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    25 June 2021, Volume 34 Issue 3
    Controllability of Quantum Systems with SU(1, 1) Dynamical Symmetry
    WU Jianwu · WU Rebing · ZHANG Jing · LI Chunwen
    2021, 34(3):  827-842.  DOI: 10.1007/s11424-020-9259-9
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    This paper presents sufficient and necessary conditions for the propagator controllability of a class of infinite-dimensional quantum systems with SU(1, 1) dynamical symmetry through the isomorphic mapping to the non-unitary representation of SU(1, 1). The authors prove that the elliptic condition of the total Hamiltonian is both necessary and sufficient for the controllability and strong controllability. The obtained results can be also extended to control systems with SO(2, 1) dynamical symmetry.

    Sampled-Data Stabilization of a Class of Stochastic Nonlinear Markov Switching System with Indistinguishable Modes Based on the Approximate Discrete-Time Models
    ZHANG Qianqian · KANG Yu · YU Peilong · ZHU Jin· LIU Chunhan · LI Pengfei
    2021, 34(3):  843-859.  DOI: 10.1007/s11424-020-9263-0
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    This paper investigates the stabilization issue for a class of sampled-data nonlinear Markov switching system with indistinguishable modes. In order to handle indistinguishable modes, the authors reconstruct the original mode space by mode clustering method, forming a new merged Markov switching system. By specifying the difference between the Euler-Maruyama (EM) approximate discrete-time model of the merged system and the exact discrete-time model of the original Markov switching system, the authors prove that the sampled-data controller, designed for the merged system based on its EM approximation, can exponentially stabilize the original system in mean square sense. Finally, a numerical example is given to illustrate the effectiveness of the method.

    The Dynamics Characteristics of Flexible Spacecraft and Its Closed-Loop Stability with Passive Control
    MENG Bin · ZHAO Yunbo
    2021, 34(3):  860-872.  DOI: 10.1007/s11424-020-9268-8
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    Passive control is the most popular methodology for flexible spacecraft while it remains an open problem whether the closed-loop performance can be achieved only with passive control subject to the coupling modes of rigid and flexibility. Also, the closed-loop performance of passive PD control based on the dynamics of the Euler angle parameterization of spacecraft, which has been widely used in practice, is yet to be addressed. Towards these challenges, by introducing the input-output exact linearization theory and Lyapunov theory, the authors show that the closed-loop performance for flexible spacecraft with rigid and flexible modes can be achieved by adjusting the parameters of the passive controllers sufficiently large. This is done by firstly transforming the flexible spacecraft dynamics into an exact feedback linearization standard form, and then analyzing the closed-loop performance of flexible spacecraft.

    Event-Triggered L1-Gain Control of Nonlinear Positive Switched Systems
    ZHANG Junfeng · LIU Laiyou · LI Shuo · DENG Xuanjin
    2021, 34(3):  873-898.  DOI: 10.1007/s11424-020-9324-4
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    This paper is concerned with the event-triggered L1-gain control of a class of nonlinear positive switched systems. First, an event-triggering condition in the form of 1-norm is presented for the systems. By virtue of the event-triggering strategy, the original system is transformed into an interval uncertain system. An event-triggered L1-gain controller is designed by decomposing the controller gain matrix into the sum of nonnegative and non-positive components. Under the design controller, the resulting closed-loop systems are positive and L1-gain stable. The obtained approach is developed for the systems subject to input saturation. All presented conditions are solvable in terms of linear programming. Finally, two examples are provided to verify the effectiveness of the design.

    Impulse Controllability and Impulse Observability of Stochastic Singular Systems
    GE Zhaoqiang
    2021, 34(3):  899-911.  DOI: 10.1007/s11424-020-9250-5
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    This paper discusses the impulse controllability and impulse observability of stochastic singular systems. Firstly, the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform. Secondly, the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory. Finally, an example is given to illustrate the effectiveness of the obtained theoretical results.

    Finite-Time Stochastic Stability of Random Impulsive Positive System
    YOU Lijie · MU Xiaowu
    2021, 34(3):  912-923.  DOI: 10.1007/s11424-020-9273-y
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    The paper focuses on the finite-time stochastic stability (FTSS) problems for positive system with random impulses. Combining Lyapunov functions with the probability property of the impulsive interval, first, the sufficient conditions of FTSS for the positive systems affected by one type of random impulses are given; second, the criteria of FTSS for positive systems suffered from multiple types of random impulses are established. Finally, two examples are presented to show the validity of results.

    H2/H∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching
    WANG Meijiao · MENG Qingxin · SHEN Yang
    2021, 34(3):  924-954.  DOI: 10.1007/s11424-020-9131-y
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    In this paper, a stochastic H2/H∞ control problem is investigated for Poisson jumpdiffusion systems with Markovian switching, which are driven by a Brownian motion and a Poisson random measure with the system parameters modulated by a continuous-time finite-state Markov chain. A stochastic jump bounded real lemma is proved, which reveals that the norm of the perturbation operator below a given threshold is equivalent to the existence of a global solution to a parameterized system of Riccati type differential equations. This result enables the authors to obtain sufficient and necessary conditions for the existence of H2/H∞ control in terms of two sets of interconnected systems of Riccati type differential equations.

    Bipartite Consensus of Linear Multi-Agent Systems by Distributed Event-Triggered Control
    YANG Ruitian · PENG Li · YANG Yongqing · ZHU Fengzeng
    2021, 34(3):  955-974.  DOI: 10.1007/s11424-020-9293-7
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    For multi-agent systems with competitive and collaborative relationships, signed graph can more intuitively express the characteristics of their interactive networks. In this paper, the bipartite consensus is investigated for multi-agent systems with structurally balanced signed graph. In order to reduce actuation burden in dynamical network environment, the event-triggering strategy is applied to bipartite consensus protocol for the multi-agent systems. The triggered condition for each agent is designed by using its own information and transmitted information of its neighbors at sampling instant and make the number of triggers of the whole systems be reduced. Based on the distributed eventtriggered control, some sufficient conditions are derived to guarantee the leaderless and leader-following bipartite consensus. Finally, some numerical examples are shown to demonstrate the effectiveness of the theoretical results.

    Stabilization with Arbitrary Convergence Rate for the Schr¨odinger Equation Subjected to an Input Time Delay
    LI Yanfang · CHEN Hao · XIE Yaru
    2021, 34(3):  975-994.  DOI: 10.1007/s11424-020-9294-6
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    The stabilization problem for the Schr¨odinger equation with an input time delay is considered from the view of system equivalence. First, a linear transform from the original system into an exponentially stable system with arbitrary decay rate, also called “target system”, is introduced. The linear transform is constructed via a kind of Volterra-type integration with singular kernels functions. As a result, a feedback control law for the original system is obtained. Secondly, a linear transform from the target system into the original closed-loop system is derived. Finally, the exponential stability with arbitrary decay rate of the closed-loop system is obtained through the established equivalence between the original closed-loop system and the target one. The authors conclude this work with some numerical simulations giving support to the results obtained in this paper.

    Distributed Finite-Time Integral Sliding-Mode Control for Multi-Agent Systems with Multiple Disturbances Based on Nonlinear Disturbance Observers
    YANG Yize · LIU Fan · YANG Hongyong · LI Yuling · LIU Yuanshan
    2021, 34(3):  995-1013.  DOI: 10.1007/s11424-020-9152-6
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    This paper proposes a finite-time consensus control algorithm based on nonlinear integral sliding-mode control for second-order multi-agent systems (MASs) with mismatched and matched disturbances. Firstly, a nonlinear finite-time disturbance observer is established to estimate the states and mismatched disturbances of the agent. Secondly, a dynamic integral sliding-mode (ISM) surface is designed by employing the estimates of mismatched disturbances. Then, based on the designed ISM and disturbance observer, the discontinuous or continuous campsite control protocols are respectively developed to guarantee the consensus for MASs in finite time with active anti-disturbance control. Finally, numerical simulation results illustrate the effectiveness of the proposed consensus control algorithm.

    Finding Key Node Sets in Complex Networks Based on Improved Discrete Fireworks Algorithm
    LIU Fengzeng · XIAO Bing · LI Hao
    2021, 34(3):  1014-1027.  DOI: 10.1007/s11424-020-9023-1
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    Finding out the key node sets that affect network robustness has great practical significance for network protection and network disintegration. In this paper, the problem of finding key node sets in complex networks is defined firstly. Because it is an NP-hard combinatorial optimization problem, discrete fireworks algorithm is introduced to search the optimal solution, which is a swarm intelligence algorithm and is improved by the prior information of networks. To verify the effect of improved discrete fireworks algorithm (IDFA), experiments are carried out on various model networks and real power grid. Results show that the proposed IDFA is obviously superior to the benchmark algorithms, and networks suffer more damage when the key node sets obtained by IDFA are removed from the networks. The key node sets found by IDFA contain a large number of non-central nodes, which provides the authors a new perspective that the seemingly insignificant nodes may also have an important impact on the robustness of the network.

    Predictive Event-Triggered Control for Disturbanced Wireless Networked Control Systems
    ZHAO Yunbo · PAN Xiaokang · YU Shiming
    2021, 34(3):  1028-1043.  DOI: 10.1007/s11424-020-9317-3
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    The control and scheduling for wireless networked control system with packet dropout and disturbance are investigated. A prediction based event triggered control is proposed to reduce data transmissions while preserving the robustness against external disturbance. First, a trigger threshold is especially designed to maintain the difference of the estimated and actual states below a proper boundary when system suffers from packet dropout. Then a predictive controller is designed to compensate for packet dropouts by utilizing the packet-based control approach. The sufficient conditions to ensure the closed-loop system being uniformly ultimately bounded are derived, with consequently the controller gain method. Numerical examples illustrate the effectiveness of the proposed approach.

    Brexit and Its Impact on the US Stock Market
    QIAO Kenan · LIU Zhengyang · HUANG Bai · SUN Yuying · WANG Shouyang
    2021, 34(3):  1044-1062.  DOI: 10.1007/s11424-020-9174-0
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    This paper firstly analyzes the Brexit’s impact on the US stock market using a novel interval methodology. The interval-valued dummy variables are proposed to measure the direction and magnitudes of the changes in the inter-day trend and the intra-day volatility of S&P500 returns simultaneously. It is found that both the trend and the volatility of S&P500 returns increased before the Brexit. Besides, the Brexit negatively affected S&P500 returns’ trend in the short term after the event, while its impact on market volatility was positive, which slowly decayed across time. Furthermore, a new interesting finding is that there are both short-term momentum effects (i.e., positive autocorrelation of trends) and volatility clustering in stock markets.

    Stochastic Petri Net Based Modeling of Emergency Medical Rescue Processes During Earthquakes
    SUN Huali · LIU Jiaguo · HAN Ziqiang · JIANG Juan
    2021, 34(3):  1063-1086.  DOI: 10.1007/s11424-020-9139-3
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    The post-disaster emergency medical rescue (EMR) is critical for people’s lives. This paper presents a stochastic Petri net (SPN) model based on the process of the rescue structure and a Markov chain model (MC), which is applied to the optimization of the EMR process, with the aim of identifying the key activities of EMR. An isomorphic MC model is developed for measuring and evaluating the time performance of the EMR process during earthquakes with the data of the 2008 Wenchuan earthquake. This paper provides a mathematical approach to simulate the process and to evaluate the efficiency of EMR. Simultaneously, the expressions of the steady state probabilities of this system under various states are obtained based on the MC, and the variations of the probabilities are analyzed by changing the firing rates for every transition. Based on the concrete data of the event, the authors find the most time consuming and critical activities for EMR decisions. The model results show that the key activities can improve the efficiency of medical rescue, providing decision-makers with rescue strategies during the large scale earthquake.

    Homotopy Analysis Method for Portfolio Optimization Problem Under the 3/2 Model
    YANG Shuquan · JIA Zhaoli · WU Qianqian · WU Huojun
    2021, 34(3):  1087-1101.  DOI: 10.1007/s11424-021-9286-1
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    This paper considers the Merton portfolio optimization problem for an investor that aims at maximizing the expected power utility of the terminal wealth and intermediate consumption. Applying the homotopy analysis method, an analytical solution for value function as well as optimal strategy under the 3/2 model is derived, respectively. Compared with the existing explicit solutions for Merton problem under the 3/2 model, the formulas provide certain parameters with less requirement since the homotopy analysis method does not depend on the existence of small parameters in the equation. Finally, numerical examples are examined with the approach, and the proposed solution provides more accurate approximation as the number of terms in infinite series increases.

    Impact of Crowdsourcee’s Vertical Fairness Concern on the Crowdsourcing Knowledge Sharing Behavior and Its Incentive Mechanism
    ZHU Binxin · LEON Williams · PAUL Lighterness · GAO Peng
    2021, 34(3):  1102-1120.  DOI: 10.1007/s11424-020-9243-4
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    This paper examines in detail the impact of the crowdsourcee’s vertical fairness concern on the knowledge sharing incentive mechanism in crowdsourcing communities. The conditions for the establishment of the incentive mechanism are analyzed and the impact of fairness concern sensitivity on expected economic revenues of both sides as well as the crowdsourcing project performance is studied by game theory and computer simulation. The results show that the knowledge sharing incentive mechanism can only be established if the ratio between the performance improvement rate and the private cost reduction rate caused by shared knowledge is within a certain range. The degree of the optimal linear incentives, the private solution efforts, and the improvement of knowledge sharing level are positively correlated with the sensitivity of vertical fairness concern. In the non-incentive mode, the ratio between the performance conversion rate of private solution effort and the performance conversion rate of knowledge sharing effort plays an important role in moderating a crowdsourcing project’s performance. The authors find that the number of participants is either conducive or nonconducive to the improvement of performance. The implementation of knowledge sharing incentive can achieve a win-win situation for both the crowdsourcer and the crowdsourcee.

    Most Likely Optimal Subsampled Markov Chain Monte Carlo
    HU Guanyu · WANG Haiying
    2021, 34(3):  1121-1134.  DOI: 10.1007/s11424-020-9335-1
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    Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. This paper proposes to approximate the log-likelihood with subsamples taken according to nonuniform subsampling probabilities, and derives the most likely optimal (MLO) subsampling probabilities for better approximation. Compared with existing subsampled MCMC algorithm with equal subsampling probabilities, the MLO subsampled MCMC has a higher estimation efficiency with the same subsampling ratio. The authors also derive a formula using the asymptotic distribution of the subsampled log-likelihood to determine the required subsample size in each MCMC iteration for a given level of precision. This formula is used to develop an adaptive version of the MLO subsampled MCMC algorithm. Numerical experiments demonstrate that the proposed method outperforms the uniform subsampled MCMC.

    Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models
    LIU Yan · REN Mingyang · ZHANG Sanguo
    2021, 34(3):  1135-1155.  DOI: 10.1007/s11424-020-9260-3
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    This paper considers tests for regression coefficients in high dimensional partially linear Models. The authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly expressed. Then, the authors propose an empirical likelihood method to test regression coefficients. The authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null hypothesis. In addition, the method is extended to test with nuisance parameters. Simulations show that the proposed method have a good performance in control of type-I error rate and power. The proposed method is also employed to analyze a data of Skin Cutaneous Melanoma (SKCM).

    Robust Regression Analysis for Clustered Interval-Censored Failure Time Data
    LUO Lin · ZHAO Hui
    2021, 34(3):  1156-1174.  DOI: 10.1007/s11424-020-9350-2
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    Clustered interval-censored failure time data often occur in a wide variety of research and application fields such as cancer and AIDS studies. For such data, the failure times of interest are interval-censored and may be correlated for subjects coming from the same cluster. This paper presents a robust semiparametric transformation mixed effect models to analyze such data and use a U-statistic based on rank correlation to estimate the unknown parameters. The large sample properties of the estimator are also established. In addition, the authors illustrate the performance of the proposed estimate with extensive simulations and two real data examples.

    Empirical Likelihood Based Diagnostics for Heteroscedasticity in Semiparametric Varying-Coefficient Partially Linear Models with Missing Responses
    LIU Feng · GAO Weiqing · HE Jing · FU Xinwei · KANG Xinmei
    2021, 34(3):  1175-1188.  DOI: 10.1007/s11424-020-9240-7
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    This paper proposes an empirical likelihood based diagnostic technique for heteroscedasticity for semiparametric varying-coefficient partially linear models with missing responses. Firstly, the authors complement the missing response variables by regression method. Then, the empirical likelihood method is introduced to study the heteroscedasticity of the semiparametric varying-coefficient partially linear models with complete-case data. Finally, the authors obtain the finite sample property by numerical simulation.

    Computing μ-Bases of Univariate Polynomial Matrices Using Polynomial Matrix Factorization
    HUANG Bingru · CHEN Falai
    2021, 34(3):  1189-1206.  DOI: 10.1007/s11424-020-9314-6
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    This paper extends the notion of μ-bases to arbitrary univariate polynomial matrices and present an efficient algorithm to compute a μ-basis for a univariate polynomial matrix based on polynomial matrix factorization. Particularly, when applied to polynomial vectors, the algorithm computes a μ-basis of a rational space curve in arbitrary dimension. The authors perform theoretical complexity analysis in this situation and show that the computational complexity of the algorithm is O(dn4+d2n3), where n is the dimension of the polynomial vector and d is the maximum degree of the polynomials in the vector. In general, the algorithm is n times faster than Song and Goldman’s method, and is more efficient than Hoon Hong’s method when d is relatively large with respect to n. Especially, for computing μ-bases of planar rational curves, the algorithm is among the two fastest algorithms.

    Feature Screening for High-Dimensional Survival Data via Censored Quantile Correlation
    XU Kai · HUANG Xudong
    2021, 34(3):  1207-1224.  DOI: 10.1007/s11424-020-9295-5
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    This paper proposes a new sure independence screening procedure for high-dimensional survival data based on censored quantile correlation (CQC). This framework has two distinctive features: 1) Via incorporating a weighting scheme, our metric is a natural extension of quantile correlation (QC), considered by Li (2015), to handle high-dimensional survival data; 2) The proposed method not only is robust against outliers, but also can discover the nonlinear relationship between independent variables and censored dependent variable. Additionally, the proposed method enjoys the sure screening property under certain technical conditions. Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors.