中国科学院数学与系统科学研究院期刊网

09 December 2024, Volume 44 Issue 12
    

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  • LIN Changjian, CHENG Yuhu, WANG Xuesong, LIU Yuhao
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3477-3490. https://doi.org/10.12341/jssms240071
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    To improve the accuracy of unmanned underwater vehicle (UUV) state estimation of non-cooperative targets, an axial attention-based target state estimation method is proposed in this paper. The state estimation mechanism of the UUV non-cooperative target based on sonar observation is analyzed. The non-Markov state-space model of the problem is transformed into a first-order Markov state-space model with memory, and a recursive filtering model is constructed. Aiming at the unreliability of forward-looking sonar observation and the unpredictability of target motion, a multi-step prediction network based on transformer is proposed to describe the complex motion process of non-cooperative target relative to sonar under nonlinear observation. Aiming at the instability of observation and the unpredictability of posterior distribution, based on the Monte Carlo approximate inference principle, the multi-step prediction network is used to map the particles in the target measurement state space to the target prediction state space, and a non-cooperative target state estimation algorithm based on the axial attention is constructed. The simulation results show that the adaptability and robustness of the proposed method to uncertain inputs.
  • WANG Jun, YANG Jiaqi
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3491-3510. https://doi.org/10.12341/jssms23559
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    In this paper, a fault-tolerant control strategy combining fixed-time state feedback control and output feedback control is designed to realize the problem of heterogeneous fault multi-agent system fault-tolerant output consensus in the presence of external finite energy interference. Firstly, an adaptive sliding mode observer is proposed to obtain the fault reconstruction value of the actuator under the condition of overcoming the external limited energy interference. Secondly, for the followers who cannot obtain the leader state, a distributed fixed-time observer is designed to realize that each follower can estimate the leader state within a fixed time. Then, the fault reconstruction value is introduced into the distributed fault-tolerant output consensus control protocol. In addition, Lyapunov stability theory is used to solve the fault-tolerant output consensus control gain. Finally, a leader and four followers conduct simulation experiments on the fixed-time fault-tolerant output consensus control of heterogeneous multi-agent systems, which verifies the effectiveness and feasibility of the proposed method.
  • YUAN Liuyang, WANG Dawei, JIA Shihui, CHI Xiaoni
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3511-3523. https://doi.org/10.12341/jssms23030
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    In this paper, based on the combination of the robust principal component analysis (WSNM-RPCA) model with weighted $S_{p}$ norm minimization and the generalized robust principal component analysis (GRPCA) model, a new generalized robust principal component analysis (GWSLRPCA) model is reconstructed by using the $l_{2,1}$ norm, which improves the accuracy of the recovery of the important rank components of the matrix, and uses the alternating direction multiplier method of random ordering to solve the new model. The numerical experiment results show that the new model GWSLRPCA can not only separate the effective low rank information of the picture and other noise parts from the picture polluted by mixed noise, but also have better image restoration effect. In terms of objective evaluation criteria, GWSLRPCA data are also better than Mean-Filter, WSNM-RPCA and GRPCA models.
  • QIN Wanyu, HE Zerong
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3524-3537. https://doi.org/10.12341/jssms23728
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    This paper is concerned with an optimal control problem, in which the state system is described by a nonlinear second-order partial integro-differential equation, the control function stands for initial population distribution, and the index gives the net benefits from the population resources after an arbitrarily fixed time. Based on some conditions on model parameters, we establish the necessary optimality conditions (i.e., maximum principle), which provide the structure of optimal strategies and are given by a truncating function of the adjoint variable. Furthermore, we show that there is one and only one optimal control policy by the means of Ekeland's variational principle and fixed points reasoning of contraction mappings. Numerical experiments display the applicability of the obtained theoretical results.
  • JI Yun, XIE Yongping, CHAI Jian
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3538-3556. https://doi.org/10.12341/jssms23787
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    The development of rural revitalization industry is the basis for stimulating the vitality of rural areas and the premise for solving all problems in rural areas. Based on the development status of the “new community factory” in the Qinba Mountains of Shaanxi Province, this paper identifies the important participants such as community factories, local governments and leading enterprises, and constructs a tripartite evolutionary game model considering factors such as cost, subsidy, investment and income, and then discusses how each subject makes strategic choices in the process of rural revitalization industry development, and conducts sensitivity analysis and numerical simulation. The results show that, on the one hand, the evolutionary stabilization strategy is affected by the local government subsidy, and the appropriate subsidy is conducive to the joint participation of the three parties. The investment of leading enterprises in production enterprises should be within a relatively reasonable range, and at the same time, it is necessary to increase the investment of all parties in society to the local government; On the other hand, for community factories and leading enterprises, reducing costs and increasing profits will be more conducive to promoting the development of rural revitalization industries such as “new community factory”.
  • CHEN Wei, LUO Wen, LIANG Kairong, BAI Chunguang
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3557-3572. https://doi.org/10.12341/jssms23770
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    This paper introduces a noncooperative-cooperative biform game model under simultaneous model, electricity generator-leader model, and electricity retailer-leader model. It delves into the decision-making problem of new energy investment in the power system. The results show that: 1) The new energy investment under different power structures depends on the cost coefficient of traditional energy investment. 2) Both generators and retailers prefer to be leaders in the supply chains, aiming to maximize their individual profits. However, the overall profit of the supply chain is optimized in the simultaneous model. 3) An increase in the cost coefficient of new energy investment will reduce the investment in new energy and the profitability of generators and retailers, but the new energy investment cost-sharing ratio of the electricity generator will increase. 4) An increase in the preference coefficient of new energy will increase the investment in new energy and the new energy investment cost-sharing ratio of the electricity retailer will increase, thus increasing the profitability of both the generator and the retailer.
  • WANG Guoling, YANG Hui, WANG Chun, YANG Guanghui, TANG Wei
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3573-3585. https://doi.org/10.12341/jssms23830
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    In this paper, variance is introduced into incomplete information static games. By setting the upper bound of variance, the feasible strategy set is obtained for each player, then Nash equilibria are defined by maximizing expected payoffs within the feasible strategy sets. First, the existence of Nash equilibria for such games is proved by Kakutani fixed point theorem. Second, the stability of Nash equilibria for such games is studied. The results show that most games are essential when payoff functions are disturbed. Finally, an example namely incomplete information static Cournot game is given to verify the existence of Nash equilibria for such games.
  • CAO Ming, XU Meng, ZHANG Chengke, ZHU Huainian
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3586-3605. https://doi.org/10.12341/jssms240114
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    Considering the uncertain situation that the presence of perturbations makes the model parameters and transfer probabilities not known precisely, this paper investigates the zero-sum game problem of uncertain discrete Markov jump system. By using the method of free-connection weighting matrix, the existence conditions of control strategy and the expression of the upper bound of performance index are proposed. Firstly, with the help of the free connection weight matrix, we derive the sufficient condition for the stability of the system when no control strategy is imposed. Secondly, based on the stability criterion, combined with the relaxation inequality and the collocation method, we give the sufficiency criterion for the existence of the suboptimal saddle-point equilibrium, an explicit expression of equilibrium strategy, and a precise upper bound on the performance index. Then, by applying the theory of zero-sum game, we solve the zero-sum game problem of the uncertain stochastic Markov jump system. And stochastic \({{H}_{\infty }}\) control are provided as an immediate application. Finally, numerical simulation is carried out with the economic system as an example to verify the validity and practicability of the research results.
  • JIANG Cuixia, NIE Yubing, XU Qifa
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3606-3625. https://doi.org/10.12341/jssms23798
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    In ordered multi-classification analysis, mixed data observation is becoming more and more common. In order to solve the problem of ordered multi-classification under a large frequency ratio, we combine the mixed data sampling (MIDAS) with ordered Logit (OLogit) model to construct an MIDAS-OLogit model. The MIDAS-OLogit model uses high-frequency explanatory variables to predict the ordered multi-classification results of the low-frequency variable, which expands the application range of OLogit model and can adapt to the ordered multi-classification analysis of mixed data under large frequency ratio. In order to verify its effectiveness, Monte Carlo numerical simulation is carried out, and the results show that the prediction performance of MIDAS-OLogit model is better than that of competitive models. In addition, we use the MIDAS-OLogit model to credit ratings the corporate bonds issued by Chinese listed companies from 2008 to 2021, and the results further verify its superior performance of classified forecasting and real-time forecasting.
  • MA Jingyu, LI Quanlin
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3626-3640. https://doi.org/10.12341/jssms23673
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    Active mining behaviour of miners is fundamental to maintaining the secure and stable operation of blockchain systems, as well as realising the sustainable development of blockchain ecosystem. Therefore, effectively incentivizing the mining behaviour of the miners is of significant theoretical and practical importance. In this paper, we focus on investigating a PoW (Proof of Work) blockchain queueing system. By establishing a continuous-time Markov reward process of the $GI/M/1$ type, we compute the expression for the miners' long-run average profit and provide a sufficient condition for their profitability. In addition, to evaluate the miners' short-run benefits and risks, we utilize RG-factorization based on the Markov reward process to obtain expectations and variances of the short-run accumulated profits. We hope that the methodology and results derived in this paper can shed light on the study of mining incentives in blockchain systems, while also provide novel ideas and mathematical analysis approaches for economics and management issues related to blockchain technology.
  • LIN Yu, WU Weiping, WANG Zhenghong, JIN Chengneng
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3641-3662. https://doi.org/10.12341/jssms23915
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    In optimal execution theory, risk-averse investors typically strive to strike a delicate balance between price impact and transaction execution risk when formulating trading decisions, with trading behavior substantially influenced by regulatory policies. Simultaneously, precise characterization of the actual limit order book (LOB) market is proved beneficial for investors in applying optimal execution theory to algorithmic trading practices. Leveraging these foundations, this paper examines the execution problems faced by investors with constant absolute risk aversion (CARA) utility preferences. The analysis is grounded in the general assumption of power-shaped stochastic market depth. Subsequently, we construct an optimal execution model grounded in this general assumption and the dynamics of the LOB market, incorporating considerations of trading risk and trading constraints. The least squares Monte Carlo (LSM) method is employed to derive the corresponding approximate trading strategy, accompanied by the provision of the theoretical upper bound for the approximation error. The numerical examples demonstrate that, within the framework of power-shaped stochastic market depth, the execution strategy for risk-averse investors exhibits a distinctive “L”-shaped characteristic. Simultaneously, the stochastic characteristics, shape profile of market depth, and trading constraints all exert significant influences on the execution strategies. Moreover, in terms of investment performance, the model presented in this paper effectively reduces execution risk and enhances the strategy's efficacy across various trading constraints. Furthermore, the trading constraints, the shape of the limit order book's market depth, and the speed at which the market rebounds also significantly impact both execution risk and the effectiveness of the strategy.
  • ZHOU Yufeng, ZHANG Qinzi, CHENG Jiahao, WU Changzhi, LI Zhi
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3663-3693. https://doi.org/10.12341/jssms23506
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    The traditional decentralized inventory management mode of blood banks and hospitals is more and more difficult to cope with the increasingly normal long periodic blood shortage in China. Therefore, this paper proposes a joint inventory optimization problem for platelets to reduce blood shortage. An age-based platelet joint inventory optimization model with transshipment is built considering the life cycle, system cost, shortage, and outdating. For comparisons, the traditional decentralized inventory management model and the joint inventory optimization model without transshipment are also built. All the three models are described as bi-objective mixed integer nonlinear programming. According to the characteristics of the proposed models, an improved NSWOA is designed. Numerical experimental results demonstrate the effectiveness of the models and algorithm. The improved NSWOA is superior to NSPSO and NSGWO. The results also show that the joint inventory management mode with transshipment can reduce shortage and outdating, and improve inventory performance under blood shortage situations.
  • XIAO Jingmei, CAI Mei
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3694-3717. https://doi.org/10.12341/jssms23700
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    To address the complementary and redundant effects of attributes and the inefficiency of adjusting inconsistent preference information in the emergency group decision-making problem, this paper constructs an emergency decision-making model based on fuzzy measure theory and the best-worst method(BWM). First, given the complexity of the emergency decision-making environment and the uncertainty of decision-makers, we use the flexible linguistic preference relation to depict the intensity of an individual's preference for attributes. We establish a minimum information loss model based on the idea of minimum preference adjustment to generate the collective pairwise comparison preference vectors of attributes. Second, to ensure the timeliness of emergency decision-making and the rationality of decision results, a nonadditive BWM optimization model considering preference adjustment efficiency is proposed. This model can not only improve the decision-making efficiency of the BWM but also reflect the impact of attribute complementary and redundant effects on the ranking of emergency alternatives. Finally, we take the extremely heavy rainstorm emergency event in Zhengzhou as an example to verify the feasibility and effectiveness of the proposed method. The results show that the proposed method can help improve the efficiency and quality of emergency decision-making, and is suitable for the complex and uncertain emergency decision-making environments.
  • SUN Linhui, SUN Yue, WU Anbo, WANG Xinping
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3718-3739. https://doi.org/10.12341/jssms23499
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    The issue of climate change is becoming increasingly severe, and today's businesses need to shift from previous economic-centric thinking to an environmentally friendly economic dual-focused mindset, actively participating in carbon emission reduction. To analyze the long-term emission reduction decisions of manufacturers and retailers in the supply chain under carbon quota trading, we introduce the concept of low-carbon goodwill to describe the impact of reference low-carbon practices on market demand. Considering members' altruistic preferences, we construct four Stackelberg differential game models: Centralized decision-making, decentralized decision-making, manufacturer altruism and retailer altruism. These models analyze the optimal equilibrium strategies for members in different scenarios and compare them. The results show that strict carbon trading policies can motivate companies to reduce carbon emissions, but the adverse effects of reference low-carbon levels should not be ignored. Altruistic behavior effectively weakens these adverse effects, leading to Pareto improvements in the carbon reduction levels of manufacturers and the low-carbon promotion levels of retailers, promoting companies' green and low-carbon transformations. Compared to scenarios where manufacturers exhibit altruistic behavior, retailers' altruism brings greater returns to the low-carbon supply chain.
  • REN Hongmei, TIAN Shoufu, ZHONG Ming, LIU Jichuan
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3740-3759. https://doi.org/10.12341/jssms2023-0473
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    In this paper, we utilize the Fourier neural operator (FNO) for the first time to investigate the derivative nonlinear Schrödinger (DNLS) equation and fractional derivative nonlinear Schrödinger (fDNLS) equation. For the DNLS equation, we successfully establish the mappings between the initial conditions of the equation and their respective solutions. The transition process of the soliton to the $M$-type wave is studied, and the periodic solution is also obtained. Simultaneously, the FNO learning method is employed to investigate the transformation process of the periodical rogue wave. Moreover, we focus on learning the mapping between the fractional order exponential space and the soliton in the fDNLS equation. By comparing the data-driven solution with the exact solution, the powerful approximation capability of the FNO network is highlighted. Finally, we discuss the effects of the full-connected layer $P$ and the activation function on the characterization ability of the network.
  • SUN Jiuyun, DONG Huanhe, FANG Yong
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3760-3778. https://doi.org/10.12341/jssms2023-0362
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    In this paper, hybrid physics-informed neural networks(PINNs) are proposed for solving partial differential equations (PDEs). In this approach, we introduce a difference scheme based on local mesh to construct the physical residuals as part of the loss function. The obvious advantage is that the hybrid PINNs are not completely dependent on automatic differentiation techniques and are more sensitive to gradient changes in the solution. In addition, since the PINNs are continuous mappings, local meshes at arbitrary points can be built. Therefore, all local meshes are independent and the hybrid PINNs are not limited by dimension. Finally, the performance of the hybrid PINNs is verified by numerical experiments, and the effects of the order of differential schemes and the size of local mesh on accuracy are discussed. The results show that the generalization ability of the hybrid PINNs is more significant better than that of the PINNs.
  • YAO Ting, TANG Yongsheng, XU Heqian
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3779-3789. https://doi.org/10.12341/jssms240011
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    A class of $\mathbb{Z}_{p^{r}}\mathbb{Z}_{p^{s}}\mathbb{Z}_{p^{t}}$-additive cyclic codes that are formed by $3$-tuples of polynomials are constructed in this paper, where $p$ is a prime number and $1\leq r \leq s \leq t$. Having established a connection between the random $\mathbb{Z}_{p^{r}}\mathbb{Z}_{p^{s}}\mathbb{Z}_{p^{t}}$- additive cyclic codes and the quasi-abelian complementary dual codes of index $3$, we construct a family of codes of increasing length whose relative minimum distances converge $\delta$ while their rates converge $\frac{1}{3}$, for $0< \delta< \frac{3}{2(1+p^{s-r}+p^{t-r})}$. Consequently, we demonstrate that a large number of $\mathbb{Z}_{p^{r}}\mathbb{Z}_{p^{s}}\mathbb{Z}_{p^{t}}$-additive cyclic codes are asymptotically good.
  • HUANG Yan, KAI Xiaoshan
    Journal of Systems Science and Mathematical Sciences. 2024, 44(12): 3790-3802. https://doi.org/10.12341/jssms23775
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    Calculating the dimensions of hull of linear codes is significant for determining the complexity of some algorithms over finite fields and constructing entangle-ment-assisted quantum error-correcting codes. In this paper, the dimension of the hull of a linear code derived from the (a+x,b+x,a+b+x)-construction over $F_2$ and the (u+v+w,2u+v,u)-construction over $F_3$ are studied. The asymptotics of the families of self-orthogonal codes and linear complementary dual codes obtained from these two constructions are determined. Some optimal or almost optimal linear codes with an explicit hull dimension and self-orthogonal codes are obtained.