Asymptotic Convergence to Steady-State Solutions for Solutions of the Initial Boundary Problem to a Simplified Hydrodynamic Model for Semiconductor

We studied the asymptotic behavior of solutions to the initial boundary value problem on the spatial interval [0,1] for a one-dimensional simplified gydrodynamic model for semiconductors wheng(t)→b *, and proved the unique global existence of smooth solutions to the initial boundary problem. We also show that the solutions converge to the corresponding steady-state solutions time-asymptotically by introducing the suitable shift functions.

CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS

This paper studies the asymptotic behavior of solutions for nonlinear RLCnetwoiks which have the following form The function p i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditiolts. Under the assumption that every element value involving voltage source is asymptotically constallt, we establish four creteria for all solutiolls of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited uonliltear circuits.This results generalize those of Brayton and Moser[1,2].

ASYMPTOTIC EXPRESSION NEAR THE ELLIPSE OF CONVERGENCE OF JACOBI SERIES IN COMPLEX PLANE

In this paper, we shall give an Abel type theorem of Jacobi series and then based on it discuss asymptotic expressions near the ellipse of convergence of Jacobi series in complex plane.

Enhancing Iterative Learning Control With Fractional Power Update Law

The P-type update law has been the mainstream technique used in iterative learning control(ILC)systems,which resembles linear feedback control with asymptotical convergence.In recent years,finite-time control strategies such as terminal sliding mode control have been shown to be effective in ramping up convergence speed by introducing fractional power with feedback.In this paper,we show that such mechanism can equally ramp up the learning speed in ILC systems.We first propose a fractional power update rule for ILC of single-input-single-output linear systems.A nonlinear error dynamics is constructed along the iteration axis to illustrate the evolutionary converging process.Using the nonlinear mapping approach,fast convergence towards the limit cycles of tracking errors inherently existing in ILC systems is proven.The limit cycles are shown to be tunable to determine the steady states.Numerical simulations are provided to verify the theoretical results.

Inertial projection algorithms for convex feasibility problem

The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem.Compared with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm.Theoretical asymptotic convergence results are presented under some suitable conditions.Numerical simulations illustrate that the new methods have better convergence than the general projection methods.The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.

NEW HMM ALGORITHM FOR TOPOLOGY OPTIMIZATION

A new hybrid MMA-MGCMMA （HMM） algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes （MMA） algorithm and the modified globally convergent version of the method of moving asymptotes （MGCMMA） algorithm in the optimization process. This algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value existing in the calculation. This algorithm can improve calculation efficiency and accelerate convergence compared with simplex MMA or MGCMMA algorithms, which is proven with an example.

More on Fixed Point Theorem of {a, b, c}-Generalized Nonexpansive Mappings in Normed Spaces

Let X be a weakly Cauchy normed space in which the parallelogram law holds, C be a bounded closed convex subset of X with one contracting point and T be an {a,b,c}-generalized-nonexpansive mapping from C into C. We prove that the infimum of the set {‖x-T（x）‖} on C is zero, study some facts concerning the {a,b,c}-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to C is singleton. Depending on the fact that the {a,b,0}-generalized-nonexpansive mapping from C into C has fixed points, accord- ingly, another version of the Browder＇s strong convergence theorem for mappings is given.

Regularization with Closed Linear Operators

In this paper, the regularization with closed linear operators is used to solve an operator equation of the first kind. When all initial data are known approximately, we choose the regular parameter by using the general Arcangeli's criterion to give the convergence and the asymptotic orders of convergence of the regular solution.

Stochastic level-value approximation for quadratic integer convex programming

We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and report some numerical results to illuminate its effectiveness.

The effect of forced oscillations on the kinetics of wave drift in an inhomogeneous plasma

The kinetics is analyzed of the drift of non-potential plasma waves in spatial positions and wavevectors due to plasma's spatial inhomogeneity. The analysis is based on highly informative kinetic scenarios of the drift of electromagnetic waves in a cold ionized plasma in the absence of a magnetic field(Erofeev 2015 Phys. Plasmas 22 092302) and the drift of long Langmuir waves in a cold magnetized plasma(Erofeev 2019 J. Plasma Phys. 85 905850104). It is shown that the traditional concept of the wave kinetic equation does not account for the effects of the forced plasma oscillations that are excited when the waves propagate in an inhomogeneous plasma.Terms are highlighted that account for these oscillations in the kinetic equations of the abovementioned highly informative wave drift scenarios.

The convergence properties of infeasible inexact proximal alternating linearized minimization

The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real applications.In the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the PALM-I.The usage of the PALM-I thus lacks a theoretical guarantee.The essential difficulty of analysis consists in the objective value nonmonotonicity induced by the infeasibility.We study in the present work the convergence properties of the PALM-I.In particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact criterion.Based upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz property.The prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.

Nonlinear Extrapolation Estimates of π

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R~2 and it is well-known that by using linear combinations of these basic estimates,modern extrapolation techniques can greatly speed up the approximation process.Similarly,when n vertices are randomly selected on the circle,the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n→∞,and by further applying extrapolation processes,faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random polygons.In this paper,we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such polygons.We focus on two types of extrapolation estimates of the forms χ_n=S_n~αA_n~β and Y_n(p)=(αS_n~p+βA_n~p)~(1/p) where α+β=1,p≠0,and Sn and An respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in R~2,and Xn may be viewed as the limit of Y_n(p) when p→0.By deriving probabilistic asymptotic expansions with carefully controlled error estimates for Xn and Y_n(p),we show that the choice α=4/3,β=-1/3 minimizes the approximation error in both cases,and their distributions are also asymptotically normal.

Precision motion control for electro-hydraulic axis systems under unknown time-variant parameters and disturbances

This article focuses on asymptotic precision motion control for electro-hydraulic axis systems under unknown time-variant parameters,mismatched and matched disturbances.Different from the traditional adaptive results that are applied to dispose of unknown constant parameters only,the unique feature is that an adaptive-gain nonlinear term is introduced into the control design to handle unknown time-variant parameters.Concurrently both mismatched and matched disturbances existing in electro-hydraulic axis systems can also be addressed in this way.With skillful integration of the backstepping technique and the adaptive control,a synthesized controller framework is successfully developed for electro-hydraulic axis systems,in which the coupled interaction between parameter estimation and disturbance estimation is avoided.Accordingly,this designed controller has the capacity of low-computation costs and simpler parameter tuning when compared to the other ones that integrate the adaptive control and observer/estimator-based technique to dividually handle parameter uncertainties and disturbances.Also,a nonlinear filter is designed to eliminate the“explosion of complexity”issue existing in the classical back-stepping technique.The stability analysis uncovers that all the closed-loop signals are bounded and the asymptotic tracking performance is also assured.Finally,contrastive experiment results validate the superiority of the developed method as well.

A Modified Integral Global Optimization Method and Its Asymptotic Convergence

In this paper, we propose a new integral global optimization algorithm for finding the solution of continuous minimization problem, and prove the asymptotic convergence of this algorithm. In our modified method we use variable measure integral, importance sampling and main idea of the cross-entropy method to ensure its convergence and efficiency. Numerical results show that the new method is very efficient in some challenging continuous global optimization problems.

Convergence Rates to Asymptotic Profile for Solutions of Quasilinear Hyperbolic Equations with Nonlinear Damping

The quasilinear hyperbolic equation with nonlinear damping is considered in this paper,a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding parabolic equation,the convergence rates of the new profile are better than that obtained by Nishihara（1997,J.Differential Equations 137,384-395） and H.-J.Zhao（2000,J.Differential Equations 167,467-494）.

Observer-based motion axis control for hydraulic actuation systems

Unknown dynamics including mismatched mechanical dynamics(i.e.,parametric uncertainties,unmodeled friction and external disturbances)and matched actuator dynamics(i.e.,pressure and flow characteristic uncertainties)broadly exist in hydraulic actuation systems(HASs),which can hinder the achievement of high-precision motion axis control.To surmount the practical issue,an observer-based control framework with a simple structure and low computation is developed for HASs.First,a simple observer is utilized to estimate mismatched and matched unknown dynamics for feedforward compensation.Then combining the backstepping design and adaptive control,an appropriate observer-based composite controller is provided,in which nonlinear feedback terms with updated gains are adopted to further improve the tracking accuracy.Moreover,a smooth nonlinear filter is introduced to shun the“explosion of complexity”and attenuate the impact of sensor noise on control performance.As a result,this synthesized controller is more suitable for practical use.Stability analysis uncovers that the developed controller assures the asymptotic convergence of the tracking error.The merits of the proposed approach are validated via comparative experiment results applied in an HAS with an inertial load as well.

Finite-time formation control for first-order multi-agent systems with region constraints

In this study,the finite-time formation control of multi-agent systems with region constraints is studied.Multiple agents have first-order dynamics and a common target area.A novel control algorithm is proposed using local information and interaction.If the communication graph is undirected and connected and the desired framework is rigid,it is proved that the controller can be used to solve the formation problem with a target area.That is,all agents can enter the desired region in finite time while reaching and maintaining the desired formation shapes.Finally,a numerical example is given to illustrate the results.

ON BLOCK PRECONDITIONERS FOR PDE-CONSTRAINED OPTIMIZATION PROBLEMS

Recently, Bal proposed a block-counter-diagonal and a block-counter-triangular precon- ditioning matrices to precondition the GMRES method for solving the structured system of linear equations arising from the Galerkin finite-element discretizations of the distributed control problems in （Computing 91 （2011） 379-395）. He analyzed the spectral properties and derived explicit expressions of the eigenvalues and eigenvectors of the preconditioned matrices. By applying the special structures and properties of the eigenvector matrices of the preconditioned matrices, we derive upper bounds for the 2-norm condition numbers of the eigenvector matrices and give asymptotic convergence factors of the preconditioned GMRES methods with the block-counter-diagonal and the block-counter-triangular pre- conditioners. Experimental results show that the convergence analyses match well with the numerical results.

ON THE SEPARABLE NONLINEAR LEAST SQUARES PROBLEMS

Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad applications in practice. Most existing algorithms for this kind of problems are derived from the variable projection method proposed by Golub and Pereyra, which utilizes the separability under a separate framework. However, the methods based on variable projection strategy would be invalid if there exist some constraints to the variables, as the real problems always do, even if the constraint is simply the ball constraint. We present a new algorithm which is based on a special approximation to the Hessian by noticing the fact that certain terms of the Hessian can be derived from the gradient. Our method maintains all the advantages of variable projection based methods, and moreover it can be combined with trust region methods easily and can be applied to general constrained separable nonlinear problems. Convergence analysis of our method is presented and numerical results are also reported.