Multiple Solutions to the Problem of Kirchhoff Type Involving the Critical Caffareli-Kohn-Niremberg Exponent, Concave Term and Sign-Changing Weights

In this paper, we establish the existence of at least four distinct solutions to an Kirchhoff type problems involving the critical Caffareli-Kohn-Niremberg exponent, concave term and sign-changing weights, by using the Nehari manifold and mountain pass theorem.

Global Topological Linearization with Unbounded Nonlinear Term

In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.

Multiple Solutions for an Elliptic Equation with Hardy-Sobolev Critical Exponent, Hardy-Sobolev-Maz’ya Potential and Sign-Changing Weights

In the present paper, an elliptic equation with Hardy-Sobolev critical exponent, Hardy-Sobolev-Maz’ya potential and sign-changing weights, is considered. By using the Nehari manifold and mountain pass theorem, the existence of at least four distinct solutions is obtained.

Parallel Control for Continuous-Time Linear Systems:A Case Study

In this paper,a new parallel controller is developed for continuous-time linear systems.The main contribution of the method is to establish a new parallel control law,where both state and control are considered as the input.The structure of the parallel control is provided,and the relationship between the parallel control and traditional feedback controls is presented.Considering the situations that the systems are controllable and incompletely controllable,the properties of the parallel control law are analyzed.The parallel controller design algorithms are given under the conditions that the systems are controllable and incompletely controllable.Finally,numerical simulations are carried out to demonstrate the effectiveness and applicability of the present method.Index Terms-Continuous-time linear systems,digital twin,parallel controller,parallel intelligence,parallel systems.

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

Self-triggered Consensus Control for Linear Multi-agent Systems With Input Saturation

In this paper, we study the consensus problem for a class of linear multi-agent systems(MASs) with consideration of input saturation under the self-triggered mechanism. In the context of discrete-time systems, a self-triggered strategy is developed to determine the time interval between the adjacent triggers. The triggering condition is designed by using the current sampled consensus error. Furthermore, the consensus control protocol is designed by means of a state feedback approach. It is shown that the considered multi-agent systems can reach consensus with the presented algorithm. Some sufficient conditions are proposed in the form of linear matrix inequalities(LMIs) to show the positively invariant property of the domain of attraction(DOA). Moreover, some sufficient conditions of controller synthesis are provided to enlarge the volume of the DOA and obtain the control gain matrix. A numerical example is simulated to demonstrate the effectiveness of the theoretical analysis results.

Dynamic linear calibration method for a wide range neutron flux monitor system in ITER

As a key part of the diagnosis system in the International Thermonuclear Experimental Reactor(ITER),the neutron flux monitor(NFM),which measures the neutron intensity of the fusion reaction,is a Counting-Campbelling system with a large dynamic counting range.A dynamic linear calibration method is proposed in this paper to solve the problem of cross-over between the different counting and Campbelling channels,and improve the accuracy of the cross-calibration for long-term operation.The experimental results show that the NFM system with the dynamic linear calibration system can obtain the neutron flux of the fusion reactor in real time and realize the seamless measurement area connection between the two channels.

Estimators of Linear Regression Model and Prediction under Some Assumptions Violation

The development of many estimators of parameters of linear regression model is traceable to non-validity of the assumptions under which the model is formulated, especially when applied to real life situation. This notwithstanding, regression analysis may aim at prediction. Consequently, this paper examines the performances of the Ordinary Least Square (OLS) estimator, Cochrane-Orcutt (COR) estimator, Maximum Likelihood (ML) estimator and the estimators based on Principal Component (PC) analysis in prediction of linear regression model under the joint violations of the assumption of non-stochastic regressors, independent regressors and error terms. With correlated stochastic normal variables as regressors and autocorrelated error terms, Monte-Carlo experiments were conducted and the study further identifies the best estimator that can be used for prediction purpose by adopting the goodness of fit statistics of the estimators. From the results, it is observed that the performances of COR at each level of correlation (multicollinearity) and that of ML, especially when the sample size is large, over the levels of autocorrelation have a convex-like pattern while that of OLS and PC are concave-like. Also, as the levels of multicollinearity increase, the estimators, except the PC estimators when multicollinearity is negative, rapidly perform better over the levels autocorrelation. The COR and ML estimators are generally best for prediction in the presence of multicollinearity and autocorrelated error terms. However, at low levels of autocorrelation, the OLS estimator is either best or competes consistently with the best estimator, while the PC estimator is either best or competes with the best when multicollinearity level is high(λ>0.8 or λ-0.49).

Perturbation Analysis of Structured Least Squares Problems and Its Application in Calibration of Interest Rate Term Structure

A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations. We apply the new error bound to study sensitivity of changing the knots for curve fitting of interest rate term structure by cubic spline.Numerical experiments are given to illustrate the sharpness of this bound.

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

Radio Frequency Low Noise Amplifier with Linearizing Bias Circuit

A 1.34 GHz-1=60 MHz low noise amplifier （LNA） designed in a 0.35 pm SiGe process is presented. The designed LNA exhibits a power gain of 21.46 dB and a noise figure （NF） of 1.27 dB at 1.34 GHz. The linearity is improved with an active biasing technique. The post-layout simulation shows an input referred 1-dB compression point （IPldn） of-11.52 dBm. Compared with the recent reported high gain LNAs, the proposed LNA has a much better linearity without degrading other performance. The LNA draws 10 mA current from a 3.3 V power supply.

基于扰动观测器和改进自适应二阶快速终端滑模的PMLSM伺服系统控制

针对永磁直线同步电动机(PMLSM)在运行时易受到摩擦力、负载扰动及环境变化等不确定影响,设计一种基于扰动观测器和自适应二阶快速终端滑模控制方法。首先,该方法在高阶滑模的基础上结合了快速终端滑模控制,有效加快了系统响应速度。其次,在二阶滑模面的基础上引入条件积分项,该项仅作用于边界层内部,能够有效避免滑模到达阶段由于积分饱和现象导致的超调量过大及响应时间过慢的问题。此外,设计自适应切换控制律,使切换增益在合理的区间内,并根据系统状态进行实时更新,从而削弱抖振现象。最后,为进一步提升系统的鲁棒性,采用扰动观测器对PMLSM系统的集总不确定性进行补偿。经实验验证,该控制方法具有良好的位置跟踪精度和强鲁棒性,且对系统抖振现象有明显削弱作用。

基于短期观测记录的重现期风速预测

在偏僻地区或山区建设重要建筑物、构筑物或桥梁时,通常在附近安装风速观测仪器,获得至少1年的短期风速记录。提出了根据短期风速记录预测指定重现期风速极值及风压方法,为结构抗风设计提供了科学依据。提出独立风暴法提取短期风速记录的最大值,建立极值I型概率分布模型,采用最好线性无偏估计方法确定概率分布参数。依据短期风速最大值概率与年风速最大值概率的变换关系,建立年发生最大值的概率分布及重现期风速、风压的表达式。算例结果表明,重现期风速预测值的离散性与风速阈值有关,在预测值离散系数较小的情况下可确定重现期风速及其置信区间。

基于时空特征的城市轨道交通短时OD估计方法

精准的短时出行地和目的地(OD)估计技术是城市轨道交通运营组织方案制定的主要依据,同时也是城轨断面客流预测的基础。为同时考虑时空双维特征,且快速实现全网OD的高精度估计,该文基于时间、空间2个维度分析了城轨客流OD分布特征,提出多维度下的最优输入因子筛选方法,构建了基于多元线性回归模型的多层级嵌套OD估计方法。以2019年工作日的南京地铁线网为例进行模型验证,结果表明,时间粒度为15 min以及60 min下,全网OD的平均绝对百分比误差(MAPE)分别为37%、24%,部分OD对在高峰时段的MAPE值小于5%;15 min粒度的均方根误差(RMSE)约为1.3。相比于现有短时OD估计方法,该文提出的方法在高峰时段预测效果更好,能够高效实现全网、全时段的OD估计。

兼顾本地与直流受端电网调峰需求的水电站群短期优化调度模型

面对巨型水电站群高压直流送端电网和受端电网日益严峻的调峰压力,建立了一种兼顾本地与直流受端电网调峰需求的梯级水电站群短期优化调度模型。模型以多电网剩余负荷最大值最小为目标,考虑常规梯级水电站群水力、电力约束,以及复杂高压直流输电线路运行约束,并引入直流线路与水电站之间耦合运行约束。在模型求解阶段,引入辅助变量将目标函数、水电运行约束、直流运行约束线性化,并采用大M法对直流线路与水电站之间双向区间耦合约束进行线性化,将原模型转换为混合整数线性规划模型。以中国西南地区某巨型水电站群冬季和夏季典型日为实例研究,结果表明:送端电网负荷峰谷差降幅高达100%,受端电网负荷峰谷差降幅分别达28.1%和31.6%。所提模型能够利用高压直流输电线路共享水电灵活性,有效实现多电网调峰,并保证直流输电线路运行在安全区间,可以为巨型梯级水电站群短期多电网调峰提供参考和借鉴。

具有多个次线性中立项的二阶非线性微分方程的振动性

该文给出一类具有多个次线性中立项的二阶微分方程一切解振动的若干新的充分条件。论文的结果不仅推广了经典的振动定理,而且改进和概括了最近文献中的振动结果,为说明所得结果的重要性,也给出了相应的例子。

The Persistence and Zonal Scale of Atmospheric Dipolar Modes

This study investigates the relationship between the persistence and the zonal scale of atmospheric dipolar modes(DMs). Results from the daily data of ERA5 and the long-term output of an idealized atmospheric model show that the atmospheric DMs with a broader(narrower) zonal scale dipolar structure possess a longer(shorter) persistence. A detailed vorticity budget analysis indicates that the persistence of a hemispheric-scale DM(1/1 DM) and a regional or sectoral DM(1/8 DM) in the model both largely rely on the persistence of the nonlinear eddy forcing. Linear terms can indirectly reduce the persistence of the anomalous nonlinear eddy forcing in a 1/8 DM by modifying the baroclinicity via the arousal of anomalous vertical motions. Therefore, the atmospheric DMs with a broader(narrower) zonal scale possess a longer(shorter) persistence because the effects of the linear terms are less(more) pronounced when the atmospheric DMs have better(worse) zonal symmetry. Further analyses show that the positive eddy feedback effect is weak or even absent in a 1/8DM and the high-frequency eddy forcing acts more like a concomitant phenomenon rather than a leading driving factor for a 1/8 DM. Thus, the hemispheric-scale DM and the regional or sectoral DMs are different, not only in their persistence but also in their dynamics.

基于SWLSTM-Stacking集成学习的源荷区间预测方法

针对光伏出力和电动汽车充电特性的随机特性对电力系统的冲击不断增强,准确及时的源荷预测是实现增强电力系统适应性和稳定性的重要课题。因此,提出一种基于共享权重长短期记忆网络(shared weight long short-term networks,SWLSTM)与Stacking集成模型相结合的源荷区间预测方法。首先,光伏出力存在时序性特征,采用局部线性嵌入改进k-means算法聚类提取特征日,在实现数据降维同时,减少了网络训练难度;其次,在Stacking集成模型的框架下,将SWLSTM作为元学习器,并通过Q统计量筛选合适的基学习器模型,从而实现多模型融合的多异学习器Stacking集成学习的源荷预测;紧接着,为了得到预测的不确定信息,引入置信度区间预测;最后,采用实测数据对本文所提方法进行验证。结果表明改进k-means算法能够降低其求解难度,加快求解速度,可以快速获取聚类特征;所引入集成学习模型和置信度区间,有效表征源荷预测的不确定性,提升区间预测模型的泛化能力。

基于LSTM的多指标股票预测

该研究通过处理平安银行股票数据生成十个比较有代表性的技术分析指标,将技术指标的值经过预处理后分别作为基于机器学习的多元线性回归、BP神经网络和LSTM神经网络三种模型的输入,通过模型训练来预测股票的涨跌,然后比较三种模型在预测准确率以及回测中年化收益率的表现,证实LSTM神经网络模型对于非线性的股票走势预测效果最好。然后设计改进了一种基于LSTM模式分类的交易择时策略,获得了更高的年化收益率,并且这种策略可行性更高,最后说明利用LSTM模型进行量化交易是可行的。

基于经验模态分解线性模型的矿压预测

为保证煤矿安全高效开采,减少顶板事故突发。本研究提出了一种新颖的多变量长时间序列矿压预测模型——经验模态分解线性模型(EMD-Mixer)。与多数固定长度的单一特征矿压预测模型不同,该模型首先引入经验模态分解(EMD)方法将矿压信号中周期性和趋势性分离出来,再通过与长时间预测线性层(LTSF-Linear)组合,形成一个用于提取时间维度特征的模块。此外,设计了时间与通道混合策略,利用处理非线性关系的通道特征模块来处理多变量矿压数据,最后将时间与通道模块的输出使用残差与输入数据相加,得到最终的预测结果。在实验中,将历史窗口设定为36个时间单位,并对预测长度分别为24、36、48和60的不同时间单位进行了测试,结果表明,EMD-Mixer模型在短期至中长期预测范围内均表现出优异的性能和稳定性。将该模型与LTSF-Linear、MTS-Mixer模型以及矿压预测中常用的长短期记忆(LSTM)模型进行了比较,并利用4种评估指标:平均绝对误差(E_(MAE))、均方误差(E_(MSE))、对称平均绝对百分比误差(E_(sMAPE))及绝对系数(R2)对预测结果进行了评价。结果显示,EMD-Mixer模型在所有指标下均展现出更高的预测精确度和预测稳定性。EMD-Mixer模型结构简单,具有较强的泛化能力,能够更有效地适应不同场景下不同级别的多变量矿压数据。为煤矿安全高效生产以及顶板事故的提前预警提供了重要的研究思路。