中国科学院数学与系统科学研究院期刊网

2023年, 第36卷, 第2期 刊出日期:2023-04-25
  

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  • CHEN Tian, LIU Ruyi, WU Zhen
    系统科学与复杂性(英文版). 2023, 36(2): 457-479. https://doi.org/10.1007/s11424-023-1272-3
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    This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon. Unlike previous works, the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion. The Markov chain is assumed to be independent of Brownian motion, thus the market is incomplete. The authors formulate this problem as a constrained stochastic linear-quadratic optimal control problem. The authors derive closed-form expressions for both the optimal portfolios and the efficient frontier. All the results are different from those in the problem with fixed time horizon.
  • XU Gehui, CHEN Guanpu, QI Hongsheng
    系统科学与复杂性(英文版). 2023, 36(2): 480-499. https://doi.org/10.1007/s11424-023-1436-1
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    This paper designs a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, the authors aim to find a generalized Nash equilibrium in the worst case. However, it is challenging to obtain the exact equilibria directly because the parameters are from general convex sets, which may not have analytic expressions or are endowed with high-dimensional nonlinearities. To solve this problem, the authors first approximate parameter sets with inscribed polyhedrons, and transform the approximate problem in the worst case into an extended certain game with resource allocation constraints by robust optimization. Then the authors propose a distributed algorithm for this certain game and prove that an equilibrium obtained from the algorithm induces an ε-generalized Nash equilibrium of the original game, followed by convergence analysis. Moreover, resorting to the metric spaces and the analysis on nonlinear perturbed systems, the authors estimate the approximation accuracy related to ε and point out the factors influencing the accuracy of ε.
  • KANG Yu, YANG Yuxiao, CHEN Cai, LÜ Wenjun, ZHAO Yunbo
    系统科学与复杂性(英文版). 2023, 36(2): 500-523. https://doi.org/10.1007/s11424-023-1011-9
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    A robust nonsingular fixed time terminal sliding mode control scheme with a time delay disturbance observer is proposed for atmospheric pollution detection lidar scanning mechanism (APDL-SM) system. Distinguished from the conventional terminal sliding mode control methods, the authors design a novel fixed-time terminal sliding surface, the convergence time of sliding mode phase of which has a constant upper bound that is designable by adjusting only one parameter. Moreover, in order to overcome the problem of unknown upper bound of lumped uncertainty including model uncertainty, friction effect and external disturbances from the port environment, the authors propose a time delay disturbance observer to provide an estimation for the system lumped uncertainty. By using the Lyapunov synthesis, the explicit analysis of the convergence time upper bound are performed. Finally, simulation studies are conducted on the APDL-SM system to show the fast convergence rate and strong robustness of the proposed control scheme.
  • YU Jinpeng, FU Cheng, LIU Jiapeng, MA Yumei
    系统科学与复杂性(英文版). 2023, 36(2): 524-539. https://doi.org/10.1007/s11424-023-1330-x
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    This paper investigates a finite-time tracking problem for the uncertainty nonlinear systems in nonstrict-feedback form, in which the output signal is restricted in a region. Based on the barrier Lyapunov function and dynamic surface control scheme, a novel adaptive neural controller is proposed by using the finite-time Lyapunov technology. Unlike the aforementioned literature on finite time tracking control, the violation of system output constraint is avoided by combining the barrier Lyapunov function method with finite-time theory. The structural characteristics of neural network is introduced to expand the adaptive neural finite-time backstepping method to the uncertainty nonlinear systems in the non-strict form. Correspondingly, the dynamic surface control is introduced to cope with the problem of “explosion of complexity” inherent in conventional backstepping scheme. It is shown that the designed controller can achieve finite-time tracking control and all the variables in the closed-loop system are bounded with output constraint guaranteed form stability analysis and simulation results.
  • FAN Xinyu, CHEN Shujin, WANG Xiaoli
    系统科学与复杂性(英文版). 2023, 36(2): 540-554. https://doi.org/10.1007/s11424-023-1250-9
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    This paper investigates the distributed H consensus problem for a first-order multi-agent system where both cooperative and antagonistic interactions coexist. In the presence of external disturbances, a distributed control algorithm using local information is addressed and a sufficient condition to get the H control gain is obtained, which make the states of the agents in the same group converge to a common point while the inputs of each agent are constrained in the nonconvex sets. Finally, a numerical simulation is exhibited to illustrate the theory.
  • WEI Yiheng, ZHAO Xuan, WEI Yingdong, CHEN Yangquan
    系统科学与复杂性(英文版). 2023, 36(2): 555-576. https://doi.org/10.1007/s11424-023-1150-z
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    This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems. In particular, both Caputo definition and Riemann-Liouville definition are under consideration. With the convex assumption, several elementary fractional difference inequalities on Lyapunov functions are developed. According to the essential features of nabla fractional calculus, the sufficient conditions are given first to guarantee the asymptotic stability for the incommensurate system by using the direct Lyapunov method. To substantiate the efficacy and effectiveness of the theoretical results, four examples are elaborated.
  • ZHU Kui, TANG Yutao
    系统科学与复杂性(英文版). 2023, 36(2): 577-590. https://doi.org/10.1007/s11424-023-1321-y
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    This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, the authors focus on the case when the exact subgradients of the local objective functions can not be accessed by the agents. To solve this problem, the authors propose a projected primal-dual dynamics using only the objective function’s approximate subgradients. The authors first prove that the formulated optimization problem can generally be solved with an error depending upon the accuracy of the available subgradients. Then, the authors show the exact solvability of this distributed optimization problem when the accumulated approximation error of inexact subgradients is not too large. After that, the authors also give a novel componentwise normalized variant to improve the transient behavior of the convergent sequence. The effectiveness of the proposed algorithms is verified by a numerical example.
  • YANG Xue, LIU Shujun
    系统科学与复杂性(英文版). 2023, 36(2): 591-612. https://doi.org/10.1007/s11424-023-1352-4
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    The optimal control problem with a long run average cost is investigated for unknown linear discrete-time systems with additive noise. The authors propose a value iteration-based stochastic adaptive dynamic programming (VI-based SADP) algorithm, based on which the optimal controller is obtained. Different from the existing relevant work, the algorithm does not need to estimate the expectation (conditional expectation) and variance (conditional variance) of states or other relevant variables, and the convergence of the algorithm can be proved rigorously. A simulation example is given to verify the effectiveness of the proposed approach.
  • YU Wenqiang, CHENG Songsong, HE Shuping
    系统科学与复杂性(英文版). 2023, 36(2): 613-631. https://doi.org/10.1007/s11424-023-1350-6
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    This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations. Firstly, the authors proposed “Consensus + Projection” flow with fractional order dynamics, which has more design freedom and the potential to obtain a better convergent performance than that of conventional first order algorithms. Moreover, the authors prove that the proposed algorithm is convergent under certain iteration order and step-size. Furthermore, the authors develop iteration order switching scheme with initial condition design to improve the convergence performance of the proposed algorithm. Finally, the authors illustrate the effectiveness of the proposed method with several numerical examples.
  • SUN Guanzhen, LU Chun
    系统科学与复杂性(英文版). 2023, 36(2): 632-655. https://doi.org/10.1007/s11424-023-1042-2
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    In this paper, the authors develop and study an HIV infection system with two distinct cell subsets and nonlinear stochastic perturbation. Firstly, the authors obtain that the solution of the system is positive and global. Secondly, for the corresponding linear case, the authors derive a critical condition $R_{0}^{S}$ similar to deterministic system. When $R_{0}^{S}>1$, the authors establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution to the stochastic system, respectively. Finally, the authors give sufficient criterions for extinction of the diseases. The proposed work provides a new method in overcoming difficulty conduced by nonlinear stochastic perturbation.
  • BAI Jinyan, CHAI Shugen
    系统科学与复杂性(英文版). 2023, 36(2): 656-671. https://doi.org/10.1007/s11424-023-1094-3
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    In this paper, the authors mainly consider the exact controllability for degenerate wave equation, which degenerates at the interior point, and boundary controls acting at only one of the boundary points. The main results are that, it is possible to control both the position and the velocity at every point of the body and at a certain time T for the wave equation with interior weakly degeneracy. Moreover, it is shown that the exact controllability fails for the wave equation with interior strongly degeneracy. In order to steer the system to a certain state, one needs controls to act on both boundary points for the wave equation with interior strongly degeneracy. The difficulties are addressed by means of spectral analysis.
  • MA Heping, LI Ruijing
    系统科学与复杂性(英文版). 2023, 36(2): 672-685. https://doi.org/10.1007/s11424-023-1089-0
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    The paper considers partially observed optimal control problems for risk-sensitive stochastic systems, where the control domain is non-convex and the diffusion term contains the control v. Utilizing Girsanov’s theorem, spike variational technique as well as duality method, the authors obtain four adjoint equations and establish a maximum principle under partial information. As an application, an example is presented to demonstrate the result.
  • CHEN Yinnan, YE Lingjuan, LI Rui, ZHAO Xinchao
    系统科学与复杂性(英文版). 2023, 36(2): 686-715. https://doi.org/10.1007/s11424-023-2406-3
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    Financial market has systemic complexity and uncertainty. For investors, return and risk often coexist. How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk are main problems to be solved in the field of portfolio optimization (PO). At present, due to the influence of modeling and algorithm solving, the PO models established by many researchers are still mainly focused on single-stage single-objective models or single-stage multi-objective models. PO is actually considered as a multi-stage multi-objective optimization problem in real investment scenarios. It is more difficult than the previous single-stage PO model for meeting the realistic requirements. In this paper, the authors proposed a mean-improved stable tail adjusted return ratio-maximum drawdown rate (M-ISTARR-MD) PO model which effectively characterizes the real investment scenario. In order to solve the multi-stage multi-objective PO model with complex multi-constraints, the authors designed a multi-stage constrained multi-objective evolutionary algorithm with orthogonal learning (MSCMOEA-OL). Comparing with four well-known intelligence algorithms, the MSCMOEA-OL algorithm has competitive advantages in solving the M-ISTARR-MD model on the proposed constructed carbon neutral stock dataset. This paper provides a new way to construct and solve the complex PO model.
  • MUSHTAQ Iram, ZHOU Qin, ZI Xuemin
    系统科学与复杂性(英文版). 2023, 36(2): 716-754. https://doi.org/10.1007/s11424-023-1143-y
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    In the era of big data, high-dimensional data always arrive in streams, making timely and accurate decision necessary. It has become particularly important to rapidly and sequentially identify individuals whose behavior deviates from the norm. Aiming at identifying as many irregular behavioral patterns as possible, the authors develop a large-scale dynamic testing system in the framework of false discovery rate (FDR) control. By fully exploiting the sequential feature of datastreams, the authors propose a screening-assisted procedure that filters streams and then only tests streams that pass the filter at each time point. A data-driven optimal screening threshold is derived, giving the new method an edge over existing methods. Under some mild conditions on the dependence structure of datastreams, the FDR is shown to be strongly controlled and the suggested approach for determining screening thresholds is asymptotically optimal. Simulation studies show that the proposed method is both accurate and powerful, and a real-data example is used for illustrative purpose.
  • BAI Xuchao, ZHANG Jieqiong, CHAI Jian
    系统科学与复杂性(英文版). 2023, 36(2): 755-770. https://doi.org/10.1007/s11424-023-1137-9
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    In this paper, the statistical inference for system stress-strength reliability with bounded strength is discussed. When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions with unequal scale and shape parameters, the maximum likelihood estimator (MLE) and bootstrap-p confidence interval for system reliability are derived. In addition, combining the score equations which are got by taking the first derivative of the log-likelihood function with respect to the model parameters, the modified generalized pivotal quantity for the system reliability is obtained. After that, two point estimators and a modified generalized confidence interval based on the modified generalized pivotal quantity for the system reliability are derived. Monte Carlo simulations are performed to compare the performances of the proposed point estimators and confidence intervals. Finally, a real data analysis is provided to illustrate the proposed procedures.
  • YUAN Wenyan, DU Hongchuan, LI Jieyi, LI Ling
    系统科学与复杂性(英文版). 2023, 36(2): 771-797. https://doi.org/10.1007/s11424-023-1378-7
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    In the age of big data, the Internet big data can finely reflect public attention to air pollution, which greatly impact ambient PM$_{2.5}$ concentrations; however, it has not been applied to PM$_{2.5}$ prediction yet. Therefore, this study introduces such informative Internet big data as an effective predictor for PM$_{2.5}$, in addition to other big data. To capture the multi-scale relationship between PM$_{2.5}$ concentrations and multi-source big data, a novel multi-source big data and multi-scale forecasting methodology is proposed for PM$_{2.5}$. Three major steps are taken: 1) Multi-source big data process, to collect big data from different sources (e.g., devices and Internet) and extract the hidden predictive features; 2) Multi-scale analysis, to address the non-uniformity and nonalignment of timescales by withdrawing the scale-aligned modes hidden in multi-source data; 3) PM$_{2.5}$ prediction, entailing individual prediction at each timescale and ensemble prediction for the final results. The empirical study focuses on the top highly-polluted cities and shows that the proposed multi-source big data and multi-scale forecasting method outperforms its original forms (with neither big data nor multi-scale analysis), semi-extended variants (with big data and without multi-scale analysis) and similar counterparts (with big data but from a single source and multi-scale analysis) in accuracy.
  • JIN Jun, LIU Shuangzhe, MA Tiefeng
    系统科学与复杂性(英文版). 2023, 36(2): 798-821. https://doi.org/10.1007/s11424-022-1197-2
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    Nowadays, researchers are frequently confronted with challenges from massive data computing by a number of limitations of computer primary memory. Modal regression (MR) is a good alternative of the mean regression and likelihood based methods, because of its robustness and high efficiency. To this end, the authors extend MR to massive data analysis and propose a computationally and statistically efficient divide and conquer MR method (DC-MR). The major novelty of this method consists of splitting one entire dataset into several blocks, implementing the MR method on data in each block, and deriving final results through combining these regression results via a weighted average, which provides approximate estimates of regression results on the entire dataset. The proposed method significantly reduces the required amount of primary memory, and the resulting estimator is theoretically as efficient as the traditional MR on the entire data set. The authors also investigate a multiple hypothesis testing variable selection approach to select significant parametric components and prove the approach possessing the oracle property. In addition, the authors propose a practical modified modal expectation-maximization (MEM) algorithm for the proposed procedures. Numerical studies on simulated and real datasets are conducted to assess and showcase the practical and effective performance of our proposed methods.
  • XU Xiaoli, ZHOU Yan, ZHANG Kongsheng, ZHAO Mingtao
    系统科学与复杂性(英文版). 2023, 36(2): 822-842. https://doi.org/10.1007/s11424-022-2109-1
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    Variable selection for varying coefficient models includes the separation of varying and constant effects, and the selection of variables with nonzero varying effects and those with nonzero constant effects. This paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal data. The proposed method can not only separate varying coefficients and constant coefficients, but also estimate and select the nonzero varying coefficients and nonzero constant coefficients. It is suitable for variable selection of linear models, varying coefficient models, and partial linear varying coefficient models. Under regularity conditions, the proposed method is consistent in both separation and selection of varying coefficients and constant coefficients. The obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation, and the estimators of nonzero constant coefficients are consistent and asymptotically normal. Finally, the authors investigate the finite sample performance of the proposed method through simulation studies and a real data analysis. The results show that the proposed method performs better than the existing competitor.
  • CHENG Jianhua, WANG Xu, WANG Dehui
    系统科学与复杂性(英文版). 2023, 36(2): 843-865. https://doi.org/10.1007/s11424-023-1051-1
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    In this paper, the authors consider the empirical likelihood method for a first-order generalized random coefficient integer-valued autoregressive process. The authors establish the log empirical likelihood ratio statistic and obtain its limiting distribution. Furthermore, the authors investigate the point estimation, confidence regions and hypothesis testing for the parameters of interest. The performance of empirical likelihood method is illustrated by a simulation study and a real data example.
  • YANG Zhengfeng, ZHAO Hanrui, ZHI Lihong
    系统科学与复杂性(英文版). 2023, 36(2): 866-883. https://doi.org/10.1007/s11424-023-1406-7
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    VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities. It calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2 (AIVISS) to verify the existence of a double solution (a singular solution of an arbitrary multiplicity) of a slightly perturbed polynomial system.
  • NGUYEN Tri Dat, NGO Lam Xuan Chau
    系统科学与复杂性(英文版). 2023, 36(2): 884-893. https://doi.org/10.1007/s11424-023-1246-5
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    This paper considers the class of autonomous algebraic ordinary differential equations (AODEs) of order one, and studies their Liouvillian general solutions. In particular, let $F(y,w)=0$ be a rational algebraic curve over $\mathbb{C}$. The authors give necessary and sufficient conditions for the autonomous first-order AODE $F(y,y')=0$ to have a Liouvillian solution over $\mathbb{C}$. Moreover, the authors show that a Liouvillian solution $\alpha$ of this equation is either an algebraic function over $\mathbb{C}(x)$ or an algebraic function over $\mathbb{C}(\exp(ax))$. As a byproduct, these results lead to an algorithm for determining a Liouvillian general solution of an autonomous AODE of order one {of} genus zero. Rational parametrizations of rational algebraic curves play an important role on this method.
  • SHI Minjia, LI Yaya, CHENG Wei, CRNKOVIĆ Dean, KROTOV Denis, SOLÉ Patrick
    系统科学与复杂性(英文版). 2023, 36(2): 894-908. https://doi.org/10.1007/s11424-023-2276-8
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    A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application (Solé, et al., 2021). The authors study the self-dual class in length at most 196. The authors use three competing methods of generation: Exhaustion, Linear Algebra and Gröbner bases. Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples. The authors conjecture that if v is an even perfect square, a self-dual bent sequence of length v always exists. The authors introduce the strong automorphism group of Hadamard matrices, which acts on their associated self-dual bent sequences. The authors give an efficient algorithm to compute that group.