Auxiliary Term Research Articles

Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising

A new deblurring and denoising algorithm is proposed, for isotropic total variation-based image restoration. The algorithm consists of an efficient solver for the nonlinear system and an acceleration strategy for the outer iteration. For the nonlinear system, the split Bregman method is used to convert it into linear system, and an algebraic multigrid method is applied to solve the linearized system. For the outer iteration, we have conducted formal convergence analysis to determine an auxiliary linear term that significantly stabilizes and accelerates the outer iteration. Numerical experiments demonstrate that our algorithm for deblurring and denoising problems is efficient.

Robust optimal control of uncertain nonaffine MIMO nonlinear discrete‐time systems with application to HCCI engines

SUMMARYMIMO optimal control of unknown nonaffine nonlinear discrete‐time systems is a challenging problem owing to the presence of control inputs inside the unknown nonlinearity. In this paper, the nonaffine nonlinear discrete‐time system is transformed to an affine‐like equivalent nonlinear discrete‐time system in the input–output form. Next, a forward‐in‐time Hamilton–Jacobi–Bellman equation‐based optimal approach, without using value and policy iterations, is developed to control the affine‐like nonlinear discrete‐time system by using both NN as an online approximator and output measurements alone. To overcome the need to know the control gain matrix in the optimal controller, a new online discrete‐time NN identifier is introduced. The robustness of the overall closed‐loop system is shown via singular perturbation analysis by using an additional auxiliary term to mitigate the higher‐order terms. Lyapunov stability of the overall system, which includes the online identifier and robust control term, demonstrates that the closed‐loop signals are bounded and the approximate control input approaches the optimal control signal with a bounded error. The proposed optimal control approach is applied to a cycle‐by‐cycle discrete‐time representation of an experimentally validated homogeneous charge compression ignition fuel‐flexible engine whose dynamics are modeled as uncertain nonlinear, nonaffine, and MIMO discrete‐time system. Simulation results are included to demonstrate the efficacy of the approach in presence of actuator disturbances. Copyright © 2012 John Wiley & Sons, Ltd.

Homotopy Perturbation Method with an Auxiliary Term

The two most important steps in application of the homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. The homotopy equation should be such constructed that when the homotopy parameter is zero, it can approximately describe the solution property, and the initial solution can be chosen with an unknown parameter, which is determined after one or two iterations. This paper suggests an alternative approach to construction of the homotopy equation with an auxiliary term; Dufing equation is used as an example to illustrate the solution procedure.

An Asymmetric Proximal Decomposition Method for Convex Programming with Linearly Coupling Constraints

The problems studied are the separable variational inequalities with linearly coupling constraints. Some existing decomposition methods are very problem specific, and the computation load is quite costly. Combining the ideas of proximal point algorithm (PPA) and augmented Lagrangian method (ALM), we propose an asymmetric proximal decomposition method (AsPDM) to solve a wide variety separable problems. By adding an auxiliary quadratic term to the general Lagrangian function, our method can take advantage of the separable feature. We also present an inexact version of AsPDM to reduce the computation load of each iteration. In the computation process, the inexact version only uses the function values. Moreover, the inexact criterion and the step size can be implemented in parallel. The convergence of the proposed method is proved, and numerical experiments are employed to show the advantage of AsPDM.

Use of fetal colon thickness for auxiliary term dating of pregnancy

Objective To verify whether fetal colon thickness can be used as a marker for estimating, independent of biometrics and fetal weight percentile, the gestational age (GA) of fetuses between 37 and 40 weeks. Methods The study group was 1296 fetuses aged between 33 and 40 weeks. The correlation between GA and colon thickness was assessed by the Pearson correlation test. For term fetuses (≥ 37 weeks), comparisons among the mean colon thickness for different weight percentiles at each GA (in weeks) were made with an analysis of variance test. Results A significant relationship was observed between GA and colon thickness ( P < 0.001, r 2 = 0.6). For term fetuses, significant differences were observed among the mean colon thickness values for different weight percentiles at 38 and 39 weeks. Of the 157 term fetuses for which biometrics would have underestimated GA by 2 weeks or more, 126 (80.3%) had a colon thickness equal to, or greater than, 14 mm. This colon thickness was also observed in 52 (70.3%) of term fetuses weighing less than the 10th percentile (n = 74). Conclusion The present study suggested that colon thickness might be a good marker for 37 weeks of gestation, and might identify term fetuses for which biometrics has underestimated the GA.

Approximate trajectory tracking of input‐disturbed PVTOL aircraft with delayed attitude measurements

AbstractIn this paper, we address the flight‐trajectory tracking problem of an input‐disturbed planar vertical take‐off and landing (PVTOL) aircraft with delayed attitude measurements. By applying the first‐order Padé approximation to deal with the time delay functions, the problem is reduced to the output tracking of a new non‐minimum‐phase system without delay. A tracking controller, consisting of a linear static‐state feedback term, a switching control term and a nonlinear auxiliary input term, is proposed for robust stabilization of the output‐tracking errors together with the internal dynamics. Numerical simulations are performed to show the main results. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Effect of attrition on particle size distribution and SO 2 capture in fluidized bed combustion under high CO 2 partial pressure conditions

In both pressurized and oxygen-enriched fluidized bed combustion the partial pressure of CO 2 in the reactor becomes high, which affects SO 2 capture by limestone. Both of these technologies are also applicable to decreasing greenhouse gas emissions; the first one by increasing the efficiency of electric energy production and the latter by enabling capture of carbon dioxide for storage. Attrition increases the reaction rate by removing the sulphated layer on the particle, thus reducing the diffusion resistance. In the well-known solution for the shrinking core model the reaction time can be presented as the sum of the contributions of the kinetics and diffusion. It is shown that the effect of attrition can be expressed as an auxiliary term in this expression. A method to extract the diffusivity of the product layer from the SO 2 response in a bench-scale fluidized bed test using a limestone sample with a wide particle size distribution is presented. Based on a population balance model, a method to estimate the particle-size-dependent attrition rate from measured particle size distributions of the feed and bed material is illustrated for a 71-MW e pressurized power plant. In addition attrition and its effect on the optimization of the limestone particle size for sulphur capture in oxygen-enriched combustion are discussed.

Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation

In this paper, we propose an improved region-based active contour model in a variational level set formulation. We define an energy functional with a local intensity fitting term, which induces a local force to attract the contour and stops it at object boundaries, and an auxiliary global intensity fitting term, which drives the motion of the contour far away from object boundaries. Therefore, the combination of these two forces allows for flexible initialization of the contours. This energy is then incorporated into a level set formulation with a level set regularization term that is necessary for accurate computation in the corresponding level set method. The proposed model is first presented as a two-phase level set formulation and then extended to a multi-phase formulation. Experimental results show the advantages of our method in terms of accuracy and robustness. In particular, our method has been applied to brain MR image segmentation with desirable results.

Low power proton exchange membrane fuel cell system identification and adaptive control

This paper proposes a systematic method of system identification and control of a proton exchange membrane (PEM) fuel cell. This fuel cell can be used for low-power communication devices involving complex electrochemical reactions of nonlinear and time-varying dynamic properties. From a system point of view, the dynamic model of PEM fuel cell is reduced to a configuration of two inputs, hydrogen and air flow rates, and two outputs, cell voltage and current. The corresponding transfer functions describe linearized subsystem dynamics with finite orders and time-varying parameters, which are expressed as discrete-time auto-regression moving-average with auxiliary input models for system identification by the recursive least square algorithm. In the experiments, a pseudo-random binary sequence of hydrogen or air flow rate is fed to a single fuel cell device to excite its dynamics. By measuring the corresponding output signals, each subsystem transfer function of reduced order is identified, while the unmodeled, higher-order dynamics and disturbances are described by the auxiliary input term. This provides a basis of adaptive control strategy to improve the fuel cell performance in terms of efficiency, as well as transient and steady state specifications. Simulation shows that adaptive controller is robust to the variation of fuel cell system dynamics, and it has proved promising from the experimental results.

Image Registration Based on Multiscale Energy Information

We propose a novel multiscale approach for the image registration problem, i.e., to find a deformation that maps one image onto another. The image registration problem is confirmed to be mathematical ill-posed due to the fact that determining the unknown components of the displacements merely from the images is an underdetermined problem. The approach presented here utilizes an auxiliary regularization term based on the energy of a plate with free edges, which incorporates smoothness constraints into the deformation field. One of the important aspects of this approach is that the energy does not penalize affine-linear functions. Consequently, the kernel of the Euler--Lagrange equation is spanned by all rigid motions. Hence, the presented approach is invariant under planar rotation and translation. In order to find an optimal deformation, we solve a sequence of subproblems with decreasing regularization parameter. In this framework the regularization parameter can be regarded as a scale parameter, which captures information at multiple spatial scales. We analyze the multiscale nature of a solution.

A Levenberg–Marquardt Scheme for Nonlinear Image Registration

This paper presents a Levenberg—Marquardt scheme to obtain a displacement vector field u(x)=(u 1(x),u 2(x)) t , which matches two images recorded with the same imaging machinery. The displacement vector should transform the image location x=(x 1,x 2) t of an image T, such that the grey level are equal to another image R. The so-called mono-modal image registration problem leads to minimize the nonlinear least squares functional D(u(x))=‖R(x)−T(x−u(x))‖2. To apply the Levenberg—Marquardt method, we replace the nonlinear functional D by its linearization around a current approximation. The resulting quadratic minimization problem is ill-posed, due to the fact that determining the unknown components of the displacements merely from the images is an underdetermined problem. We use an auxiliary Lagrange term borrowed from linear elasticity theory, which incorporates smoothness constraints to the displacement field. Finally, numerical experiments demonstrate the robustness and effectiveness of the proposed approach.

MORE ON GENERALIZED SIMPLICIAL CHIRAL MODELS

By generalizing the auxiliary field term in the Lagrangian of simplicial chiral models on a (d-1)-dimensional simplex, the generalized simplicial chiral models has been introduced in Ref. 1. These models can be solved analytically only in d=0 and d=2 cases at large-N limit. In the d=0 case, we calculate the eigenvalue density function in strong regime and show that the partition function computed from this density function is consistent with one calculated by path integration directly. In the d=2 case, it is shown that all V= Tr (AA†)n models have a third order phase transition, the same as the two-dimensional Yang–Mills theory.

Adaptive radial basis function neural network control with variable variance parameters

The paper presents a direct adaptive control architecture for a class of nonlinear dynamic systems, which are either ill defined or rather complex. The direct adaptive architecture employs radial basis function (RBF) neural network (NN) systems to reconstruct the ideal feedback linearization control. With the modified adaptation algorithm proposed herein, the on-line function approximation capability of the RBF NN a system is enhanced to remove the auxiliary control term and switching element in a conventional RBF-NN-based controller; simultaneously, the tracking performance is upgraded. Global asymptotic stability of the on-line algorithm is established in the Lyapunov sense to guarantee that the tracking error can converge to a small neighbourhood of the origin. Simulation validations for an inverted pendulum system are finally performed to verify the effectiveness of the proposed controller and the theoretical discussion.

Perturbation theory for particle in a box

Recently developed strong-coupling theory opens up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum mechanics of a point particle in a one-dimensional box. Introducing an auxiliary harmonic frequency term ω, the ground-state energy E (0) can be expanded perturbatively in powers of π 2/ ωd 2, where d is the box size. The removal of the infrared cutoff ω requires the resummation of the series at an infinitely strong coupling. We show that strong-coupling theory yields a fast-convergent sequence of approximations to the well-known quantum-mechanical energy E (0)= π 2/2 d 2.

Introducing Virtual Axis to Path Control System Using Superficial Evaluation Term

For a path control problem, we previously proposed a preview control system which has a superficial evaluation term in its performance index, and showed that the system is not effective for application to the following two cases. The first is when the tracking position lies along the velocity vector of the desired path. The second is when the desired path does not change. In both cases, the term becomes zero, and the path error becomes large. To solve the problem caused by the first case, we previously proposed the introduction of an auxiliary superficial evaluation term into the performance index. In this paper, to solve the problem caused by the second case, we propose the introduction of a virtual axis. The synthesis method for the new path control system is presented. To evaluate the effectiveness of the system, simulation studies are carried out. The simulation results show that the path tracking ability is markedly improved.

Coupling the auxiliary problem principle with descent methods of pseudoconvex programming

The descent auxiliary problem method allows one to find the solution of minimization problems by solving a sequence of auxiliary problems which incorporate a linesearch strategy. We derive the basic algorithm and study its convergence properties within the framework of infinite dimensional pseudoconvex minimization. We also introduce a partial descent type auxiliary problem method which partially linearizes the objective functional and includes the auxiliary term only for of subset of variables. Numerous examples of this very general scheme are provided.

Introducing Virtual Axis to Path Control System Using Superficial Evaluation Term.

Presently, tracking control with high speed and high accuracy is seriously required in the field of robotics and machine tools. For the control problem, we previously proposed a preview control system which has a superficial evaluation term in its performance index, and we showed that the preview system is not effective for applying the problem in two cases. The first is when the tracking position is on the velocity vector of the desired signal. The second is when the desired signal does not change. In both cases, the term becomes zero, then the path error becomes large. To overcome the problem caused by the first case, we proposed intoducing an auxiliary superficial term into the perpormance index of the preview control system. In this paper, to overcome the problem caused by the second case, we propose the intoduction of a virtual axis to the system. The synthesis method for the new path control system is presented. To evaluate the effectiveness of the proposed control system, simulation studies are carried out. The simulation results show that the path tracking ability is markedly improved.

Problems of the Superficial Evaluation Term Applied to Path Control and Introducing Auxiliary Superficial Term.

Presently, tracking control with high speed and high accuracy is required in the fields of robotics and machine tools. For the control problem, we proposed a preview control system which has a superficial evaluation term in its performance index. In this paper, we consider the physical meaning of the term for application to the problem. As a result, it becomes obvious that two cases are important. The first one is when tracking position is on the velocity vector of the desired signal. The second one is when the desired signal does not change. In both cases, the term becomes zero ; then the path error becomes large. To improve the problem caused by the first case, we introduce an auxiliary superficial term into the performance index of the preview control system. The synthesis of the new path control system is presented. To evaluate the effectiveness of the proposed control system, simulation studies are carried out. The simulation results show that path tracking ability is markedly improved.

Termination by completion

This paper presents a completion procedure for proving termination of term rewrite systems. It works as follows. Given a term rewrite systemR supposed to terminate and a term rewrite systemT used to transformR, the completion builds an auxiliary term rewrite systemS, the system transformed ofR byT. The termination ofS andT associated with a property called local cooperation implies the termination ofR. If the process terminates this provides a mechanical proof of the termination ofR.

History of Psoriasis and Parapsoriasis

Parapsoriasis is not a disease entity. It is an auxiliary term introduced in 1902 to group several dermatoses with a faint similarity to psoriasis. The historical development leading to the creation of the term parapsoriasis is outlined and the history of psoriasis is briefly reviewed.