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    25 August 2022, Volume 35 Issue 4
    Measuring Environmental Performance of Provincial Thermal Power Plants in China: A Malmquist DEA Approach with Fixed-Sum Undesirable Outputs
    HOU Wenhui, ZHENG Yunwen, LIANG Liang, LI Yongjun
    2022, 35(4):  1201-1224.  DOI: 10.1007/s11424-022-0055-6
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    With the development of China's economy, environmental pollution has become cumulatively serious. The primary source of environmental pollution is thermal power generation, which has attracted the attention of governments and academia in recent years. To effectively reduce environmental pollution, research should study how to constrain the undesirable output of thermal power plants, that is, to limit the total undesirable output of the plants to a certain fixed sum. However, few studies have suggested that these undesirable outputs should be fixed-sum outputs. Moreover, no previous research publication about thermal power plants has analyzed their environmental performance changes. To address these gaps, a novel Malmquist-DEA approach is proposed for evaluate the environmental performance of thermal power plants in this paper. This approach generalizes the equilibrium efficient frontier DEA model with fixed-sum undesirable outputs and incorporates the model into the Malmquist productivity index (MPI). The authors apply this approach to the analysis of provincial thermal power plant environmental performance in China and analyze such plants' trends based on panel data from 2011 to 2014. The empirical research shows that the environmental performance of regional thermal power plants was positively affected by efficiency change and negatively affected by technical change. Finally, the authors provide policy suggestions based on our findings.
    Positive-Controllability, Positive-Near-Controllability, and Canonical Forms of Driftless Discrete-Time Bilinear Systems
    TIE Lin
    2022, 35(4):  1225-1243.  DOI: 10.1007/s11424-022-0335-1
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    Controllable canonical forms play important roles in the analysis and design of control systems. In this paper, a fundamental class of discrete-time bilinear systems are considered. Such systems are of interest since, on one hand, they have the most complete controllability theory. On the other hand, they can be nearly-controllable even if controllability fails. Firstly, controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived. Then, controllable canonical forms and nearly-controllable canonical forms of the systems are presented, respectively, where the corresponding transformation matrices are also explicitly constructed. Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.
    Distributed Communication-Sliding Mirror-Descent Algorithm for Nonsmooth Resource Allocation Problem
    WANG Yinghui, TU Zhipeng, QIN Huashu
    2022, 35(4):  1244-1261.  DOI: 10.1007/s11424-022-0187-8
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    This paper considers a distributed nonsmooth resource allocation problem of minimizing a global convex function formed by a sum of local nonsmooth convex functions with coupled constraints. A distributed communication-efficient mirror-descent algorithm, which can reduce communication rounds between agents over the network, is designed for the distributed resource allocation problem. By employing communication-sliding methods, agents can find a ε-solution in O($\frac{1}{\varepsilon }$) communication rounds while maintaining O($\frac{1}{\varepsilon ^2}$) subgradient evaluations for nonsmooth convex functions. A numerical example is also given to illustrate the effectiveness of the proposed algorithm.
    RHC-Based Consensus of Multi-Agent Systems with Simultaneous Packet Dropout and Input Delay
    XU Juanjuan, ZHANG Zhaorong
    2022, 35(4):  1262-1277.  DOI: 10.1007/s11424-022-0260-3
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    This paper is concerned with the multi-agent systems with both packet dropout and input delay. A novel receding horizon control (RHC) based consensus protocol is proposed by solving a distributed RHC based optimization problem. The novelty of the optimization problem lines in the involvement of the neighbours' predictor information in the cost functions. Based on the derived RHC based consensus protocol, the necessary and sufficient condition for the mean-square consensus is obtained. In addition, the authors give a specific sufficient condition to guarantee the mean-square consensus.
    Mean-Square Stabilization of Networked Sampled-Data Systems with Packet Losses: Critical Sampling Intervals
    WANG Chao, WANG Bingchang
    2022, 35(4):  1278-1292.  DOI: 10.1007/s11424-022-0188-7
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    This paper studies the stabilizing problem of networked sampled-data linear systems with independent and identically distribution (i.i.d.) packet dropouts. First of all, for the sampled-data system without packet losses, the necessary and sufficient conditions for the critical sampling intervals are given to ensure the mean square stability where zero order holder and generalized holder are adopted, respectively. Secondly, for the sampled-data system with i.i.d. packet losses, necessary and sufficient conditions for the critical sampling intervals are given to ensure the mean square stability where the zero order holder control is adopted. The random sampling framework is used to examine the case that the value of the control signal is not zero when the packet loss occurs, but the value of the previous control signal when the data packet is not lost. For the sampled-data system with i.i.d. packet losses, the range of the sampling interval is given to ensure the mean square stability where the generalized holder control is adopted. Some numerical simulations are provided to validate the theoretical results.
    Active Disturbance Rejection Control of Second-Order Nonlinear Uncertain Systems with Guaranteed Transient and Steady State Tracking Error Bounds
    CHEN Zhixiang
    2022, 35(4):  1293-1309.  DOI: 10.1007/s11424-022-1010-2
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    This paper presents an active disturbance rejection control (ADRC) method for a class of second-order nonlinear uncertain systems with guaranteed transient and steady state tracking error bounds. To deal with the tracking error constraint, an output error transformation and sliding surface technique are introduced to transform the constrained second-order system into an equivalent unconstrained first-order one. Then, an ADRC method is developed to achieve output tracking of the transformed uncertain system. The author proves that the closed-loop system is semi-globally uniformly bounded and it is sufficient to guarantee the tracking error constraint for the original system. Simulation results of a system of two inverted pendulums connected by a spring and a damper demonstrate the effectiveness of the proposed control method.
    Boundary Control of Coupled Wave Systems with Spatially-Varying Coefficients
    FENG Xiaodan, ZHANG Zhifei
    2022, 35(4):  1310-1329.  DOI: 10.1007/s11424-021-0214-1
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    This paper considers the stabilization of the coupled wave systems with spatially-varying coefficients. The authors design a state feedback controller by backstepping method. In contrast to the previous work in the literature, the kernel equations become more complicated and the main difficulty lies in proving the existence and uniqueness of the solution to the kernel equations. Firstly, using the backstepping approach, the authors verify the kernel equations, which is a system of coupled hyperbolic equations with spatially-varying coefficients. Then, the existence and uniqueness of the kernel matrices is obtained. Finally, the authors use a Lyapunov function to get the exponential stabilization of the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed controller.
    Distributed Event-Triggered Tracking Control of Heterogeneous Discrete-Time Multi-Agent Systems with Unknown Parameters
    YANG Ruohan, ZHOU Deyun
    2022, 35(4):  1330-1347.  DOI: 10.1007/s11424-022-1003-1
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    In this paper, a novel design framework is developed to solve the cooperative tracking problem of heterogeneous discrete-time multi-agent systems with unknown agent parameters and directed communication topologies. First, a distributed event-triggered observer is developed to handle the heterogeneity of the multi-agent systems. An event-triggering mechanism is proposed to reduce the amount of data transmission between neighboring agents. Then, based on the proposed observer, a discrete-time distributed model reference adaptive controller is presented to deal with the unknown parameters of the multi-agent systems. It is shown that by using the proposed observer and the model reference adaptive controller, the proposed design framework could achieve output tracking of the unknown multi-agent systems for any communication graph containing a directed spanning tree. Finally, an example is presented to illustrate the effectiveness of the proposed controller.
    Equilibria and Stability Analysis of Cohen-Grossberg BAM Neural Networks on Time Scale
    LIU Mingshuo, FANG Yong, DONG Huanhe
    2022, 35(4):  1348-1373.  DOI: 10.1007/s11424-022-0250-5
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    This paper considers the Cohen-Grossberg BAM neural networks (CG-BAMNNs) on time scale, which can unify and generalize the continuous and discrete systems. First, the criteria for the existence and uniqueness of the equilibrium of CG-BAMNNs are derived on time scale. Then based on that, the authors give the criteria for the stability and estimation of equilibrium of the CG-BAMNNs on time scale. The method proposed in this paper unifies and generalizes the continuous and discrete CGBAMNNs systems, and is applicable to some other neural network systems on time scale with practical meaning. The effectiveness of the proposed criteria for delayed CG-BAMNNs is demonstrated by numerical simulation.
    Asynchronous Dissipative Control and Robust Exponential Mean Square Stabilization for Uncertain Fuzzy Neutral Markov Jump Systems
    WANG Jie, ZHUANG Guangming, XIA Jianwei, CHEN Guoliang, ZHAO Junsheng
    2022, 35(4):  1374-1397.  DOI: 10.1007/s11424-021-1005-4
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    This paper researches the strict dissipative control problem for uncertain fuzzy neutral Markov jump systems by Takagi-Sugeno fuzzy rules. The asynchronous phenomenon is considered between the uncertain fuzzy neutral Markov jump systems modes and asynchronous fuzzy P-D feedback controller modes, which is described by a hidden Markov model. Via using linear matrix inequalities, the desired asynchronous fuzzy P-D feedback controller is obtained, which can ensure that the closed-loop uncertain fuzzy neutral Markov jump systems satisfies robustly exponential mean square stabilization with strict dissipativity. A numerical example and a single-link robot arm are utilized to demonstrate the effectiveness of the method.
    An Automatic Classification Pipeline for the Complex Synaptic Structure Based on Deep Learning
    SHEN Lijun, MA Chao, LUO Jie, HONG Bei
    2022, 35(4):  1398-1414.  DOI: 10.1007/s11424-022-0307-5
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    As a hallmark of brain complexity, synapses in the nervous system have always received extensive attentions. The diversity of the synaptic structure reflects various functions and mechanisms, some research indicates that, as one of the complex synaptic structures, multiple synapses can strengthen the synaptic connection, what's more, it is closely associated with the procedure of memory and learning. Accompanied by the fast advancement of electron microscopy (EM) technology, it is possible to detect the composition of multiple synapse with high resolution. On this basis, there have been various meaningful studies concerning the relationship between the multiple synapse and cognitive abilities. Despite the extensive studies have been made by different researchers on multiple synapse, no attention has been paid to the classification accuracy of the type of multiple synapse. The current research puts forward an effective method for the automatic classification of multiple synapse, which should be performed in three steps, namely the segmentation of synaptic clefts, the segmentation of vesicle bands, as well as the segmentation of multiple synapses. According to experimental results based on four data sets, the mean classification rate of the method is approximately 97%. In addition, the experimental result on the public dataset shows that the accuracy can reach 96.5%. The classification results provide a basis for quantitative statistics of follow-up studies. Moreover, this automatic classification method can reduce the time in artificial statistics, and thus researchers can focus more attention on the analysis of statistical results.
    On Basis and Pure Nash Equilibrium of Finite Pure Harmonic Games
    LIU Aixin, LI Haitao, LI Ping, YANG Xinrong
    2022, 35(4):  1415-1428.  DOI: 10.1007/s11424-022-0032-0
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    This paper investigates the basis and pure Nash equilibrium of finite pure harmonic games (FPHGs) based on the vector space structure. First, a new criterion is proposed for the construction of pure harmonic subspace, based on which, a more concise basis is constructed for the pure harmonic subspace. Second, based on the new basis of FPHGs and auxiliary harmonic vector, a more easily verifiable criterion is presented for the existence of pure Nash equilibrium in basis FPHGs. Third, by constructing a pure Nash equilibrium cubic matrix, the verification of pure Nash equilibrium in three-player FPHGs is given.
    Large Dynamic Covariance Matrix Estimation with an Application to Portfolio Allocation: A Semiparametric Reproducing Kernel Hilbert Space Approach
    PENG Siyang, GUO Shaojun, LONG Yonghong
    2022, 35(4):  1429-1457.  DOI: 10.1007/s11424-021-0168-3
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    The estimation of high dimensional covariance matrices is an interesting and important research topic for many empirical time series problems such as asset allocation. To solve this dimension dilemma, a factor structure has often been taken into account. This paper proposes a dynamic factor structure whose factor loadings are generated in reproducing kernel Hilbert space (RKHS), to capture the dynamic feature of the covariance matrix. A simulation study is carried out to demonstrate its performance. Four different conditional variance models are considered for checking the robustness of our method and solving the conditional heteroscedasticity in the empirical study. By exploring the performance among eight introduced model candidates and the market baseline, the empirical study from 2001 to 2017 shows that portfolio allocation based on this dynamic factor structure can significantly reduce the variance, i.e., the risk, of portfolio and thus outperform the market baseline and the ones based on the traditional factor model.
    Optimal Reinsurance and Investment Strategies Under Mean-Variance Criteria: Partial and Full Information
    ZHU Shihao, SHI Jingtao
    2022, 35(4):  1458-1479.  DOI: 10.1007/s11424-022-0236-3
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    This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution to the HJB equation in the full information case. Some numerical illustrations are also provided.
    Stock Efficiency Evaluation Based on Multiple Risk Measures: A DEA-Like Envelopment Approach
    LI Jun, GAO Hengxuan, LI Yongjun, JIN Xi, LIANG Liang
    2022, 35(4):  1480-1499.  DOI: 10.1007/s11424-022-0034-y
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    This paper proposes a new approach for stock efficiency evaluation based on multiple risk measures. A derived programming model with quadratic constraints is developed based on the envelopment form of data envelopment analysis (DEA). The derived model serves as an input-oriented DEA model by minimizing inputs such as multiple risk measures. In addition, the Russell input measure is introduced and the corresponding efficiency results are evaluated. The findings show that stock efficiency evaluation under the new framework is also effective. The efficiency values indicate that the portfolio frontier under the new framework is more externally enveloped than the DEA efficient surface under the standard DEA framework.
    Limited Memory BFGS Method for Least Squares Semidefinite Programming with Banded Structure
    XUE Wenjuan, SHEN Chungen, YU Zhensheng
    2022, 35(4):  1500-1519.  DOI: 10.1007/s11424-022-0015-1
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    This work is intended to solve the least squares semidefinite program with a banded structure. A limited memory BFGS method is presented to solve this structured program of high dimension. In the algorithm, the inverse power iteration and orthogonal iteration are employed to calculate partial eigenvectors instead of full decomposition of n×n matrices. One key feature of the algorithm is that it is proved to be globally convergent under inexact gradient information. Preliminary numerical results indicate that the proposed algorithm is comparable with the inexact smoothing Newton method on some large instances of the structured problem.
    Regression Analysis of Interval-Censored Data with Informative Observation Times Under the Accelerated Failure Time Model
    ZHAO Shishun, DONG Lijian, SUN Jianguo
    2022, 35(4):  1520-1534.  DOI: 10.1007/s11424-021-0209-y
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    This paper discusses regression analysis of interval-censored failure time data arising from the accelerated failure time model in the presence of informative censoring. For the problem, a sieve maximum likelihood estimation approach is proposed and in the method, the copula model is employed to describe the relationship between the failure time of interest and the censoring or observation process. Also I-spline functions are used to approximate the unknown functions in the model, and a simulation study is carried out to assess the finite sample performance of the proposed approach and suggests that it works well in practical situations. In addition, an illustrative example is provided.
    Test on Stochastic Block Model: Local Smoothing and Extreme Value Theory
    WU Fan, KONG Xinbing, XU Chao
    2022, 35(4):  1535-1556.  DOI: 10.1007/s11424-021-0154-9
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    In this paper, to obtain a consistent estimator of the number of communities, the authors present a new sequential testing procedure, based on the locally smoothed adjacency matrix and the extreme value theory. Under the null hypothesis, the test statistic converges to the type I extreme value distribution, and otherwise, it explodes fast and the divergence rate could even reach n in the strong signal case where n is the size of the network, guaranteeing high detection power. This method is simple to use and serves as an alternative approach to the novel one in Lei (2016) using random matrix theory. To detect the change of the community structure, the authors also propose a two-sample test for the stochastic block model with two observed adjacency matrices. Simulation studies justify the theory. The authors apply the proposed method to the political blog data set and find reasonable group structures.
    Genetic Pleiotropy Test by Quasi p-Value with Application to Typhoon Data in China
    WU Qiang, ZHONG Shaojun, TONG Xingwei
    2022, 35(4):  1557-1572.  DOI: 10.1007/s11424-022-0287-5
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    To test genetic pleiotropy, the main difficulty lies in the failure to find a test statistic and calculate its p-value for determining whether to reject the null hypothesis or not. To deal with this issue, the authors propose a quasi p-value, which plays the similar role as the usual p-value in genetic pleiotropy test. In the formula of the quasi p-value, the main task is to determine the weights. In this paper, the authors present two weighted methods based on the Bayesian rule and extend the proposed methods to study a single binary trait using a data-driven EM algorithm. Extensive simulation studies are conducted for the assessment of the two proposed methods and illustrate that the proposed methods improve the performance of power by comparing with the two-stage method. In addition, the authors apply the proposed methods to the data of tropical storms that occurred on the mainland of China since 1949, investigating the relationship between the landing site and predictive features of tropical storms, and showing that the landing site has a large influence on at least two features of typhoon.
    Recurrences for Callan's Generalization of Narayana Polynomials
    CHEN Xi, YANG Arthur Li Bo, ZHAO James Jing Yu
    2022, 35(4):  1573-1585.  DOI: 10.1007/s11424-021-0216-z
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    By using Chen, Hou and Mu's extended Zeilberger algorithm, the authors obtain two recurrence relations for Callan's generalization of Narayana polynomials. Based on these recurrence relations, the authors further prove the real-rootedness and asymptotic normality of Callan's Narayana polynomials.
    High Speed Machining for Linear Paths Blended with G3 Continuous Pythagorean-Hodograph Curves
    ZHAO Kai, LI Shurong
    2022, 35(4):  1586-1607.  DOI: 10.1007/s11424-022-0258-x
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    Previously, many studies have illustrated corner blend problem with different parameter curves. Only a few of them take a Pythagorean-hodograph (PH) curve as the transition arc, let alone corresponding real-time interpolation methods. In this paper, an integrated corner-transition mixing-interpolation-based scheme (ICMS) is proposed, considering transition error and machine tool kinematics. Firstly, the ICMS smooths the sharp corners in a linear path through blending the linear path with G3 continuous PH transition curves. To obtain optimal PH transition curves globally, the problem of corner smoothing is formulated as an optimization problem with constraints. In order to improve optimization efficiency, the transition error constraint is deduced analytically, so is the curvature extreme of each transition curve. After being blended with PH transition curves, a linear path has become a blend curve. Secondly, the ICMS adopts a novel mixed interpolator to process this kind of blend curves by considering machine tool kinematics. The mixed interpolator can not only implement jerk-limited feedrate scheduling with critical points detection, but also realize self-switching of two interpolation modes. Finally, two patterns are machined with a carving platform based on ICMS. Experimental results show the effectiveness of ICMS.
    The Center Problem and Time-Reversibility with Respect to a Quadratic Involution for a Class of Polynomial Differential Systems with Order 2 or 3
    YANG Jing, YANG Ming, LU Zhengyi
    2022, 35(4):  1608-1636.  DOI: 10.1007/s11424-021-0040-5
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    Most studies of the time-reversibility are limited to a linear or an affine involution. In this paper, the authors consider the case of a quadratic involution. For a polynomial differential system with a linear part in the standard form (-y, x) in $\mathbb{R}^2$, by using the method of regular chains in a computer algebraic system, the computational procedure for finding the necessary and sufficient conditions of the system to be time-reversible with respect to a quadratic involution is given. When the system is quadratic, the necessary and sufficient conditions can be completely obtained by this procedure. For some cubic systems, the necessary and sufficient conditions for these systems to be time-reversible with respect to a quadratic involution are also obtained. These conditions can guarantee the corresponding systems to have a center. Meanwhile, a property of a center-focus system is discovered that if the system is time-reversible with respect to a quadratic involution, then its phase diagram is symmetric about a parabola.