable controller (RC) design of strongly interacting multi-input multi-output system is a challenging problem for the designer. In this paper, a parametric right eigenstructure assignment based multiobjective dynamic reconfigurable controller through state feedback is proposed against partial actuator failure for a benchmark three-tank system. The practical aspects of controller design require the conflicting objectives of robust stability to parameter perturbation and smaller controller gain to improve the transient response of the system. These design objectives rise to the minimum condition number of closed-loop eigenvector and minimum norm of feedback controller gain of closed-loop system respectively. Fast and elitist multiobjective genetic algorithm known as nondominated sorting genetic algorithm-II is successfully applied to select the pareto-optimal eigenstructure of closed-loop system. Further, RC has been designed to accommodate partial actuator failure which is considered as loss of control effectiveness in actuators. Added value of this work, the controller uses complex-valued chromosomes. The effectiveness of the proposed controller is illustrated for different actuator fault scenarios through simulation and its performance is analysed.

Minimal condition number for positive definite Hankel matrices using semidefinite programming

We present a semidefinite programming approach for computing optimally conditioned positive definite Hankel matrices of order n. Unlike previous approaches, our method is guaranteed to find an optimally conditioned positive definite Hankel matrix within any desired tolerance. Since the condition number of such matrices grows exponentially with n, this is a very good test problem for checking the numerical accuracy of semidefinite programming solvers. Our tests show that semidefinite programming solvers using fixed double precision arithmetic are not able to solve problems with n>30. Moreover, the accuracy of the results for 24⩽n⩽30 is questionable. In order to accurately compute minimal condition number positive definite Hankel matrices of higher order, we use a Mathematica 6.0 implementation of the SDPHA solver that performs the numerical calculations in arbitrary precision arithmetic. By using this code, we have validated the results obtained by standard codes for n⩽24, and we have found optimally conditioned positive definite Hankel matrices up to n=100.

Stokes polarimeter optimization in the presence of shot and gaussian noise

:An error minimization method is presented for Stokes polarimeters applicable when the detected signals are affected by a combination of shot and Gaussian noise. The expectation of the Stokes vector variance is used as a performance measure. This measure is compared with the condition number of a polarization state analyzer matrix that is commonly used as a figure of merit. We show that a polarimeter with the minimum condition number is not necessarily optimal. The approach is used to optimize existing prism based polarimeters giving improvements in the performance when shot-noise cannot be neglected.

Visual motor control of a 7DOF redundant manipulator using redundancy preserving learning network

SUMMARYThis paper deals with the design and implementation of a visual kinematic control scheme for a redundant manipulator. The inverse kinematic map for a redundant manipulator is a one-to-many relation problem; i.e. for each Cartesian position, multiple joint angle vectors are associated. When this inverse kinematic relation is learnt using existing learning schemes, a single inverse kinematic solution is achieved, although the manipulator is redundant. Thus a new redundancy preserving network based on the self-organizing map (SOM) has been proposed to learn the one-to-many relation using sub-clustering in joint angle space. The SOM network resolves redundancy using three criteria, namely lazy arm movement, minimum angle norm and minimum condition number of image Jacobian matrix. The proposed scheme is able to guide the manipulator end-effector towards the desired target within 1-mm positioning accuracy without exceeding physical joint angle limits. A new concept of neighbourhood has been introduced to enable the manipulator to follow any continuous trajectory. The proposed scheme has been implemented on a seven-degree-of-freedom (7DOF) PowerCube robot manipulator successfully with visual position feedback only. The positioning accuracy of the redundant manipulator using the proposed scheme outperforms existing SOM-based algorithms.

An efficient spectral code for incompressible flows in cylindrical geometries

An efficient and accurate numerical scheme is proposed to solve the incompressible Navier–Stokes equations in a bounded cylinder. The scheme is based on a projection method formulated in primitive variables to maintain the incompressibility constraint, with a second-order semi-implicit scheme for the time integration, and a pseudospectral approximation for the space variables. The Chebyshev-collocation method applied in the radial and axial directions, and the Fourier–Galerkin approximation used in the azimuthal direction lead to a sequence of two-dimensional Helmholtz and Poisson equations for every azimuthal coefficient that are solved by a diagonalization technique. Radial expansions are considered in the diameter of the cell in order to avoid clustering about the axis, and the number of points are selected to ensure that r = 0 is not a collocation point. A minimal number of regularity conditions are imposed implicitly at the origin by forcing the proper parity of the Fourier expansions in the radial direction. The method has been tested on analytical solutions and compared with other reliable three-dimensional results. The improvements introduced in the treatment of the spatial discretization reduce significantly the difficulty of implementation of the code, and facilitate the use of high resolutions. Different boundary conditions can also be easily implemented.