A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

中子平衡节块离散纵标法及CMFD加速技术研究

本文基于横向积分离散纵标方程,解析得到横向积分通量中出射通量与入射通量的关系,并根据类似于扩散方程节块展开法的输运节块中子平衡方程形式,得到了一种高效的节块离散纵标法数值迭代策略。数值结果表明,本文提出的方法可行且数值结果正确。此外,粗网有限差分(CMFD)加速技术在节块离散纵标法中也取得了非常好的应用效果。     

Optimization of quinacridone magenta,Cu-phthalocyanine cyan,and arylide yellow ink films formulated for maximum color gamut

Investigation of ink formulation options with the purpose to obtain color-gamut-optimal set of Cyan Magenta and Yellow CMY inks is reported. Implementation of the thickness dependent Kubelka-Munk model on multiple ink layers having different and well-defined thicknesses, provides characteristic absorption and scattering (K, S ) spectra of the ink ingredients. These data enable accurate computation of the reflectance spectrum and thus the L*a*b* color coordinates for any given ink thickness or substrate. Pigment materials investigated are quinacridone as magenta, copper-phthalocyanine as cyan, and arylide yellow. Scaling the peak of the absorption band to the number of molecules per unit area for the specific pigments studied in this article provides the molar extinction coefficients, 1.21 × 10⁴ , 4.7 × 10⁴ , and 3.3 × 10⁴ cm²/millimole respectively, regardless of the different ink formulations used, in accord with Avogadro's principle. Having a set of three pairs of K, S spectra is used to compute the color gamut of any CMY color combination in the L*a*b* space as a function of ink layer thickness and formulation. Using an iterative algorithm, a color-gamut-optimal set of CMY inks is obtained.     

Ca2+ doping effects on the structural and electrical properties of Na0.5Bi4.5Ti4O15 piezoceramics

Bismuth layer structured Na_0.5Bi_4.5Ti₄O₁₅ (NBT) ferroelectric is one of the most promising materials for potential applications at high temperature. However, it is challenged to achieve a balance between high Curie temperature piezoelectric coefficient and excellent thermal stability for NBT piezoceramics. Here, through chemical modification at the A site of NBT with Ca²⁺, novel (Na_0.5Bi_0.5)_1-xCa_xBi₄Ti₄O₁₅ piezoceramics with excellent properties fabricated by solid state reaction were studied. After doping of Ca²⁺, the Curie temperature T_C increased from 648 °C to 662 °C while the piezoelectric coefficient d₃₃ increased from 14 pC/N to 22 pC/N which can be attributed to the intrinsic contribution of TiO₆ octahedral lattice distortion (tilting and rotation) and the extrinsic contribution of the increased density of domain walls. The composition of (Na_0.5Bi_0.5)_0.95Ca_0.05Bi₄Ti₄O₁₅ ceramics with x = 0.05 has the optimal performance with high T_C of 655 °C, large d₃₃ of 22 pC/N, high electrical resistivity ρ close to 10⁷ Ω cm at 500 °C and especially excellent thermal stability of d₃₃ only about 5% reduction after being annealed at 625 °C. The work effectively reveals the great potential of CNBT-5 ceramics for high-temperature piezoelectric applications.     

马尔可夫跳变线性系统最优控制的研究现状与进展

马尔可夫跳变线性系统（MJLS）是一种具有多个模态的随机系统，系统在各个模态之间的跳变转移由一组马尔可夫链来决定。MJLS模型因其在表示过程中可以产生突变而更能精确的描述实际工程应用中的系统。近年来，MJLS的最优控制问题成为了研究的热点，动态规划、极大值原理以及线性矩阵不等式等成为了解决此类问题的主流方法。本文对MJLS最优控制领域的研究现状进行了综述。分别对一般情况下、带有噪声的情况下、带有时滞的情况下以及某些特定情况下的MLJS最优控制问题的国内外研究现状进行论述。最后进行了总结并提出MJLS最优控制领域未来值得关注的研究方向。     

Nonuniform linear array DOA estimation using EM criterion

In this letter, we address the problem of Direction of Arrival (DOA) estimation with nonuniform linear array in the context of sparse Bayesian learning (SBL) framework. The nonuniform array output is deemed as an incomplete-data observation, and a hypothetical uniform linear array output is treated as an unavailable complete-data observation. Then the Expectation-Maximization (EM) criterion is directly utilized to iteratively maximize the expected value of the complete-data log likelihood under the posterior distribution of the latent variable. The novelties of the proposed method lie in its capability of interpolating the actual received data to a virtual uniform linear array, therefore extending the achievable array aperture. Simulation results manifests the superiority of the proposed method over off-the-shelf algorithms, specially on circumstances such as low SNR, insufficient snapshots, and spatially adjacent sources.     

The generalized discrete ‐centroid problem

The ‐centroid problem or leader–follower problem is generalized considering different customer choice rules where a customer may use facilities belonging to different firms, if the difference in travel distance (or time) is small enough. Assuming essential goods, some particular customer choice rules are analyzed. Linear programming formulations for the generalized ‐medianoid and ‐centroid problems are presented and an exact solution approach is applied. Some computational examples are included.     

应用膨胀算法提取目标的直接定位算法

为了解决被动雷达系统中的多发射源定位问题，提出了一种基于多重信号分类(MUSIC)算法和图像膨胀(IE)算法的直接定位方法。该方法结合了谱分析中的MUSIC思想，通过对接收量测协方差矩阵进行特征分析求解目标的位置。首先，在目标个数未知的前提下，利用Akaike信息准则(AIC)来确定模型阶数；然后，推导了基于MUSIC的定位代价函数；之后，利用图像膨胀算法处理得到的代价函数平面；最后，膨胀处理后的输出为目标个数及目标位置的估计值。提出的算法有效地解决了目标检测及提取的问题，能够确定多个目标的位置坐标，为后续的定位性能分析提供可能性，也保证了算法的完整性。进一步地分析了多个临近目标情况下影响目标提取性能的主要因素。