中国科学院数学与系统科学研究院期刊网

25 January 2024, Volume 44 Issue 1
    

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  • DONG Haozu, XIAO Min, DING Jie, ZHOU Ying
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 1-16. https://doi.org/10.12341/jssms22546
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    Hopf bifurcation is a kind of simple but important dynamic bifurcation problem, which means that when the system parameter changes past the critical value, the equilibrium point changes from stable to unstable and a limit cycle is generated. Based on Hopf bifurcation, this paper proposes a time-delay reaction-diffusion rumor propagation model with saturated control, which better reflects the characteristics of rumor propagation in real life, and studies the Turing instability and Hopf bifurcation. Meanwhile, the time delay is selected as the bifurcation parameter, and the analytic expression of the bifurcation threshold is given. Finally, the correctness of the theoretical results is verified by numerical simulation. The results show that both diffusion and time delay are the causes of the system instability. The traditional rumor propagation model only considers the time evolution, while the model depicts the traditional rumor propagation model from the two dimensions of time and space, making it more appropriate to reflect the law of rumor propagation in real life, and providing new ideas for the governance of rumor propagation.
  • TAN Xufeng, LI Yuan, LIU Yang
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 17-30. https://doi.org/10.12341/jssms23366
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    An adaptive dynamic programming (ADP) algorithm is proposed for a class of model-free stochastic linear quadratic (SLQ) optimal tracking problem with time-delay. Firstly, the equivalent system of the original time-delay system is derived using the double causal coordinate transformation. A new augmented system consisting of the equivalent system and the command generator is constructed, and then the stochastic algebraic equations of the augmented system are given. Secondly, in order to solve the SLQ tracking control problem, the stochastic problem is transformed into deterministic problem. Then the ADP algorithm is proposed and its convergence analysis is given. For the purpose of realizing the ADP algorithm, three neural networks are designed, which approximate the optimal cost function, the optimal control gain matrix and the system model respectively. Finally, the effectiveness of the algorithm is verified by a numeric example.
  • KE Lin, YANG Xiaoxiao, CHEN Zhibin
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 31-44. https://doi.org/10.12341/jssms23177
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    Traveling salesman problem (TSP) is a typical problem in combinatorial optimization, and the relevance of solving the TSP is significant. Using deep reinforcement learning (DRL) models to automatically design learning algorithms has become a recent research hotspot as DRL is widely used in industry. In order to enhance the generalization ability of the DRL model on the large-scale TSP, this paper proposes a hybrid model of dynamic graph convolutional network to encode and spatial attention mechanism to decode for tackling the large-scale TSP. Dynamic graph convolution module can dynamically encode node information so as to efficiently update the hidden layer state of each node. Spatial attention facilitates capturing the global connections between nodes, and then calculating and extracting key features by weighting all local features. Experimental results show that our model outperforms the previous DRL model for optimization when generalizing the training strategy of TSP50 to TSP250/500/750/1000, and the test results on the standard dataset of TSPlib also show the improvement of the model for optimization performance.
  • TAN Yan, WU Liucang
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 45-59. https://doi.org/10.12341/jssms23313
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    Transient behavior, steady-state precision, regulation time, and convergence rate are the four key indicators for evaluating closed-loop control system performance. In this paper, the authors propose a tracking control design scheme that simultaneously satisfies the above four indicators for unmatched uncertain pure feedback nonlinear systems. This scheme ensures that the system output signal always stays within the envelope range formed by the performance function by setting the performance function. At the same time, under a novel error transformation mechanism control, the steady-state precision and regulation time of the closed-loop system can be pre-set. The authors use neural networks to approximate completely unknown nonlinear functions, where the weights of the neural network can be updated online by adaptive laws. In addition, the authors add the σ-correction term in the adaptive law to avoid parameter estimation drift phenomenon. Finally, simulation results validate the effectiveness of the proposed control method and its superiority in control performance.
  • WU Mengyang, YANG Jikang, YU Jinwei
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 60-70. https://doi.org/10.12341/jssms23219
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    The region constrained consensus of flexible-joint robot manipulators is studied. A consensus control torque for flexible-joint robot manipulators is proposed based on the regional potential functions, which can effectively guarantee the range of the synchronization state of flexible manipulators without calculating the final synchronization state, so it is suitable for cooperative control and application of multiple flexible-joint manipulators in the task space. Further more, a sufficient condition for solving region consensus problems is presented based on the structure of network topology. Finally, the effectiveness of the obtained theoretical results is verified by numerical simulations.
  • WANG Jun, WEI Yaping
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 71-85. https://doi.org/10.12341/jssms23433
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    The prescribed-time bipartite consensus control problem for linear cooperative-competitive multi-agent systems (MAS) based on the event-triggered mechanism is studied considering the possible external disturbances. Firstly, a disturbance observer is designed to estimate the external disturbances to the system, and an event-triggered condition is given for each agent to reduce the communication frequency between agents and save the limited communication network resources, while proving to avoid the Zeno phenomenon. Secondly, in order to explicitly pre-allocate the settling time, a prescribed-time event-triggered control protocol in a cooperative and competitive topology is designed in conjunction with the estimated value of the disturbance observer to ensure that all agents achieve bipartite consensus despite external disturbances. Finally, the feasibility and effectiveness of the proposed method are verified using simulation examples.
  • LUO Ping, JIANG Yi
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 86-98. https://doi.org/10.12341/jssms22390
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    In reflexive Banach spaces, the time optimal control problem for linear control systems is considered. By virtue of nonsmooth analysis, the properties of the minimal time function which has two variables with the initial point and the size of control set are studied such as continuity. The results that the target point should be the origin are generalized to be an arbitrary point.
  • LI Li, LU Yanrong, SONG Shenyi
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 99-114. https://doi.org/10.12341/jssms22362
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    This paper considers the problem of preview saturated control for uncertain periodic discrete-time systems with actuator saturation. The classical difference operator method in preview control theory can not be applied due to the existence of time-varying uncertain matrix and input saturation. The state auxiliary variable is introduced and the usual state difference is replaced by the the difference between the state vector and the state auxiliary variable. Therefore, the augmented error system of uncertain discrete system with input saturation is successfully constructed. By constructing the augmented model, the problem of designing the preview saturation controller of the original system is transformed into the problem of stabilization of the augmented error system. A sufficient condition for the asymptotic stability of the closed-loop system is derived by using the improved sector condition to deal with the saturation nonlinearity and the LMI technique. Finally, a simulation example is given to illustrate the validity of the results.
  • ZHANG Yilin, YE Hanrui, ZHANG Lingling, XUE Yiming
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 115-131. https://doi.org/10.12341/jssms22891
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    In the field of equipment fault diagnosis, text data such as operation instructions and maintenance records have great application value, thus fully mining and utilizing text data can significantly improve the efficiency of fault diagnosis. Semantic feature extraction and unsupervised clustering methods are commonly used to mine text data for the purpose of assisting in fault location, but such methods are not able to explain the cause of faults and give reasons for providing corresponding repair solutions. Furthermore, repair solutions generated by those methods are not easy to understand. Based on the existing mature pre-trained language model BERT (bidirectional encoder representation from transformers), this paper proposed a BERT-based short text classification model combined with knowledge graph for fault location, in order to fully explore and utilize the knowledge and laws contained in the text data of CIR equipment. Firstly, fault modules were determined by functional hierarchical relationships of CIR equipment. Then, this paper used BERT-based text classification model to obtain the preliminary fault location. Finally, causes and other information were further recognized with the assistance of knowledge graph to assist in fault diagnosis. Proving fault repair solutions based on the fault diagnosis knowledge accumulated by the knowledge graph makes solutions easy to be understood by maintenance personnel, and helps in knowledge management and engineering efficiency. In terms of text classification techniques, this paper used fault maintenance ledger records of CIR equipment to do experiments, and results proved that the performance of our BERT-based model had been greatly improved compared with traditional classification models. In terms of fault diagnosis, the proposed fault location method combining text classification and knowledge graph also provided support for rapid fault diagnosis by inexperienced equipment maintenance personnel, as well as obtaining certain practical significance.
  • WANG Changjun, XUE Rumeng
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 132-150. https://doi.org/10.12341/jssms22133
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    The digitalization of cross-border trade motivates the development of cross-border e-commerce (CBEC). To inspire the small and medium-sized companies to participate in the innovative CBEC practice, 165 CBEC comprehensive pilot zones have been established in different batches and the so-called “no-ticket exemption” policy has also been introduced. In this paper, the integrated optimization of the CBEC supply chain network design and the tax-declaring strategies are studied, and both the comprehensive experimental zones and the “no-ticket exemption” policy are taken into account. A two-stage nonlinear stochastic programming model is developed, in which, uncertain demands and exchange rates are involved. To optimally solve it, the proposed model is linearized and an optimally dedicated L-shaped algorithm is designed. The case study shows that the “no-ticket exemption” policy can significantly decrease the tax burden of the CBEC companies, and then, attract the CBEC companies to deploy their hubs in the comprehensive pilot zones. Moreover, the introduction of the “Regional Comprehensive Economic Partnership” agreement would alleviate the difference between overseas warehouses and domestic warehouses and inspire the CBEC companies to concentrate cargo logistics to a few overseas warehouses with geographical superiority. Both of the two policies can reduce the layout cost of supply chain network of the CBEC companies.
  • XU Linming, HE Xinjuan
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 151-163. https://doi.org/10.12341/jssms22846
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    For the purpose of comparing the development level of multiple objects to be evaluated at different times and the overall development level in a certain period of time, dynamic evaluation is required. In order to overcome the shortage of Euclidean distance calculation of closeness in traditional TOPSIS, this paper introduces the idea of set-pair analysis connection degree into TOPSIS, uses connection vector distance instead of Euclidean distance to calculate closeness, adds time dimension, and proposes a dynamic TOPSIS evaluation method based on connection degree. This method can not only obtain the evaluation value and the ranking result reflecting the difference degree of the evaluation index value, but also obtain the evaluation value and the ranking result reflecting the increase degree of the evaluation index value, and the comprehensive evaluation value and the ranking result considering the above two situations at the same time. Finally, an empirical analysis of green development level of the Yangtze River Economic Belt is used to verify the effectiveness of the proposed method.
  • YANG Peng
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 164-178. https://doi.org/10.12341/jssms23498
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    This paper studies the robust optimal reinsurance and investment problem under the ambiguity aversion and inflation risks are considered, simultaneously. The surplus process of an insurance company is defined by the diffusion approximation model, and the financial market consists of a risk-free asset and a risky asset. The insurance company can reduce the risk of claims by adopting proportional reinsurance and increase his wealth by investing in the financial market. The price of the risky asset is converted by inflation, and then the influence of inflation on investment is obtained. By using Radon-Nikodym derivative and Girsanov theorem, the wealth process of the insurance company under ambiguity aversion is obtained. With the goal of maximizing expected utility, the analytical solution of robust optimal reinsurance and investment strategy is obtained. Finally, the influence of model parameters on the theoretical results is discussed through numerical experiments, and the research results can effectively guide the reinsurance and investment decisions of the insurance company.
  • WU Xin, LIU Jian, ZHANG Yongming, TANG Yanqun, ZHANG Ying
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 179-199. https://doi.org/10.12341/jssms23492
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    Along with the rise of Internet public welfare, e-commerce platforms represented by Alibaba and JD have injected a strong impetus into the development of Chinese public welfare. However, the public practices of platforms and merchants often contain both public welfare and profit motives. In this paper, three differential game models are constructed for platforms and merchants to discuss their cooperation question about carrying out joint cause-related marketing (CRM), considering the government’s subsidy policy for platforms and the characteristics that engaging in social welfare is multi-cycle and dynamic. Our main results are as follows: 1) The government subsidies can incentivize platforms and merchants to provide more investments for social welfare, and motivate platforms to be willing to share more CRM costs for merchants. 2) Under certain conditions, platforms share a certain percentage of CRM costs for merchants can not only enhance its social welfare investment, but also achieve Pareto improvement of profits for both. 3) Government subsidies can improve the Pareto effect of CRM cost-sharing contracts on the profits of platforms and merchants, but platforms may retain some of the government subsidies and will not invest them all in social welfare. 4) In the joint CRM case, the benefits of platforms, merchants, and the whole system as well as the consumer surplus and social welfare are all optimal. Finally, our main results are verified via numerical simulation, hoping to provide a theoretical basis and reference for the joint CRM of platforms and merchants.
  • LIN Zhibing, ZHANG Juan
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 200-216. https://doi.org/10.12341/jssms23034
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    In the context of carbon trading mechanism, considering the low carbon preference of consumers, this paper studies the selection of the optimal emission reduction technology authorization strategy for innovation-oriented enterprises by constructing a competitive duopoly market, analyzes the three authorization modes of fixed fee, franchise fee and two-system fee, and explores the impact of technology authorization strategy on the environment. The results show that: 1) The two-part licensing strategy is always the best for the technology owning enterprises, and the advantages and disadvantages of fixed-fee licensing and licensing fee licensing are determined by the substitution degree and emission reduction rate between products; 2) Regardless of the degree of innovation, fixed-fee authorization has the greatest impact on the environment. When the emission reduction rate is very small, the total carbon emission generated by the two-part fee authorization is the minimum; Otherwise, the total carbon emission generated by the license fee authorization is the minimum.
  • ZHUANG Weiqing, CAO Yongbo
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 217-235. https://doi.org/10.12341/jssms23312
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    As the core of coordinating urban traffic, intelligent transportation system (ITS) is developing rapidly, as well as, the traffic flow prediction is an important part of ITS, which is regarded as the key factor for successful deployment of ITS. Because of the complex spatial topological structure of the traffic network, the traffic flow shows higher-order nonlinearity and dynamic spatial-temporal complexity. In order to better predict the traffic grid data, this paper proposes a new spatial-temporal network model DCSTGCN, which has the following characteristics: 1) The Chebyshev polynomial (Ch) is applied to the graph convolutional neural network, and the traditional fixed traffic topology is converted with self-diffused convolution to make it more random and dynamic; 2) The spatial Transformer model is added. While considering the data heterogeneity, the multi head self attention mechanism is used to consider the multi attribute problems of nodes, local neighbors, and non local nodes, and the hidden feature information between nodes is considered from the high-dimensional subspace; 3) Combining the temporal transformer with a 1 × 1 2D convolutional neural network (Conv2d). Multiple weights are assigned to the traffic flow time series information to obtain important time features, and the Conv2d network is used to predict the output. The experimental verification shows that the method model is better than a variety of comparative baseline models.
  • ZHENG Jingli, YAN Huan, YIN Yahua
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 236-259. https://doi.org/10.12341/jssms23485
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    Innovation and entrepreneurship is an effective choice to shape a new engine of development. As a new development form, the digital economy can provide new opportunities for enhancing the entrepreneurial vitality of the region. First, based on the panel data of selected 30 provinces in China from 2010 to 2020, this paper constructs the fixed-effects model, mediation model, and threshold model. Second, the models are applied to analyze the impacts and mechanism of the digital economy on entrepreneurial vitality from the perspectives of the labor and data factors. Third, this paper explores the boundary effects of intellectual property protection. The study shows that: 1) The development of digital economy has a significant positive effect on the entrepreneurial vitality, among which it improves the entrepreneurial vitality in the two aspects of Internet application and digital finance, while the role of the basic dimension of informatization is not obvious. 2) Digital economy can promote entrepreneurial vitality through two paths: “Labor factor allocation” and “data factor utilization”. 3) In the southeast half of the “Hu Huanyong Line”, the digital economy has a significant impact on the entrepreneurial vitality. 4) As an important institutional guarantee, intellectual property protection plays a threshold role in regulating the relationship between digital economy and entrepreneurial vitality, and can play the maximum effect when its level is in the optimal range. Accordingly, to stimulate the entrepreneurial vitality, all regions need to further improve the information infrastructure and the application level of digital technology, and optimize the allocation of regional elements. Besides, based on location characteristics, adopt the different strategy of independent innovation, and cooperation to create an entrepreneurial environment that is compatible with the development level of the digital economy.
  • XIAO Caiyun, SUN Xiangkai
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 260-268. https://doi.org/10.12341/jssms22400
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    This paper is concerned with the robust feasibility for a class of support vector machine problems with uncertain data. Firstly, a robust counterpart problem of the uncertain support vector machine problem is introduced in terms of robust optimization. Then, a reformulation of the robust counterpart problem of the uncertain support vector machine problem is given. Finally, by using this reformulation and the so-called epigraphical set, an exact formula for the radius of robust feasibility of the uncertain support vector machine problem is obtained.
  • WANG Weixian, YIN Xianjun, ZHANG Juanjuan, TIAN Maozai
    Journal of System Science and Mathematical Science Chinese Series. 2024, 44(1): 269-284. https://doi.org/10.12341/jssms21675
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    Bayesian quantile regression can well estimate the parameters in the linear mixed effect model. Gibbs sampling is commonly used in Bayesian parameter estimation. In order to obtain accurate estimation results, Gibbs sampling method requires multiple sampling. When the model parameter dimension is high, the Gibbs sampling will be very time-consuming. Therefore, we use variational inference to approximate the posterior distribution of parameters. Variational inference uses unconditional distribution to approximate the conditional distribution obtained by Gibbs method, thus making the calculation more efficient. In this paper, a priori assumption of the parameters of the model is normal distribution, and the variation inference of the parameters of the unpunished linear mixed effect model is carried out. Considering the high dimensional situation, we assume the prior distribution of the model parameters as Laplace distribution, and make variational inference for the parameters of the double penalty linear mixed effect model. From the simulation results, although the accuracy of variational inference for model parameter estimation is slightly less than that of Gibbs sampling, it runs faster. In the case of high dimension, the improvement of operation efficiency is more obvious. In the era of big data, the consumption of time and resources is the first factor we need to consider. Therefore, the method proposed in this paper can be applied to the high-dimensional linear mixed effect model.