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    25 November 2022, Volume 35 Issue 6
    Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay
    IMEN Akrouti, NADHEM Echi
    2022, 35(6):  2029-2045.  DOI: 10.1007/s11424-022-1061-4
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    This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances. In case there is no perturbation, the exponential convergence of the observer was confirmed. When external disturbances appear in the system, a separation principle is established, and the authors show that the closed loop system is exponentially practical stable. By choosing a suitable Lyapunov-Krasovskii functional, the authors derive new sufficient conditions to guarantee the exponential stability of the systems. Finally, a physical model is performed to prove the efficiency and applicability of the suggested approach.
    Fully Actuated System Approach for Linear Systems Control: A Frequency-Domain Solution
    DUAN Guang-Ren, ZHOU Bin
    2022, 35(6):  2046-2061.  DOI: 10.1007/s11424-022-1361-8
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    This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description (PMD). For a controllable first-order linear state-space system model, by using the right coprime factorization of its transfer function matrix, under the condition that the denominator matrix in the right coprime factorization is column reduced, it is equivalently transformed into a fully actuated PMD model, whose time-domain expression is just a high-order fully actuated (HOFA) system model. This method is a supplement to the previous one in the time-domain, and reveals a connection between the controllability of the first-order linear state-space system model and the full-actuation of its PMD model. Both continuous-time and discrete-time linear systems are considered. Some numerical examples are worked out to illustrate the effectiveness of the proposed approaches.
    Trust-Region Based Stochastic Variational Inference for Distributed and Asynchronous Networks
    FU Weiming, QIN Jiahu, LING Qing, KANG Yu, YE Baijia
    2022, 35(6):  2062-2076.  DOI: 10.1007/s11424-022-2085-5
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    Stochastic variational inference is an efficient Bayesian inference technology for massive datasets, which approximates posteriors by using noisy gradient estimates. Traditional stochastic variational inference can only be performed in a centralized manner, which limits its applications in a wide range of situations where data is possessed by multiple nodes. Therefore, this paper develops a novel trust-region based stochastic variational inference algorithm for a general class of conjugate-exponential models over distributed and asynchronous networks, where the global parameters are diffused over the network by using the Metropolis rule and the local parameters are updated by using the trust-region method. Besides, a simple rule is introduced to balance the transmission frequencies between neighboring nodes such that the proposed distributed algorithm can be performed in an asynchronous manner. The utility of the proposed algorithm is tested by fitting the Bernoulli model and the Gaussian model to different datasets on a synthetic network, and experimental results demonstrate its effectiveness and advantages over existing works.
    Stability of a Variable Coefficient Star-Shaped Network with Distributed Delay
    ZHANG Hai-E, XU Gen-Qi, CHEN Hao, LI Min
    2022, 35(6):  2077-2106.  DOI: 10.1007/s11424-022-1157-x
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    The paper deals with the exponential stability problem of a variable coefficient star-shaped network, whose strings are coupled at a common end in a star-shaped configuration and the common connection of all strings can be moved. Two kinds of media materials with a component of viscous and another simply elastic are distributed on each string. Under suitable hypothesis on the coefficient functions $\mu_j(x)$ of damping terms and the kernels $\eta_j(s)$ of distributed delay terms, the well-posedness of the system is obtained by means of resolvent family theory. In addition, the allocation proportion of the two parts and the property of the material character functions are discussed when the star-shaped network is exponentially stable. Meanwhile, the sufficient condition of exponential stability is established. Numerical simulations are also included to verify the main results.
    Controllability of General Linear Discrete Multi-Agent Systems with Directed and Weighted Signed Network
    ZHAO Lanhao, JI Zhijian, LIU Yungang, LIN Chong
    2022, 35(6):  2107-2130.  DOI: 10.1007/s11424-022-1036-5
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    This paper investigates the controllability of general linear discrete-time multi-agent systems with directed and weighted signed networks by using graphic and algebraic methods. The non-delay and delay cases are considered respectively. For the case of no time delay, the upper bound condition of the controllable subspace is given by using the equitable partition method, and the influence of coefficient matrix selection of individual dynamics is illustrated. For the case of single delay and multiple delays, the equitable partition method is extended to deal with time-delay systems, and some conclusions are obtained. In particular, some simplified algebraic criteria for controllability of systems with time delay are obtained by using augmented system method and traditional algebraic controllability criteria.
    Algebraic Verification of Finite Group-Based Potential Games with Vector Payoffs
    WANG Yuanhua, LI Haitao
    2022, 35(6):  2131-2144.  DOI: 10.1007/s11424-022-1064-1
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    This paper studies a class of strategic games, where players often collaborate with other players to form a group when making decisions, and the payoff functions of players in such games are presented as vector functions. First, using the semi-tensor product (STP) method, it is proved that a finite game with vector payoffs is potential if and only if its potential equation has solution. By adding a suitable weight vector to the vector payoffs of each player, a finite game with vector payoffs that is not potential can be converted into a potential game. Second, as a natural generalization, the authors consider the verification problem of the group-based potential games with vector payoffs. By solving a linear potential equation, a simple formula is obtained to calculate the corresponding potential function. Finally, some examples are presented and discussed in detail to illustrate the theoretical results.
    Access Control Method for EV Charging Stations Based on State Aggregation and Q-Learning
    TANG Ziyu, LUO Yonglong, FANG Daohong, ZHAO Chuanxin
    2022, 35(6):  2145-2165.  DOI: 10.1007/s11424-022-1155-z
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    This paper presents intelligent access control for a charging station and a framework for dynamically and adaptively managing charging requests from randomly arriving electric vehicles (EVs), to increase the revenue of the station. First, charging service requests from random EV arrivals are described as an event-driven sequential decision process, and the decision-making relies on an event-extended state that is composed of the real-time electricity price, real-time charging station state, and EV arrival event. Second, a state aggregation method is introduced to reduce the state space by first aggregating the charging station state in the form of the remaining charging time and then further aggregating it via sort coding. Besides, mathematical calculations of the code value are provided, and their uniqueness and continuous integer characteristics are proved. Then, a corresponding Q-learning method is proposed to derive an optimal or suboptimal access control policy. The results of a case study demonstrate that the proposed learning optimisation method based on the event-extended state aggregation performs better than flat Q-learning. The space complexity and time complexity are significantly reduced, which substantially improves the learning efficiency and optimisation performance.
    Event-Triggered Adaptive Fuzzy Finite Time Control of Fractional-Order Non-Strict Feedback Nonlinear Systems
    XIN Chun, LI Yuanxin, NIU Ben
    2022, 35(6):  2166-2180.  DOI: 10.1007/s11424-022-1244-z
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    In this article, the problem of event-triggered adaptive fuzzy finite time control of non-strict feedback fractional order nonlinear systems is investigated. By using the property of fuzzy basis function, the obstacle caused by algebraic loop problems is successfully circumvented. Moreover, a new adaptive event-triggered scheme is designed under the unified framework of backstepping control method, which can largely reduce the amount of communications. The stability of the closed-loop system is ensured through fractional Lyapunov stability analysis. Finally, the effectiveness of the proposed scheme is verified by simulation examples.
    Positivity and Stability of Fractional-Order Linear Time-Delay Systems
    HAO Yilin, HUANG Chengdai, CAO Jinde, LIU Heng
    2022, 35(6):  2181-2207.  DOI: 10.1007/s11424-022-1018-7
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    This article focuses on the positivity and the asymptotic stability of fractional-order linear time-delay systems (FOLTDSs) which are composed of $N$ $(N\geq2)$ subsystems. Firstly, a sufficient and necessary condition is given to ensure the positivity of FOLTDSs. The solutions of the studied systems are obtained by using the Laplace transform method, and it can be observed that the positivity of FOLTDSs is completely determined by the series of matrices and independent of the magnitude of time-delays. Secondly, a theorem is given to prove the asymptotic stability of positive FOLTDSs. By considering the monotonicity and asymptotic properties of systems with constant time-delay, it is further shown that the asymptotic stability of positive FOLTDSs is independent of the time-delay. Next, a state-feedback controller, whose gain matrix is derived by resolving a linear programming question, is designed such that the state variables of the systems are nonnegative and asymptotically convergent. When the order of the FOLTDSs is greater than one, by utilizing a proposed property of Caputo derivative, a sufficient condition for the positivity of FOLTDS is presented. Finally, simulation examples are presented to verify the validity and practicability of the theoretical analysis.
    Orthogonal Decomposition of Incomplete-Profile Finite Game Space
    DAI Xiaoyan, WANG Jinhuan, XU Yong
    2022, 35(6):  2208-2222.  DOI: 10.1007/s11424-022-1019-6
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    This work studies the orthogonal decomposition of the incomplete-profile normal finite game (IPNFG) space using the method of semi-tensor product (STP) of matrices. Firstly, by calculating the rank of the incomplete-profile potential matrix, the bases of incomplete-profile potential game subspace ($\mathcal{G}_P^{\it\Omega}$) and incomplete-profile non-strategic game subspace ($\mathcal{N}^{\it\Omega}$) are obtained. Then the bases of incomplete-profile pure potential game subspace ($\mathcal{P}^{\it\Omega}$) and incomplete-profile pure harmonic game subspace ($\mathcal{H}^{\it\Omega}$) are also revealed. These bases offer an expression for the orthogonal decomposition. Finally, an example is provided to verify the theoretical results.
    Finite-Time Stability for Interval Type-2 Fuzzy Nonlinear Systems via an Observer-Based Sliding Mode Control
    LIU Yu'an, XIA Jianwei, WANG Jing, SHEN Hao
    2022, 35(6):  2223-2247.  DOI: 10.1007/s11424-022-1106-8
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    This work focuses on the design of a sliding mode controller for a class of continuous-time interval type-2 fuzzy-model-based nonlinear systems with unmeasurable state information over a finite-time interval. Aiming at describing the nonlinearities containing parameter uncertainties that inevitably appear in practice, the interval type-2 fuzzy sets are employed to model the studied system. To improve the designing flexibility, a fuzzy observer model non-parallel distribution compensation scheme is designed to estimate the state information of the plant, i.e., the observer is allowed to have a mismatching premise structure from the system. On this basis, the appropriate fuzzy sliding surface and fuzzy controller are constructed by following the same premise variables as the designed fuzzy observer. Then, by means of the sliding mode control theory and the Lyapunov function method, some novel sufficient criteria are established to ensure the finite-time boundedness for the studied systems via a partitioning strategy including the reaching phase, the sliding motion phase and the whole time interval. Furthermore, the designed gains are acquired by solving the matrix convex optimization problem. Finally, the effectiveness of the developed method is demonstrated by two simulation examples.
    Task-Space Tracking Control of Robotic Manipulator Via Intermittent Controller
    MA Mihua, CAI Jianping
    2022, 35(6):  2248-2262.  DOI: 10.1007/s11424-022-1139-z
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    An intermittent controller for robotic manipulator in task space was developed in this paper. In task space, for given a desired time-varying trajectory, the robot end-effector can track the desired target under the designed intermittent controller. Different from most of the existing works on control of robotic manipulator, the intermittent control for robotic manipulator is discussed in task space instead of joint space. Besides, the desired trajectory can be time-varying and not limited to constant. As a direct application, the authors implemented the proposed controller on tracking of a two-link robotic manipulator in task space. Numerical simulations demonstrate the effectiveness and feasibility of the proposed intermittent control strategy.
    Comparison of Covariate Balance Weighting Methods in Estimating Treatment Effects
    ZHAN Mingfeng, FANG Ying, LIN Ming
    2022, 35(6):  2263-2277.  DOI: 10.1007/s11424-022-1037-4
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    Different covariate balance weighting methods have been proposed by researchers from different perspectives to estimate the treatment effects. This paper gives a brief review of the covariate balancing propensity score method by Imai and Ratkovic (2014), the stable balance weighting procedure by Zubizarreta (2015), the calibration balance weighting approach by Chan, et al. (2016), and the integrated propensity score technique by Sant'Anna, et al. (2020). Simulations are conducted to illustrate the finite sample performance of both the average treatment effect and quantile treatment effect estimators based on different weighting methods. Simulation results show that in general, the covariate balance weighting methods can outperform the conventional maximum likelihood estimation method while the performance of the four covariate balance weighting methods varies with the data generating processes. Finally, the four covariate balance weighting methods are applied to estimate the treatment effects of the college graduate on personal annual income.
    Multiple Change Points Detection in High-Dimensional Multivariate Regression
    MA Xiaoyan, ZHOU Qin, ZI Xuemin
    2022, 35(6):  2278-2301.  DOI: 10.1007/s11424-022-1205-6
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    This paper considers the problem of detecting structural changes in a high-dimensional regression setting. The structural parameters are subject to abrupt changes of unknown magnitudes at unknown locations. The authors propose a new procedure that minimizes a penalized least-squares loss function via a dynamic programming algorithm for estimating the locations of change points. To alleviate the computational burden, the authors adopt a prescreening procedure by eliminating a large number of irrelevant points before implementing estimation procedure. The number of change points is determined via Schwarz's information criterion. Under mild assumptions, the authors establish the consistency of the proposed estimators, and further provide error bounds for estimated parameters which achieve almost-optimal rate. Simulation studies show that the proposed method performs reasonably well in terms of estimation accuracy, and a real data example is used for illustration.
    Optimal Pricing and Return-Freight Insurance: Strategic Analysis of E-Sellers in the Presence of Reputation Differentiation
    YANG Ying, CHAI Rui, SUN Xinyu, LI Yiming
    2022, 35(6):  2302-2318.  DOI: 10.1007/s11424-022-1262-x
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    Motivated by the practice that e-sellers cooperate with insurance companies to offer consumers the return-freight insurance (RI), this paper aims to investigate the competing e-sellers' RI strategies. Regarding the information asymmetry in the online context, reputation system is widely applied by e-platforms. In an online market with two competing e-sellers that sell the same product but are differentiated in their reputation, this paper builds an analytical model to explore the e-sellers optimal pricing and RI strategies. Combined with sellers' reputation and their RI strategies, the equilibrium outcomes under four cases are discussed. This paper reveals the conditions that e-sellers are willing to offer RI. Specifically, the findings demonstrate that low reputation e-seller is more likely to offer RI. Moreover, when the sellers are more divergent, they are more likely to co-exist in the market. Insurance premium and RI compensation play critical roles in their decisions. RI introduction tends to increase the price, thus offsets the benefits of RI, but does not affect the total consumer surplus.
    Opinion Dynamics Induced by Agents with Particular Goal
    LI Zhenpeng, TANG Xijin, HONG Zhenjie
    2022, 35(6):  2319-2335.  DOI: 10.1007/s11424-022-1092-x
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    The authors investigate the opinion dynamics in a setting where some special agents induce public opinions towards their desired direction, with Particular Goal (PG agents for short) to manipulate beliefs. Based on the bounded confidence model, the authors find PG agents can significantly improve the level of consensus. The authors also study how opinion pattern is influenced by varying the model in terms of changing the network structure, different parameters, and PG agents choosing strategy. The authors conduct the comparison of model results with empirical data from on line social networks. The authors hope the study may shade a light on public opinion control and regulation.
    B-Spline Method for Spatio-Temporal Inverse Model
    WANG Hongxia, ZHAO Zihan, WU Yuehua, LUO Xuehong
    2022, 35(6):  2336-2360.  DOI: 10.1007/s11424-022-1206-5
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    Inverse models can be used to estimate surface fluxes in terms of the observed atmospheric concentration measurement data. This paper proposes a new nonparametric spatio-temporal inverse model and provides the global expressions for the estimates by employing the B-spline method. The authors establish the asymptotic normality of the estimators under mild conditions. The authors also conduct numerical studies to evaluate the finite sample performance of the proposed methodologies. Finally, the authors apply the method to anthropogenic carbon dioxide (CO${}_{2}$) emission data from different provinces of Canada to illustrate the validity of the proposed techniques.
    Partially Linear Single-Index Model in the Presence of Measurement Error
    LIN Hongmei, SHI Jianhong, TONG Tiejun, ZHANG Riquan
    2022, 35(6):  2361-2380.  DOI: 10.1007/s11424-022-1112-x
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    The partially linear single-index model (PLSIM) is a flexible and powerful model for analyzing the relationship between the response and the multivariate covariates. This paper considers the PLSIM with measurement error possibly in all the variables. The authors propose a new efficient estimation procedure based on the local linear smoothing and the simulation-extrapolation method, and further establish the asymptotic normality of the proposed estimators for both the index parameter and nonparametric link function. The authors also carry out extensive Monte Carlo simulation studies to evaluate the finite sample performance of the new method, and apply it to analyze the osteoporosis prevention data.
    Incorporating Variation and Quality of the Underlying Effects in Meta-Analysis
    FU Jinyu, LIN Jinguan
    2022, 35(6):  2381-2397.  DOI: 10.1007/s11424-022-1429-5
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    This paper proposes a model to further explore the effects of the quality information and variation of the underlying effects on the summary effect measure in meta-analysis. A shape parameter is used in this model to quantify the asymmetry of the effect sizes of studies that are included. Estimation of the proposed model parameters is carried out by the Bayesian MCMC method. Performances of the resultant estimates are examined in the simulations and empirical case with data obtained from a total of 22 meta-analyses taken from three different designs. A conclusion would be drawn that it is advisable to take the proposed model, when quality information becomes available, in particular with a situation where the underlying effects approximately follow a normal distribution. If, however, the quality information is absent, the skew-normal distribution for random effect model should be adopted.
    Nonparametric Two-Step Estimation of Drift Function in the Jump-Diffusion Model with Noisy Data
    YE Xuguo, ZHAO Yanyong, LIN Jinguan, LONG Weifang
    2022, 35(6):  2398-2429.  DOI: 10.1007/s11424-022-1041-8
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    This paper considers a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. A two-step approach to estimate the drift function of a jump-diffusion model {in noisy settings} is proposed. The proposed estimator is shown to be consistent and asymptotically normal in the presence of finite activity jumps. Simulated experiments and a real data application are undertaken to assess the finite sample performance of the newly proposed method.
    The Invertibility of Rational Univariate Representations
    XIAO Shuijing, ZENG Guangxing
    2022, 35(6):  2430-2451.  DOI: 10.1007/s11424-022-1070-3
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    In this paper, the so-called invertibility is introduced for rational univariate representations, and a characterization of the invertibility is given. It is shown that the rational univariate representations, obtained by both Rouillier's approach and Wu's method, are invertible. Moreover, the ideal created by a given rational univariate representation is defined. Some results on invertible rational univariate representations and created ideals are established. Based on these results, a new approach is presented for decomposing the radical of a zero-dimensional polynomial ideal into an intersection of maximal ideals.
    Heilbronn's Problem of Eight Points in the Square
    DEHBI Lydia, ZENG Zhenbing
    2022, 35(6):  2452-2480.  DOI: 10.1007/s11424-022-1220-7
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    In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the ${8\choose 3}$ triangles formed by them is maximal. Symbolic computations are employed to reduce the problem into a nonlinear programming problem and find its optimal solution. All computations are done using Maple.