Table of Content

    25 February 2022, Volume 35 Issue 1
    Hierarchical Mean-Field Type Control of Price Dynamics for Electricity in Smart Grid
    FRIHI Zahrate El Oula, CHOUTRI Salah Eddine, BARREIRO-GOMEZ Julian, TEMBINE Hamidou
    2022, 35(1):  1-17.  DOI: 10.1007/s11424-021-0176-3
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    This paper solves a mean-field type hierarchical optimal control problem in electricity market. The authors consider $n-1$ prosumers and one producer. The $i$th prosumer, for $1 < i < n$, is a leader of the $(i-1)$th prosumer and is a follower of the $(i+1)$th prosumer. The first player (agent) is the follower at the bottom whereas the $n$th is the leader at the top. The problem is described by a linear jump-diffusion system of conditional mean-field type, where the conditioning is with respect to common noise, and a quadratic cost functional involving, the square of the conditional expectation of the controls of the agents. The authors provide a semi-explicit solution of the corresponding mean-field-type hierarchical control problem with common noise. Finally, the authors illustrate the obtained result via a numerical example with two different scenarios.
    Stability of Traveling Waves Solutions for Nonlinear Cellular Neural Networks with Distributed Delays
    GUO Yingxin, GE Shuzhi Sam, ARBI Adnène
    2022, 35(1):  18-31.  DOI: 10.1007/s11424-021-0180-7
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    This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks. As a continuity of the past work (Wu and Niu, 2016; Yu,et al., 2011) on the existence and uniqueness of the traveling wave solutions, it is very reasonable and interesting to consider the exponential stability of the traveling wave solutions. By the weighted energy method, comparison principle and the first integral mean value theorem, this paper proves that, for all monotone traveling waves with the wave speed $c < c_1^* < 0$ or $c > c_2^* > 0$, the solutions converge time-exponentially to the corresponding traveling waves, when the initial perturbations decay at some fields.
    On Con-Numbers and Con-Matrices with Applications to Control Systems
    WU Aiguo
    2022, 35(1):  32-57.  DOI: 10.1007/s11424-021-0081-9
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    In this paper, the concepts of con-numbers and con-matrices are proposed by the introduction of conjugate operators into the field of complex numbers, and some properties of these two concepts are derived. In addition, two potential applications of these two concepts are addressed in details. Specifically, a class of quantum systems is expressed in terms of the proposed con-numbers, and the R-linear mapping is represented by con-matrices. These two applications imply the importance of the con-numbers and con-matrices. In addition, some methods are discussed on the construction of the conjugate-operator-induced numbers. Also, some further research directions are provided on these extended numbers and matrices with their applications to systems control.
    Signed PageRank on Online Rating Systems
    GU Ke, FAN Ying, DI Zengru
    2022, 35(1):  58-80.  DOI: 10.1007/s11424-021-0124-2
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    The ratings in many user-object online rating systems can reflect whether users like or dislike the objects, and in some online rating systems, users can directly choose whether to like an object. So these systems can be represented by signed bipartite networks, but the original unsigned node evaluation algorithm cannot be directly used on the signed networks. This paper proposes the Signed PageRank algorithm for signed bipartite networks to evaluate the object and user nodes at the same time. Based on the global information, the nodes can be sorted by the Signed PageRank values in descending order, and the result is SR Ranking. The authors analyze the characteristics of top and bottom nodes of the real networks and find out that for objects, the SR Ranking can provide a more reasonable ranking which combines the degree and rating of node, and the algorithm also can help us to identify users with specific rating patterns. By discussing the location of negative edges and the sensitivity of object SR Ranking to negative edges, the authors also explore that the negative edges play an important role in the algorithm and explain that why the bad reviews are more important in real networks.
    A Composite Adaptive Fault-Tolerant Attitude Control for a Quadrotor UAV with Multiple Uncertainties
    WANG Ban, ZHANG Youmin, ZHANG Wei
    2022, 35(1):  81-104.  DOI: 10.1007/s11424-022-1030-y
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    In this paper, a composite adaptive fault-tolerant control strategy is proposed for a quadrotor unmanned aerial vehicle (UAV) to simultaneously compensate actuator faults, model uncertainties and external disturbances. By assuming knowledge of the bounds on external disturbances, a baseline sliding mode control is first designed to achieve the desired system tracking performance and retain insensitive to disturbances. Then, regarding actuator faults and model uncertainties of the quadrotor UAV, neural adaptive control schemes are constructed and incorporated into the baseline sliding mode control to deal with them. Moreover, in terms of unknown external disturbances, a disturbance observer is designed and synthesized with the control law to further improve the robustness of the proposed control strategy. Finally, a series of comparative simulation tests are conducted to validate the effectiveness of the proposed control strategy where a quadrotor UAV is subject to inertial moment variations and different level of actuator faults. The capabilities and advantages of the proposed control strategy are confirmed and verified by simulation results.
    Constrained Consensus of Continuous-Time Heterogeneous Multi-Agent Networks with Nonconvex Constraints and Delays
    MO Lipo, YU Yongguang, REN Guojian, YUAN Xiaolin
    2022, 35(1):  105-122.  DOI: 10.1007/s11424-021-0092-6
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    This paper studies the continuous-time constrained consensus of heterogeneous multi-agent networks with nonconvex input and velocity constraints, where each agent's dynamic is modeled by a first-order or second-order integrator, the communication delays are assumed to be time-varying, nonuniform, bounded and the communication graph is changing over time. An improved distributed control algorithm with time-varying gains is proposed and the heterogeneous consensus is changed into the homogeneous consensus by a coordination transformation. Then, it is proved that the constrained consensus can be reached by analyzing six connection cases between agents if the joint graph has a directed spanning tree over each bounded interval. Finally, simulations are done to show the correctness of the theorem.
    Tensor Decomposition and High-Performance Computing for Solving High-Dimensional Stochastic Control System Numerically
    CHEN Yidong, LU Zhonghua
    2022, 35(1):  123-136.  DOI: 10.1007/s11424-021-0126-0
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    The paper presents a numerical method for solving a class of high-dimensional stochastic control systems based on tensor decomposition and parallel computing. The HJB solution provides a globally optimal controller to the associated dynamical system. Variable substitution is used to simplify the nonlinear HJB equation. The curse of dimensionality is avoided by representing the HJB equation using separated representation. Alternating least squares (ALS) is used to reduced the separation rank. The experiment is conducted and the numerical solution is obtained. A high-performance algorithm is designed to reduce the separation rank in the parallel environment, solving the high-dimensional HJB equation with high efficiency.
    Multi-Cluster Flocking Behavior Analysis for a Delayed Cucker-Smale Model with Short-Range Communication Weight
    QIAO Zhengyang, LIU Yicheng, WANG Xiao
    2022, 35(1):  137-158.  DOI: 10.1007/s11424-021-0026-3
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    This paper analyzes the multi-cluster flocking behavior of a Cucker-Smale model involving delays and a short-range communication weight. In each sub-flocking group, the velocity between agents is alignment and the position locates at a limited domain; but in different sub-flocking groups, the position between agents is unbounded. By constructing dissipative differential inequalities of subensembles together with Lyapunov functional methods, the authors provide the sufficient condition for the multi-cluster flocking emerging. The sufficient condition includes the estimation of the range of coupling strength and the upper bound of time delay. As a result, the authors show that the coupling strength among agents and initial threshold value determine the multi-cluster flocking behavior of the delayed Cucker-Smale model.
    Stability and Hopf Bifurcation Analysis of an (n + m)-Neuron Double-Ring Neural Network Model with Multiple Time Delays
    XING Ruitao, XIAO Min, ZHANG Yuezhong, QIU Jianlong
    2022, 35(1):  159-178.  DOI: 10.1007/s11424-021-0108-2
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    Up till the present moment, researchers have always featured the single-ring neural network. These investigations, however, disregard the link between rings in neural networks. This paper highlights a high-dimensional double-ring neural network model with multiple time delays. The neural network has two rings of a shared node, where one ring has n neurons and the other has m+1 neurons. By utilizing the sum of time delays as the bifurcation parameter, the method of Coates' flow graph is applied to obtain the relevant characteristic equation. The stability of the neural network model with bicyclic structure is discussed by dissecting the characteristic equation, and the critical value of Hopf bifurcation is derived. The effect of the sum of time delays and the number of neurons on the stability of the model is extrapolated. The validity of the theory can be verified by numerical simulations.
    Research on Image Signal Identification Based on Adaptive Array Stochastic Resonance
    ZHAO Jingjing, MA Yumei, PAN Zhenkuan, ZHANG Huage
    2022, 35(1):  179-193.  DOI: 10.1007/s11424-021-0133-1
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    Aiming at the problems of low accuracy of image signal identification and poor anti-noise signal interference ability under strong noise environment, a signal identification method of correlated noisy image based on adaptive array stochastic resonance (SR) is proposed in this paper. Firstly, the two-dimensional grayscale image is transformed to a one-dimensional binary pulse amplitude modulation (BPAM) signal with periodicity by the row or column scanning method, encoding and modulation. Then, the one-dimensional low signal-to-noise ratio BPAM signal can be applied to the saturating nonlinearity array SR module for image signal identification processing and part of the noise energy is converted into signal energy. Finally, the one-dimensional image signal processed by the nonlinearities is demodulated, decoded and reverse scanned to get the restored grayscale image. The simulation results show that the image signal identification method proposed in this paper is highly efficient and accurate for the identification of noisy image signals of different sizes, and the bit error rate (BER) is also significantly reduced.
    Controllability and Observability of Stochastic Singular Systems in Banach Spaces
    GE Zhaoqiang
    2022, 35(1):  194-204.  DOI: 10.1007/s11424-021-0164-7
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    Exact (approximate) controllability and exact (approximate) observability of stochastic singular systems in Banach spaces are discussed. Firstly, the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces. Secondly, the necessary and sufficient conditions for the exact (approximate) controllability and exact (approximate) observability of the systems considered are derived in terms of GE-semigroup, and the dual principle is given. Thirdly, an illustrative example is given.
    A Mean-Field Optimal Control for Fully Coupled Forward-Backward Stochastic Control Systems with Lévy Processes
    HUANG Zhen, WANG Ying, WANG Xiangrong
    2022, 35(1):  205-220.  DOI: 10.1007/s11424-021-0077-5
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    This paper is concerned with a class of mean-field type stochastic optimal control systems, which are governed by fully coupled mean-field forward-backward stochastic differential equations with Teugels martingales associated to Lévy processes. In these systems, the coefficients contain not only the state processes but also their marginal distribution, and the cost function is of mean-field type as well. The necessary and sufficient conditions for such optimal problems are obtained. Furthermore, the applications to the linear quadratic stochastic optimization control problem are investigated.
    Heterogeneous Round-Trip Trading and the Emergence of Volatility Clustering in Speculation Game
    2022, 35(1):  221-244.  DOI: 10.1007/s11424-021-0147-8
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    This study is a detailed analysis of Speculation Game, a simple agent-based model of financial markets, in which the round-trip trading and the dynamic wealth evolution with variable trading volumes are implemented. Instead of herding behavior, the authors find that the heterogeneous holding periods in round-trip trades can contribute to the emergence of volatility clustering. In particular, the spontaneous redistribution of market wealth through repetitions of round-trip trades with non-uniform horizons can widen the wealth disparity and establish the Pareto distribution of the capital size. As a result, the intermittent placements of relatively big orders from endogenously emerged rich traders can bring on large fluctuations in price return. Empirical data are used to support the scenario derived from the model.
    Simple Contracts to Coordinate the Capacity Procurement Model with Asymmetric Demand Information
    LI Linqiu, LIU Ke
    2022, 35(1):  245-263.  DOI: 10.1007/s11424-021-0031-6
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    This paper studies the important problem of how to coordinate the capacity procurement model with asymmetric demand information. Under the model, the supplier has to secure necessary capacity before receiving a firm order from the manufacturer who possesses private demand information for her product. Optimal supply chain performance requires the manufacturer to share her forecast truthfully and the supplier to build enough capacity. In the literature, some elaborate contracts are designed to solve the problem. However, the authors prove that two simple conventional contracts (linear capacity reservation contract and payback agreement) can coordinate the supply chain and guarantee credible information sharing. Besides, the authors propose a new mechanism in which punishment is imposed in the payment function to bind the parties. To avoid punishment, the firms will choose the best decision for the entire supply chain. The contracts in this paper are all simple and easy to implement. The authors believe this work provides some insights to design coordination contracts in theory or in practice.
    Model Averaging Estimation for Varying-Coefficient Single-Index Models
    LIU Yue, ZOU Jiahui, ZHAO Shangwei, YANG Qinglong
    2022, 35(1):  264-282.  DOI: 10.1007/s11424-021-0158-5
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    The varying-coefficient single-index model (VCSIM) is widely used in economics, statistics and biology. A model averaging method for VCSIM based on a Mallows-type criterion is proposed to improve prodictive capacity, which allows the number of candidate models to diverge with sample size. Under model misspecification, the asymptotic optimality is derived in the sense of achieving the lowest possible squared errors. The authors compare the proposed model averaging method with several other classical model selection methods by simulations and the corresponding results show that the model averaging estimation has a outstanding performance. The authors also apply the method to a real dataset.
    American Barrier Option Pricing Formulas for Currency Model in Uncertain Environment
    GAO Rong, LIU Kaixiang, LI Zhiguo, LANG Liying
    2022, 35(1):  283-312.  DOI: 10.1007/s11424-021-0039-y
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    Option pricing problem is one of the central issue in the theory of modern finance. Uncertain currency model has been put forward under the foundation of uncertainty theory as a tool to portray the foreign exchange rate in uncertain finance market. This paper uses uncertain differential equation involved by Liu process to dispose of the foreign exchange rate. Then an American barrier option of currency model in uncertain environment is investigated. Most important of all, the authors deduce the formulas to price four types of American barrier options for this currency model in uncertain environment by rigorous derivation.
    Estimation in Partially Observed Functional Linear Quantile Regression
    XIAO Juxia, XIE Tianfa, ZHANG Zhongzhan
    2022, 35(1):  313-341.  DOI: 10.1007/s11424-020-0019-7
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    Currently, working with partially observed functional data has attracted a greatly increasing attention, since there are many applications in which each functional curve may be observed only on a subset of a common domain, and the incompleteness makes most existing methods for functional data analysis ineffective. In this paper, motivated by the appealing characteristics of conditional quantile regression, the authors consider the functional linear quantile regression, assuming the explanatory functions are observed partially on dense but discrete point grids of some random subintervals of the domain. A functional principal component analysis (FPCA) based estimator is proposed for the slope function, and the convergence rate of the estimator is investigated. In addition, the finite sample performance of the proposed estimator is evaluated through simulation studies and a real data application.
    Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models
    PENG Yunjie, ZHENG Xiaoqian, YU Wei, HE Kaixin, WANG Xuejun
    2022, 35(1):  342-360.  DOI: 10.1007/s11424-020-0098-5
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    This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent (END, for short) random variables. Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided. In particular, the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product. The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables. As an application, the authors investigate the errors-in-variables (EV, for short) regression models and establish the strong consistency for the least square estimators. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.
    Fisher Information in Moving Extreme Ranked Set Sampling with Application to Parameter Estimation
    YAO Dongsen, CHEN Wangxue, YANG Rui, LONG Chunxian
    2022, 35(1):  361-372.  DOI: 10.1007/s11424-021-0177-2
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    In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling called moving extremes ranked set sampling (MERSS) is considered for the Fisher information matrix for the location-scale family. The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS. In order to give more insight into the performance of MERSS with respect to simple random sampling, the Fisher information matrix for usual locationscale distributions are respectively computed under the two sampling. The numerical results show that MERSS provides more information than simple random sampling in parametric inference.
    Quantum Algorithm for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems
    CHEN Yu-Ao, GAO Xiao-Shan
    2022, 35(1):  373-412.  DOI: 10.1007/s11424-020-0028-6
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    This paper presents a quantum algorithm to decide whether a Boolean equation system $\mathcal{F}$ has a solution and to compute one if $\mathcal{F}$ does have solutions with any given success probability. The runtime complexity of the algorithm is polynomial in the size of $\mathcal{F}$ and the condition number of certain Macaulay matrix associated with $\mathcal{F}$. As a consequence, the authors give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are polynomial in the size of $\mathcal{F}$. The authors apply the proposed quantum algorithm to the cryptanalysis of several important cryptosystems:The stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the corresponding condition numbers are large. This leads to a new criterion for designing such cryptosystems which are safe against the attack of quantum computers:The corresponding condition number.
    Solving Multivariate Polynomial Matrix Diophantine Equations with Gröbner Basis Method
    XIAO Fanghui, LU Dong, WANG Dingkang
    2022, 35(1):  413-426.  DOI: 10.1007/s11424-021-0072-x
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    Different from previous viewpoints, multivariate polynomial matrix Diophantine equations are studied from the perspective of modules in this paper, that is, regarding the columns of matrices as elements in modules. A necessary and sufficient condition of the existence for the solution of equations is derived. Using powerful features and theoretical foundation of Gröbner bases for modules, the problem for determining and computing the solution of matrix Diophantine equations can be solved. Meanwhile, the authors make use of the extension on modules for the GVW algorithm that is a signature-based Gröbner basis algorithm as a powerful tool for the computation of Gröbner basis for module and the representation coefficients problem directly related to the particular solution of equations. As a consequence, a complete algorithm for solving multivariate polynomial matrix Diophantine equations by the Gröbner basis method is presented and has been implemented on the computer algebra system Maple.
    An Improvement for GVW
    ZHENG Licui, LI Dongmei, LIU Jinwang
    2022, 35(1):  427-436.  DOI: 10.1007/s11424-021-9051-5
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    Gao, et al. (2015) gave a simple algorithm to compute Gröbner bases named GVW. It can be used to compute Gröbner bases for both ideals and syzygies at the same time, and the latter plays an important role in free resolutions in homological algebra. In GVW algorithms the authors need to compute all the J-pairs firstly and then use GVW criterion (which refers the criterions used in GVW) to determine which one is useless or which one the authors should do top-reduction. In this paper, based on the study of relations between J-pairs, the authors propose the concept of factor. This concept allows the authors to filter the useless J-pairs in a rather convenient way. Moreover, by using this concept, the authors may easily determine which two pairs' J-pair need not to be computed. Besides, the Gröbner basis which the authors obtained is relatively simpler than the one in GVW.