由《现代控制理论》教材习题引发的讨论

许多文献对状态转移矩阵eAt的性质和计算方法进行了广泛的讨论.但给定一个矩阵函数,如何判断它是否是某一连续时间线性时不变系统的状态转移矩阵,在相关的教材中却没有涉及.本文根据常微分方程解的唯一性得到了判断一个矩阵函数是某一连续时间线性时不变系统的状态转移矩阵的充分必要条件,并求出了其对应的系统矩阵.此外,若状态转移矩阵Φ(t)已知,本文也给出了求解对应的系统矩阵的三种方法.     

状态方程求解方法的探讨

本文对状态方程求解方法作了一般性探讨，提出用一个P阵将系统矩阵A化为对角阵后导出矩阵指数函数e[P-1AP]t来求得状态转移矩阵Φ（t），从而求出状态方程的解x（t）。这在网络系统较复杂的情况下优于传统作法。     

基于矩阵分析的同步捕获性能研究新方法

该文提出了一种利用概率转移矩阵计算捕获传输函数的方法,通过将以往分析方法中的流程图转换为概率转移矩阵,仅需知道一步转移概率矩阵,利用现代计算机编程语言(如MAPLE,MATLAB等)的符号运算功能,即可得到捕获系统的传输函数;通过对传输函数求导,可计算平均捕获时间。矩阵分析方法可完整地计算出捕获系统的传输函数,可弥补流程图方法在分析传统连续搜索捕获方案的传输函数时所忽略的项;可纠正流程图方法在分析非连续搜索捕获方案的传输函数时所引起的误差。     

基于马尔科夫识别的敌我目标识别新方法

针对敌我识别系统在现代战争中的保密要求,提出一种将马尔科夫系统识别技术应用于敌我识别的新方法,每个发射机按照系统分配的转移矩阵发射随机码,接收机利用已知的不同我方作战单元的转移矩阵,判断码序列所属,实现我方目标的识别。与传统方法相比,发射机每次按照一定的转移概率发射服从马尔科夫分布的随机编码,大大提高了敌方截获和破译的难度,提升了系统的抗欺骗干扰性能。仿真结果表明,该方法在发射序列比较长的情况下,可以获得准确的识别结果。     

部分转移概率离散奇异Markov跳变系统的镇定

针对具有更广泛意义的部分转移概率未知情况下的离散时间奇异 Markov跳变线性系统,给出了使开环系统正则、因果、随机稳定的充分条件,并表示为严格线性矩阵不等式形式,且消除了等式约束条件。部分转移概率未知的条件包括了完全开关系统和随机跳变转移概率完全未知的情况,适用范围更广泛;在此基础上,通过求解严格线性矩阵不等式的可行解,设计了模式依赖状态反馈控制器,使闭环系统正则、因果、随机稳定,实现了系统的镇定;最后,给出一个仿真算例验证了所提方法的有效性。     

基于状态转移矩阵逼近的椭圆球面波函数求解方法

该文针对现有椭圆球面波函数(PSWFs)求解算法存在的效率低、硬件实现复杂度高,尤其是精度不可控的问题,结合线性时变系统理论,提出一种基于微分方程状态转移矩阵逼近的PSWFs求解方法。该算法通过求解小区间上的状态转移矩阵来逼近整个时间区间上的状态转移矩阵,进而求得离散时间点上的系统运动轨迹,即PSWFs数值解。理论推导了求解误差并修正了算法,修正后算法具有简明的误差表达式,与Parr算法和Legendre多项式逼近算法在求解精度和复杂度上进行了对照分析。结果表明,该文算法求解精度高且可控,时间和空间复杂度低,易于硬件实现。     

磁光存储多层膜系统的光学与热分析方法

采用光学转移矩阵法计算激光照射下磁光存储多层膜的磁光及光学响应，光强分布及焦耳热损失分布，再用有限元方法求解在这种多层膜中的热传导方程，从而得到激光照射下多层膜系统中的温度场分布，这种方法可用于磁光光盘的光学与热学设计。     

开放微波传输线的准静态有限元分析

本文用相似剖分有限元方法，对整个无限空间进行了有限元剖分，引入一转移矩阵Ｘ来构造一等效刚度矩阵用以模拟开域边界，常规有限元法开域边界处理中的近似性完全得到避免。     

一种面向实时风险预测的工业报警优先级评估方法

报警优先级在特定的工艺条件下对操作者传达报警产生的危害严重性。由于过程变量受到外界的随机干扰,具有时变的状态转移概率。为了实时预测过程变量的危害程度,首先定义两项风险量化指标幅值裕度和时间裕度,其次建立动态Markov过程模型,利用粒子滤波方法(Particle Filter)实时更新模型中的状态转移矩阵,预测未来时刻的报警转移矩阵,然后结合实时预测的幅值裕度和时间裕度,实时反映状态量的变化,给报警系统优先级评估提供了一个新的定量化分析方法。实例研究证明,该方法具有有效性。     

固定和切换拓扑下异构多智能体分组一致性

针对一阶和二阶智能体组成的异构多智能体系统，研究了固定和切换拓扑下异构系统分组一致性问题。在设计分组一致性协议中加入了特殊变量并设计各组智能体的收敛位置，让各组智能体分别向着各自目标点聚集，各组内部智能体状态达到一致。方法上主要将异构系统状态矩阵进行变换，将异构系统的状态矩阵转化成同阶系统矩阵，让异构系统的分组一致性问题等价于同构系统的一致性问题，之后分析出固定拓扑下系统实现一致性所需条件。当系统含有切换拓扑时，将系统状态矩阵拆分成有限个非周期不可约分矩阵的乘积，通过证明有限个矩阵乘积为常数向量，即系统矩阵状态值最终收敛。在切换拓扑图的并集包含一个有向生成树下对系统矩阵进行分析得到系统实现分组一致性的条件。最后数值仿真验证了理论的正确性。     

T-matrix and its applications in image processing

A T-matrix used for image scrambling is proposed and its periodicity is proved. The T-matrix has a simple conformation and a period twice as long as the Arnold matrix. It can be applied to image encryption and pre-processing in image processing such as image watermarking algorithms. Two examples of applications are given.     

Scatteration and Absorption Characteristics of Multilayered Gratings Embedded in a Dielectric Slab*

A rigorous and simple method of analyzing scattering and absorbing characteristics of multilayered gratings embedded in a dielectric slab has been proposed. The method combines a generalized scattering matrix with a lattice sums matrix and a T-matrix of an isolated single cylinder instead of the aggregate T-matrix. The validity of the present method has been confirmed by several numerical experiments and comparisons with other published results. Numerical examples show that the absorbing characteristics become very complex and are not linear with the decreasing of cylinders’ conductivity, when the arrays are stacked to a multilayered structure and are embedded in a dielectric slab.     

Modified transfer matrix formulation for bragg grating strain sensors

This paper presents a formulation for the application of the transfer matrix method to Bragg grating strain sensors. A modified T-matrix representation is detailed for the sensor problem based on an effective period derived from the coupling coefficients. This modified T-matrix formulation is shown to converge to the coupled-mode equations solution for a large number of grating segments, even in the presence of significant strain gradients. Several numerical examples are presented to demonstrate the importance of inclusion of the strain gradient in the calculation. In addition, the current formulation is validated by application to previously published experimental data.     

Spaceborne Mesh Reflector Antennas With Complex Weaves: Extended PO/Periodic-MoM Analysis

Reflector antennas with complex mesh weave patterns are numerically analyzed by using extended physical optics (PO) combined with the periodic method of moments (MoM). The method applies the periodic MoM with Rao-Wilton-Glisson (RWG) basis and testing functions. It calculates the transmission coefficient matrix (T-matrix) of the realistic, complex weave pattern of the planar mesh, in order to calculate the modified PO current on the mesh reflector. When analyzed, the planar grid mesh is found to be compatible with the commonly used wire-grid model. The modified PO current on the locally planar mesh is implemented on the curved reflector surface for the diffraction analysis of the mesh reflector antennas. The far-field pattern of the offset parabolic antenna with grid mesh, modelled using periodic MoM, agreed well with those obtained from the wire-grid model. T-matrix calculated from the tabulated T-matrix data using the interpolation method is sufficiently accurate and compares well with the one calculated using the direct method, allowing users to choose one of the T-matrix calculation methods depending on the problem. The analysis of the mesh reflectors with two different complex weave patterns (single Satin and single Atlas at Ka band) is performed to exemplify the application of the extended PO/periodic MoM algorithm. It is shown that differences were observed in cross-polarization discrimination (XPD) for circular polarization operations depending on the weave patterns. This result demonstrates the usefulness of the proposed technique in accurate performance prediction of mesh reflector antennas with complex weave patterns     

Rigorous Mode Analysis of Coupled Cavity Waveguides in Two-Dimensional Photonic Crystals*

A new approach for modal analysis of coupled cavity waveguides (CCW) in two-dimensional photonic crystals is presented. The mode propagation constants and the mode field profiles can be accurately derived by a simple matrix calculation, using a one-dimensional lattice sums, a T-matrix of an isolated circular cylinder, and generalized reflection matrices. Numerical examples have confirmed that the convergence of numerical solutions is very fast and the accuracy is very high.     

A T-matrix approach for EM scattering by a perfectly conducting periodic surface

The novel use of a Fourier exponential representation of the field induced on a perfectly conducting periodic surface is shown to yield a T-matrix which is numerically stable for deeply corrugated surfaces. Whereas the Rayleigh hypothesis limited the maximum slope of the surface to less than 0.448 in Waterman's original T-matrix scheme [1], our T-matrix is applicable even when the maximum slopes are of the order of 1.5.     

T矩阵在光扭矩分析中的应用

在一定条件下经过高数值孔径聚焦后的激光可以捕获微米量级的微粒,这种技术称为光镊。光阱与捕陷粒子间存在角动量传递会产生光扭矩,采用T矩阵方法实现了显微量级光扭矩的测量。仿真结果验证了T矩阵方法的计算高效性,同时分析了光阱参数对光扭矩效率的影响,为光扭矩的实际应用提供了理论依据。微光扭矩的测量具有广阔的应用前景。     

Time-harmonic impedance tomography using the T-matrix method

A time-harmonic formulation for the electrical impedance tomography (EIT) inverse problem accounting for electrodynamic effects is derived. This work abandons the standard electrostatic impedance model for a full-wave T-matrix model. The advantage of this method is an accurate physical model that includes finite frequency effects, such as diffusion phenomena, and electrode contact impedance effects. This model offers the potential for increased resolution and larger invertible contrast objects than other methods when used on experimental data, because it may represent a more realistic physical model. Also, an accurate gradient matrix is used in the Newton iterative method so the image reconstruction converges in a few iterations. These advantages are realized with no increase in the computational complexity of this algorithm, compared to the static finite element model. A calibration technique is suggested for measurement systems, to test the validity of a theoretical model that includes electrode contact impedance effects.     

修正T矩阵公式及半空间随机球粒媒质的电磁波多散射

本文将“两外空间”概念与普通Ｔ矩阵公式相结合,提出了修正Ｔ矩阵公式,作为应用实例,本文用修正Ｔ矩阵理论研究了半空间随机球粒媒质的电磁波多散射,在Ｆｏｌｄｙ近似下得到了确定媒质有效波散的一个超越方程,低频时的数值结果表明：修正Ｔ矩阵方法当颗粒稀疏分时是可行的,当颗粒致密分布时,尚需采用引入颗粒对分布函数的准晶近似。