Table of Content

    25 April 2021, Volume 34 Issue 2
    The Time-Dependent Von K′arm′an Shell Equation as a Limit of Three-Dimensional Nonlinear Elasticity
    QIN Yizhao · YAO Peng-Fei
    2021, 34(2):  465-482.  DOI: 10.1007/s11424-020-9146-4
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    The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered, as the thickness h of the shell tends to zero. Given the appropriate scalings of the applied force and of the initial data in terms of h, it’s verified that three-dimesional solutions of the nonlinear elastodynamic equations converge to solutions of the time-dependent von K′arm′an equations or dynamic linear equations for shell of arbitrary geometry.

    Convergence in Distribution for Uncertain Random Sequences with Dependent Random Variables
    GAO Rong · AHMADZADE Hamed
    2021, 34(2):  483-501.  DOI: 10.1007/s11424-020-9192-y
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    Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and uncertain variables, uncertain random variable is introduced as a tool to deal with complex phenomena including randomness and uncertainty simultaneously. For uncertain random variables, a basic and important topic is to discuss the convergence of its sequence. Specifically, this paper focuses on studying the convergence in distribution for a sequence of uncertain random sequences with different chance distributions where random variables are not independent. And the result of this paper is a generalization of the existing literature. Relations among convergence theorems are studied. Furthermore, the theorems are explained by several examples.

    Fuzzy Modeling of Non-Uniformly Sampling Nonlinear Systems Based on Clustering Method and Convergence Analysis
    WANG Hongwei · XIE Lirong
    2021, 34(2):  502-519.  DOI: 10.1007/s11424-020-9119-7
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    The studying motivation of this paper is that there exist many modeling issues of nonuniformly sampling nonlinear systems in industrial systems. Based on multi-model modeling principle, the corresponding model of non-uniformly sampling nonlinear systems is described by the nonlinear weighted combination of some linear models at local working points. Fuzzy modeling based on multimodel scheme is a common method to describe the dynamic process of non-linear systems. In this paper, the fuzzy modeling method of non-uniformly sampling nonlinear systems is studied. The premise structure of the fuzzy model is confirmed by GK fuzzy clustering, and the conclusion parameters of the fuzzy model are estimated by the recursive least squared algorithm. The convergence perfromance of the proposed identification algorithm is given by using lemmas and martingale theorem. Finally, the simulation example is given to demonstrate the effectiveness of the proposed method.

    A Second-Order Sliding Mode Controller of Quad-Rotor UAV Based on PID Sliding Mode Surface with Unbalanced Load
    KANG Bing · MIAO Yan · LIU Fu · DUAN Jilu · WANG Ke · JIANG Shoukun
    2021, 34(2):  520-536.  DOI: 10.1007/s11424-020-9306-6
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    Quad-rotor unmanned aerial vehicle (UAV) is a typical multiple-input-multiple-output underactuated system with couplings and nonlinearity. Usually, the flying environment is very complex, so that it is impossible for the UAV to avoid effects derived from disturbances and uncertainties. In order to improve the reliability of flight control, we established the dynamic model of quad-rotor UAV by Newton-Euler equation in unbalanced load conditions. Considering external disturbances in the attitude, a second-order sliding mode controller was designed with PID sliding mode surface and Extended State Observer (ESO). The simulation experiments have got good control performance, illustrating the effectiveness of our controller. Meanwhile, the controller was implemented in a quadrotor UAV, which carried a pan-tilt camera for aerial photography. The actual flight experiments proved that this paper dealt with the high stabilization flight control problem for the quad-rotor UAV, which laid a good foundation for autonomous flight of the UAV.

    Approximate Controllability for Degenerate Heat Equation with Bilinear Control
    LI Lingfei · GAO Hang
    2021, 34(2):  537-551.  DOI: 10.1007/s11424-020-9082-3
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    This paper investigates the nonnegative approximate controllability for the one-dimensional degenerate heat equation governed by bilinear control. Both non-controllability and approximate controllability are studied for the system. If the control is restricted to act on a fixed domain, it is not controllable. If the control is allowed to mobile, it is approximately controllable.

    Adaptive Backstepping Sliding Mode Control of Uncertain Semi-Strict Nonlinear Systems and Application to Permanent Magnet Synchronous Motor
    WANG Fang · WANG Jian-mei · WANG Kun · ZONG Qun · HUA Changchun
    2021, 34(2):  552-571.  DOI: 10.1007/s11424-020-9132-x
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    A disturbance observer (DOB) based-backstepping sliding mode control scheme is discussed for a class of semi-strict nonlinear system with unknown parameters and mismatched uncertainty. Firstly, adaptive technique and DOB are respectively applied to tackle the unknown parameters and mismatched uncertainty, where the DOB can effectively alleviate the chattering problem of sliding mode control (SMC). Then, exponential sliding mode surface is proposed to improve the convergence rate of the sliding mode state. The ‘explosion of complexity’ problem inherent in conventional backstepping control is overcome by designing the novel first-order filter. The stability of the closed-loop system is analyzed in the framework of Lyapunov stability theory, in which the tracking error converges to an arbitrarily small neighborhood around zero (ASNZ). At last, two examples are given to illustrate the effectiveness of the proposed control strategy.

    Maximum Principle for Non-Zero Sum Stochastic Differential Game with Discrete and Distributed Delays
    ZHANG Qixia
    2021, 34(2):  572-587.  DOI: 10.1007/s11424-020-9068-1
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    This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays. Not only the state variable, but also control variables of players involve discrete and distributed delays. By virtue of the duality method and the generalized anticipated backward stochastic differential equations, the author establishes a necessary maximum principle and a sufficient verification theorem. To explain theoretical results, the author applies them to a dynamic advertising game problem.

    Sampling Dependent Stability Results for Aperiodic Sampled-Data Systems
    SHAO Hanyong · YUAN Guangxia
    2021, 34(2):  588-601.  DOI: 10.1007/s11424-020-9057-4
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    This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent, and not imposed to be definite positive. Based on the system information on the sampling interval wholly rather than partly, a new Lyapunovlike functional is constructed, which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the sampled state. To take advantage of the integral of the system state, integral equations of the sampled-data system are explored when estimating the derivative of the extended functional. By the Lyapunov-like functional theory, a new sampling dependent stability result is obtained for sampled-data systems without uncertainties. Then, the stability result is applied to sampled-data systems with polytopic uncertainties and a robust stability result is derived. At last, numerical examples are given to illustrate that the stability results improve over some existing ones.

    Optimal Output Tracking Control and Stabilization of Networked Control Systems with Packet Losses
    LIU Yue · HAN Chunyan
    2021, 34(2):  602-617.  DOI: 10.1007/s11424-020-9093-0
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    This paper studies the optimal output tracking control and stabilization for networked control systems with packet losses via output feedback control. Both finite-horizon and infinite-horizon cases are considered. For the finite-horizon case, the authors introduce an augmented system according to the state variable and the reference trajectory for the first time. Based on a set of difference Riccati equations, an optimal output feedback tracking controller is proposed by applying the stochastic maximum principle. And an optimal estimator is presented. For the infinite-horizon case, a necessary and sufficient condition for the stabilization of the system is provided. And an optimal output feedback stabilizing tracking controller is obtained by establishing a set of algebraic Riccati equations. Finally, numerical examples are given to verify the proposed results.

    Projective Group Consensus of Multi-Agent Systems with Arbitrary Parameter
    CHEN Liangkang · GUO Liuxiao · YANG Yongqing
    2021, 34(2):  618-631.  DOI: 10.1007/s11424-020-9137-5
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    In this paper, the projective group consensus issue for second order multi-agent systems (MASs) in directed graphs with a dynamic leader is investigated. The proposed projective group consensus with arbitrary parameter includes traditional consensus, reverse group consensus and cluster consensus as its special cases. Novel distributed control protocols are designed to obtain projective group consensus without analyzing signed directed graph as in most current literatures on bipartite consensus problem. On the basis of Lyapunov stability property, algebraic graph and some necessary matrix theory, sufficient conditions for delay and delay-free cases are derived. Finally, simulations of nonlinear chaotic MASs are adopted to testify the theoretical results.

    New Lyapunov-Krasovskii Functional for Stability Analysis of Linear Systems with Time-Varying Delay
    LIN Huichao · ZENG Hongbing · WANG Wei
    2021, 34(2):  632-641.  DOI: 10.1007/s11424-020-9179-8
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    This paper focuses on the problem of delay-dependent stability of linear systems with time-varying delay. A new delay-product-type augmented Lyapunov-Krasovskii functional (LKF) is constructed. Based on the LKF and by employing a generalized free-matrix-based integral inequality, less conservative delay-dependent stability criteria are obtained. Finally, two well-known numerical examples are used to confirm the effectiveness and the superiority of the presented stability criteria.

    The Irregular Linear Quadratic Control Problem for Deterministic Case with Time Delay
    LI Tongxing · LI Lin · LEI Jing · JIN Nana · JU Peijun
    2021, 34(2):  642-656.  DOI: 10.1007/s11424-020-9136-6
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    This study deals with the irregular linear quadratic control problem governed by continuous time system with time delay. Linear quadratic (LQ) control for irregular Riccati equation with time delay remains challenging since the controller could not be solved from the equilibrium condition directly. The merit of this paper is that based on a new approach of ‘two-layer optimization’, the controller entries of irregular case with time delay are deduced from two equilibrium conditions in two different layers, which is fundamentally different from the classical regular LQ control. The authors prove that the irregular LQ with time delay is essentially different from the regular case. Specifically, the predictive controller bases on the feedback gain matrix and the state is given in the last part. The presented conclusions are completely new to our best knowledge. Examples is presented to show the effectiveness of the proposed approach.

    Forecasting US Stock Market Returns: A Japanese Candlestick Approach
    MENG Xiaoge · MA Jun · QIAO Han · XIE Haibin
    2021, 34(2):  657-672.  DOI: 10.1007/s11424-020-9126-8
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    A Japanese candlestick chart consists of not only the closing price but also the high, low and opening price information. Using the Japanese candlestick, this paper investigates the forecasting power of the shadow in Japanese candlestick chart. Empirical studies performed with the US stock market show that 1) there is a significant Halloween effect in the shadow; 2) shadow is valuable for predicting the stock market returns in both statistical and economic sense; 3) the predictability reported by the shadow can not be explained by either the CAPM model or the Fama-French three-factor model. This paper confirms that predictability of the stock market can be improved if more price information is used.

    A Dynamic Multi-Player Bargaining Game with Veto Players
    LIU Jia · WANG Xianjia
    2021, 34(2):  673-691.  DOI: 10.1007/s11424-020-9191-z
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    This paper studies the effect of veto right on players’ income in multi-player dynamic bargaining game. Based on a basic multi-person dynamic bargaining model generalized by the Rubinstein’s two-person alternating-offer bargaining model, the authors construct a dynamic multi-player bargaining game with veto players by adding a constraint to its negotiation process, which is obtained by studying the influence of exercising the veto right exercised by veto players. The authors emphatically describe the strategic game form of this dynamic bargaining game and study its equilibrium, then we analyze the relationship between the minimum acceptable payoff of the veto players and the equilibrium income. The research shows that veto right may increase the benefits of veto players and decrease the benefits of non-veto players. Veto players will not affect the players’ benefits and the form of equilibrium when the minimum acceptable payoff of every veto player is relatively low. When the minimum acceptable payoff of the veto player is high enough, he can only get the minimum acceptable payoff, and his benefit increases as his minimum acceptable payoff increases. In this case, the veto player has intention to obtain more resources by presenting a higher minimum acceptable payoff.

    A Kind of Equivalence of Three Nonlinear Scalarization Functions in Vector Optimization
    LI Fei · YANG Xinmin
    2021, 34(2):  692-705.  DOI: 10.1007/s11424-020-9086-z
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    In this paper, by the notions of base functionals and augmented dual cones, the authors indicate firstly that the norms, Gerstewitz functionals and oriented distance functions have common characteristics with base functionals. After that, the equivalence of these three sublinear functions on the ordering cone is established by using the structures of augmented dual cones under the assumption that it has a bounded base. However, the authors show that two superlinear functions do not have similar relations with the norms ahead. More generally, the equivalence of three sublinear functions outside the negative cone has also been obtained in the end.

    Input-Output Production Structure and Non-Linear Production Possibility Frontier
    JIANG Weimin · FAN Jin · TIAN Kailan
    2021, 34(2):  706-723.  DOI: 10.1007/s11424-020-9079-y
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    Input-output (Leontief) production function is widely used in economic analysis. And diminishing marginal rate of return is a very well accepted economic fact. Leontief production function normally results in a linear production possibility frontier (PPF) due to its linear feature, whereas diminishing marginal rate of return implies a non-linear PPF. In this paper, the authors aim to fix this problem by considering multiple primary inputs in a simplified two-sector economy. The authors find that it is possible to curve a non-linear PPF by using Leontief production function when the authors add heterogeneous primary inputs. The authors also discuss the PPF using non-linear production function. Furthermore, the authors propose that three commonly used economic presumptions cannot hold in the same framework. These presumptions are “single primary input”, “fixed-proportion inputs” and “law of diminishing marginal returns”.

    Estimating Cumulative Treatment Effect Under an Additive Hazards Model
    L¨U Xiaoliang · ZHANG Baoxue · SUN Liuquan
    2021, 34(2):  724-734.  DOI: 10.1007/s11424-020-0067-z
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    In clinical and epidemiologic studies of time to event, the treatment effect is often of direct interest, and the treatment effect is not constant over time. In this paper, the authors propose an estimator for the cumulative hazard difference under a stratified additive hazards model. The asymptotic properties of the resulting estimator are established, and the finite-sample properties are examined through simulation studies. An application to a liver cirrhosis data set from the Copenhagen Study Group for Liver Diseases is provided.

    Integrated Square Error of Hazard Rate Estimation for Survival Data with Missing Censoring Indicators
    ZOU Yuye · FAN Guoliang · ZHANG Riquan
    2021, 34(2):  735-758.  DOI: 10.1007/s11424-021-9307-0
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    The problem of hazard rate estimation under right-censored assumption has been investigated extensively. Integrated square error (ISE) of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation. But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random (MAR) so far. This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR. At the same time, an asymptotic representation of the mean integrated square error (MISE) is also presented. The finite sample behavior of the estimator is investigated via one simple simulation.

    The Asymptotic Properties of Scad Penalized Generalized Linear Models with Adaptive Designs
    GAO Qibing · ZHU Chunhua · DU Xiuli · ZHOU Xingcai · YIN Dingxin
    2021, 34(2):  759-773.  DOI: 10.1007/s11424-020-9134-8
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    This paper discusses the asymptotic properties of the SCAD (smoothing clipped absolute deviation) penalized quasi-likelihood estimator for generalized linear models with adaptive designs, which extend the related results for independent observations to dependent observations. Under certain conditions, the authors proved that the SCAD penalized method correctly selects covariates with nonzero coefficients with probability converging to one, and the penalized quasi-likelihood estimators of non-zero coefficients have the same asymptotic distribution they would have if the zero coefficients were known in advance. That is, the SCAD estimator has consistency and oracle properties. At last, the results are illustrated by some simulations.

    Bootstrap Inference on the Variance Component Functions in the Two-Way Random Effects Model with Interaction
    YE Rendao · GE Wenting · LUO Kun
    2021, 34(2):  774-791.  DOI: 10.1007/s11424-017-6232-3
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    In this paper, using the Bootstrap approach and generalized approach, the authors consider the one-sided hypothesis testing problems for variance component functions in the two-way random effects model. Firstly, the test statistics and confidence intervals for the sum of variance components are constructed. Next, the one-sided hypothesis testing problems for the ratio of variance components are also discussed. The Monte Carlo simulation results indicate that the Bootstrap approach is better than the generalized approach in most cases. Finally, the above approaches are applied to the real data examples of mice blood pH and molded plastic part’s dimensions.

    Analyzing Boolean Functions via Solving Parametric Polynomial Systems
    HUANG Zhenyu · SUN Yao · LIN Dongdai
    2021, 34(2):  792-808.  DOI: 10.1007/s11424-020-9216-7
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    In this paper, a new method to analyze Boolean functions is proposed. By this method, one can analyze the balancedness, the nonlinearity, and the input-output correlation of vectorial Boolean functions. The basic idea of this method is to compute the refined covers of some parametric Boolean polynomial systems which are equivalent to these problems. By a refined cover, the parameter space is divided into several disjoint components, and on each component, the parametric Boolean polynomial system has a fixed number of solutions. An efficient algorithm based on the characteristic set method to compute refined covers of parametric Boolean polynomial systems is presented. The experimental results about some instances generated from cryptanalysis show that this new method is efficient and can solve some instances which can not be solved in reasonable time by other methods.

    On the Complexity of Computing the Topology of Real Algebraic Space Curves
    JIN Kai · CHENG Jinsan
    2021, 34(2):  809-826.  DOI: 10.1007/s11424-020-9164-2
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    This paper presents an algorithm to compute the topology of an algebraic space curve. This is a modified version of the previous algorithm. Furthermore, the authors also analyse the bit complexity of the algorithm, which is  O(N20), where N = max{d, τ}, d and τ are the degree bound and the bit size bound of the coefficients of the defining polynomials of the algebraic space curve. To our knowledge, this is the best bound among the existing work. It gains the existing results at least N2. Meanwhile, the paper contains some contents of the conference papers (CASC 2014 and SNC 2014).