二维六角形晶格伊辛模型的重正化群解

选取六角形晶格为Kadanoff集团 ,用重正化群方法求得临界点和与之相应的各临界指数 .与三角形晶格重正化群解相比 ,其精度提高了 1 5 %

特殊流形上的三相交流异步电机传动系统

介绍微分几何反馈控制方法,应用电压激励来实现控制PWM逆变器异步电动机系统,在特殊的流行上,构造性地给出了变换性矩阵的形成方法,采用非线性变换和非线性反馈,把这种多变量、非线性、强耦合的传动系统映射为2个独立的线性子系统,仿真结果表明可以实现系统的动态解耦和局部线性化。

永磁同步电动机混沌系统的串级控制

根据永磁同步电动机的数学模型,研究如何运用串级PD控制器来控制混沌。首先在理论上运用劳斯(Routh)判据分析永磁同步电动机模型串级PD控制混沌的可行性,然后通过在平衡点处线性化的雅克比(Jacobian)矩阵来求取PD参数的值。最后在MATLAB/Simulink仿真平台上利用数值仿真实验验证其有效性。通过研究可知,运用串级PD控制可以较好地消除混沌使系统达到一个稳定的状态。该方法具有一定的参考实用性,为永磁同步电动机混沌运动分析或控制打下了研究基础。

对《二维六角形晶格伊辛模型的重正化群解》一文的进一步计算

针对《二维六角形晶格伊辛模型的重正化群解》一文中有关〈V〉0的计算进行了修正,给出了新的重正化群的变换、重正化群的线性化变换矩阵以及临界指数.

T-S-fuzzy-model-based quantized control for nonlinear networked control systems

In order to overcome data-quantization, networked-induced delay, network packet dropouts and wrong sequences in the nonlinear networked control system, a novel nonlinear networked control system model is built by the T-S fuzzy method. Two time-varying quantizers are added in the model. The key analysis steps in the method are to construct an improved interval-delay-dependent Lyapunov functional and to introduce the free-weighting matrix. By making use of the parallel distributed compensation technology and the convexity of the matrix function, the improved criteria of the stabilization and stability are obtained. Simulation experiments show that the parameters of the controllers and quantizers satisfying a certain performance can be obtained by solving a set of LMIs. The application of the nonlinear mass-spring system is provided to show that the proposed method is effective.

Decentralized H_∞ state feedback control for large-scale interconnected uncertain systems with multiple delays

Decentralized H_∞ control was studied for a class of interconnected uncertain systems with multiple delays in the state and control and time varying but norm-bounded parametric uncertainties. A sufficient condition which makes the closed-loop system decentralized asymptotically stable with H_∞ performance was derived based on Lyapunov stability theorem. This condition is expressed as the solvability problem of linear matrix inequalities. The method overcomes the limitations of the existing algebraic Riccati equation method. Finally, a numerical example was given to demonstrate the design procedure for the decentralized H_∞ state feedback controller.

Applications of Lodrigues Matrix in 3D Coordinate Transformation

Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms：① the traditional rotation angles θ,φ,ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.

LMI Approach to Mixed H_/H_∞ Fault Detection Observer Design

To investigate the robust fault detection （RFD） observer design for linear uncertain systems, the H_index and H∞ norm are used to describe this observer design as optimization problems. Conditions for the existence of such a fault detection observer are given in terms of matrix inequalities. The solution is obtained by new iterative linear matrix inequality （ILMI） algorithms. The RFD observer design over finite frequency range in which Of does not have full column rank for a system is also considered. Numerical example demonstrates that the designed fault detection observer has high sensitivity to the fault and strong robustness to the unknown input.

Two-Hop Gaussian Relay Channel with Linear Relaying： Achievable Rate and Optimization Design

The relay node with linear relaying transmits the linear combination of its past received signals.The optimization of two-hop relay channel with linear relaying is discussed in this paper.The capacity for the two-hop Gaussian relay channel with linear relaying is derived,which can be formulated as an optimization problem over the relaying matrix and the covariance matrix of the signals transmitted at the source.It is proved that the solution to this optimization problem is equivalent to a "single-letter" optimization problem.We also show that the solution to this "single-letter" optimization problem has the same form as the expression of the rate achieved by Time-Sharing Amplify and Forward(TSAF).In order to solve this equivalent problem,we proposed an iterative algorithm.Simulation results show that if channel gain of one hop is relatively smaller,the achievable rate with TSAF is closer to the max-flow min-cut capacity bound,but at a lower complexity.

Using Self-referencing Interlaced Submatrices to Determine the Number of Chemical Species in a Mixture

Determining the number of chemical species is the first step in analyses of a chemical or biological system. A novel method is proposed to address this issue by taking advantage of frequency differences between chemical information and noise. Two interlaced submatrices were obtained by downsampling an original data spectra matrix in an interlacing manner. The two interlaced submatrices contained similar chemical information but different noise levels. The number of relevant chemical species was determined through pairwise comparisons of principal components obtained by principal component analysis of the two interlaced submatrices. The proposed method, referred to as SRISM, uses two self-referencing interlaced submatrices to make the determination. SRISM was able to selectively distinguish relevant chemical species from various types of interference factors such as signal overlapping, minor components and noise in simulated datasets. Its performance was further validated using experimental datasets that contained high-levels of instrument aberrations, signal overlapping and collinearity. SRISM was also applied to infrared spectral data obtained from atmospheric monitoring. It has great potential for overcoming various types of interference factor. This method is mathematically rigorous, computationally efficient, and readily automated.

Synchronization criteria based on a general complex dynamical network model

Many complex dynamical networks display synchronization phenomena. We introduce a general complex dynamical network model. The model is equivalent to a simple vector model of adopting the Kronecker product. Some synchronization criteria,including time-variant networks and time-varying networks,are deduced based on Lyapunov's stability theory,and they are proven on the condition of obtaining a certain synchronous solution of an isolated cell. In particular,the inner-coupling matrix directly determines the synchronization of the time-invariant network; while for a time-varying periodic dynamical network,the asymptotic stability of a synchronous solution is determined by a constant matrix which is related to the fundamental solution matrices of the linearization system. Finally,illustrative examples are given to validate the results.

New Integrable Decomposition of Super AKNS Equation

In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKNSequation is presented.

Nonlinear Control of Induction Motor： A Combination of Nonlinear Observer Design and Input-Output Linearization Technique

This paper deals with a nonlinear control strategy of induction motor that combines an input-output linearization control technique and a nonlinear observer design. It is well known that induction motors are the most widely used motors in electrical appliances, industrial control and automation. However, it is also known that induction motor control is a complex task that is due to its nonlinear characteristics. Two main features of the proposed approach are worth to be mentioned. Firstly, a nonlinear control is carried out using a nonlinear feedback linearization technique involving non available state variable measurements of the induction motor system. Secondly, a nonlinear observer is designed to estimate these pertinent but unmeasurable state variables of the machine. The circle-criterion approach is performed to compute the observer gain matrices as a solution of LMI （linear matrix inequalities） that ensure the stability conditions, in the sense of Lyapunov, of the estimated state error dynamics of the designed observer. Simulation results are presented to validate the effectiveness of the proposed approach.

Tensor absolute value equations

This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization of the well-known absolute value equations in the matrix case. We prove that tensor absolute value equations are equivalent to some special structured tensor complementary problems. Some sufficient conditions are given to guarantee the existence of solutions for tensor absolute value equations. We also propose a Levenberg-Marquardt-type algorithm for solving some given tensor absolute value equations and preliminary numerical results are reported to indicate the efficiency of the proposed algorithm.

Norm estimates of w-circulant operator matrices and isomorphic operators for w-circulant algebra

An n × n ω-circulant matrix which has a specific structure is a type of important matrix. Several norm equalities and inequalities are proved for ω-circulant operator matrices with ω = e^(iθ)(0≤θ < 2π) in this paper. We give the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norms. Pinching type inequality is also proposed for weakly unitarily invariant norms. Meanwhile,we present that the set of ω-circulant matrices with complex entries has an idempotent basis. Based on this basis, we introduce an automorphism on the ω-circulant algebra and then show different operators on linear vector space that are isomorphic to the ω-circulant algebra. The function properties, other idempotent bases and a linear involution are discussed for ω-circulant algebra. These results are closely related to the special structure of ω-circulant matrices.

A Finite Genus Solution of the Veselov's Discrete Neumann System

The Veselov's discrete Neumann system is derived through nonlinearization of a discrete spectral problem.Based on the commutative relation between the Lax matrix and the Darboux matrix with finite genus potentials,a special solution is calculated with the help of the Baker-Akhiezer-Kriechever function.

A NONMONOTONE LINE SEARCH FILTER METHOD WITH REDUCED HESSIAN UPDATING FOR NONLINEAR OPTIMIZATION

This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.

Robust linear optimization under matrix completion

Linear programming models have been widely used in input-output analysis for analyzing the interdependence of industries in economics and in environmental science.In these applications,some of the entries of the coefficient matrix cannot be measured physically or there exists sampling errors.However,the coefficient matrix can often be low-rank.We characterize the robust counterpart of these types of linear programming problems with uncertainty set described by the nuclear norm.Simulations for the input-output analysis show that the new paradigm can be helpful.