Contact Problem in Decagonal Two-Dimensional Quasicrystal

As a new structure of solid matter quasicrystal brings profound new ideas to the traditional condensed matter physics, its elastic equations are more complicated than that of traditional crystal. A contact problem of decagonal two? dimensional quasicrystal material under the action of a rigid flat die is solved satisfactorily by introducing displacement function and using Fourier analysis and dual integral equations theory, and the analytical expressions of stress and displacement fields of the contact problem are achieved. The results show that if the contact displacement is a constant in the contact zone, the vertical contact stress has order -1/2 singularity on the edge of contact zone, which provides the important mechanics parameter for contact deformation of the quasicrystal.

Virtual Machine Scheduling for Improving Energy Efficiency in laaS Cloud

In IaaS Cloud,different mapping relationships between virtual machines(VMs) and physical machines(PMs) cause different resource utilization,so how to place VMs on PMs to reduce energy consumption is becoming one of the major concerns for cloud providers.The existing VM scheduling schemes propose optimize PMs or network resources utilization,but few of them attempt to improve the energy efficiency of these two kinds of resources simultaneously.This paper proposes a VM scheduling scheme meeting multiple resource constraints,such as the physical server size(CPU,memory,storage,bandwidth,etc.) and network link capacity to reduce both the numbers of active PMs and network elements so as to finally reduce energy consumption.Since VM scheduling problem is abstracted as a combination of bin packing problem and quadratic assignment problem,which is also known as a classic combinatorial optimization and NP-hard problem.Accordingly,we design a twostage heuristic algorithm to solve the issue,and the simulations show that our solution outperforms the existing PM- or network-only optimization solutions.

L~∞-Error Estimate of a Nonconfoming Rectangular Plate Element

In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.

A Remark on the Positive Definite Problem of a Binary Quartic Form

In this paper,we discussed the positive definite problem of binary quartic forms and obtained a necessary and sufficient conditions.

A novel PID controller tuning method based on optimization technique

An approach for parameter estimation of proportional-integral-derivative(PID) control system using a new nonlinear programming(NLP) algorithm was proposed.SQP/IIPM algorithm is a sequential quadratic programming(SQP) based algorithm that derives its search directions by solving quadratic programming(QP) subproblems via an infeasible interior point method(IIPM) and evaluates step length adaptively via a simple line search and/or a quadratic search algorithm depending on the termination of the IIPM solver.The task of tuning PI/PID parameters for the first-and second-order systems was modeled as constrained NLP problem. SQP/IIPM algorithm was applied to determining the optimum parameters for the PI/PID control systems.To assess the performance of the proposed method,a Matlab simulation of PID controller tuning was conducted to compare the proposed SQP/IIPM algorithm with the gain and phase margin(GPM) method and Ziegler-Nichols(ZN) method.The results reveal that,for both step and impulse response tests,the PI/PID controller using SQP/IIPM optimization algorithm consistently reduce rise time,settling-time and remarkably lower overshoot compared to GPM and ZN methods,and the proposed method improves the robustness and effectiveness of numerical optimization of PID control systems.

Cooperative merging control strategy of connected and automated vehicles on highways

To improve traffic performance when on-ramp vehicles merge into the mainstream,a collaborative merging control strategy is proposed to determine the merging sequence and trajectory control of vehicles.Merging trajectory planning takes the minimization of vehicle acceleration as the optimization objective.Either the variational method or the quadratic programming method is utilized to determine arrival time,optimal time and control variables for each vehicle.As a supplement,the adaptive cruise control(ACC)model is used to calculate each control variable in each time interval on special occasions.Simulation results show that the cooperative merging control strategy outperforms the optimal control strategy.The root mean square(RMS)of acceleration and the root mean square error(RMSE)of time headway are significantly decreased,with the reductions up to 90.1%and 25.2%,respectively.Under the cooperative control strategy,the difference between the average speed and desired speed consistently approaches zero.In addition,few or no collisions occur.To conclude,the proposed strategy favours the improvements in passenger comfort,traffic efficiency,traffic stability and safety around highway on-ramps.

A Comparison of Arithmetic Operations for Dynamic Process Optimization Approach

A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming(rSQP)simultaneous approach with respect to equality constrained optimization problems is presented.Through the detail comparison of arithmetic operations,it is concluded that the average iteration number within differential algebraic equations(DAEs)integration of quasi-sequential approach could be regarded as a criterion.One formula is given to calculate the threshold value of average iteration number.If the average iteration number is less than the threshold value,quasi-sequential approach takes advantage of rSQP simultaneous approach which is more suitable contrarily.Two optimal control problems are given to demonstrate the usage of threshold value.For optimal control problems whose objective is to stay near desired operating point,the iteration number is usually small.Therefore,quasi-sequential approach seems more suitable for such problems.

Some Notes on the Positive Definite Problem of a Binary Quartic Form

In this paper, we discuss the positive definite problem of a binary quartic form and obtain a necessary and sufficient condition. In addition we give two examples to show that there are some errors in the paper [1].

Filter-sequence of quadratic programming method with nonlinear complementarity problem function

A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.

Initial Value Problems for Second Order Impulsive Integro-Differential Equation in Banach Spaces

By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differential equation in Banach spaces is obtained and the related results are essentially improved.At the same time, another sufficient condition of existence of minimal and maximal solutions based on the Kuratowski measure of noncompactness is given.

A new hybrid algorithm for global optimization and slope stability evaluation

A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.

Robust Model Predictive Controller Design： Finite and Infinite Horizon

This paper addresses to the problem of designing, modeling and practical realization of robust model predictive control for finite and infinite prediction horizon which ensures a parameter dependent quadratic stability and guaranteed cost for linear polytopic uncertain systems. The model predictive controller design procedure based on BMI and LMI is reduced to off-line output feedback gain calculation. A numerical examples and an application to a real process is given to illustrate the effectiveness of the proposed method.

ANISOTROPIC BIQUADRATIC ELEMENT WITH SUPERCLOSE RESULT

The main aim of this paper is to study the convergence of biquadratic finite element tor the second order problem on anisotropic meshes. By using some novel approaches and techniques, the optimal error estimates are obtuined. At the same time, the anisotropic superclose results are also achieved. Furthermore, the numerical results are given to demonstrate our theoretical analysis.

STOCHASTIC DIFFERENTIAL EQUATIONS AND STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM WITH LEVY PROCESSES

In this paper, tile authors first study two kinds of stochastic differential equations （SDEs） with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimensional backward stochastic differential equations （BSDEs） driven by Levy pro- cesses, the authors proceed to study a stochastic linear quadratic （LQ） optimal control problem with a Levy process, where the cost weighting matrices of the state and control are allowed to be indefinite. One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results.

Optimal variational principle for backward stochastic control systems associated with Lévy processes

The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.

Homogenization of Elliptic Problems with Quadratic Growth and Nonhomogenous Robin Conditions in Perforated Domains

This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L^2(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator.Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.

Bivariate Gonarov polynomials and integer sequences

Univariate Gonarov polynomials arose from the Goncarov interpolation problem in numerical analysis.They provide a natural basis of polynomials for working with u-parking functions,which are integer sequences whose order statistics are bounded by a given sequence u.In this paper,we study multivariate Goncarov polynomials,which form a basis of solutions for multivariate Goncarov interpolation problem.We present algebraic and analytic properties of multivariate Gonarov polynomials and establish a combinatorial relation with integer sequences.Explicitly,we prove that multivariate Goncarov polynomials enumerate k-tuples of integers sequences whose order statistics are bounded by certain weights along lattice paths in Nk.It leads to a higher-dimensional generalization of parking functions,for which many enumerative results can be derived from the theory of multivariate Goncarov polynomials.

BACKWARD LINEAR-QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO-SUM DIFFERENTIAL GAME PROBLEM WITH RANDOM JUMPS

This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations.The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed.All these results develop those of Lim, Zhou(2001) and Yu,Ji(2008).