中国科学院数学与系统科学研究院期刊网

2025年, 第38卷, 第3期 刊出日期:2025-05-30
  

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  • LIU Wudong, VIETOR Thomas, LU Weijun, WU Guangqiang
    系统科学与复杂性(英文). 2025, 38(3): 953-971. https://doi.org/10.1007/s11424-025-4286-1
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    The Proportional-Integral-Derivative (PID) control has enjoyed significant success and widespread adoption in aviation, automotive, robotics, and various other domains. However, to align with the current trend of networked control systems and optimize communication resource utilization, the authors introduce an extended PID (EPID) control framework that leverages an event-triggered mechanism. This controller is designed for single-input single-output (SISO) high-order affine nonlinear systems, overcoming the limitation of traditional PID control, which typically guarantees stability only for second-order systems. Leveraging the open unbounded parameter manifold and event-triggered conditions of the controller parameters, the authors prove through the Lyapunov method that our proposed controller achieves uniformly ultimately bounded stability and guarantees the absence of the Zeno phenomenon in the event-triggered EPID (ET-EPID) system. The efficacy of the ET-EPID control system approach is exhibited through simulation of a third-order system as well as practical experiment conducted on a second-order direct current motor.
  • WANG Danjing, XIN Bin, WANG Yipeng, ZHANG Jia, DENG Fang, WANG Xianpeng
    系统科学与复杂性(英文). 2025, 38(3): 972-999. https://doi.org/10.1007/s11424-025-4232-2
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    The allocation of heterogeneous battlefield resources is crucial in Command and Control (C2). Balancing multiple competing objectives under complex constraints so as to provide decision-makers with diverse feasible candidate decision schemes remains an urgent challenge. Based on these requirements, a constrained multi-objective multi-stage weapon-target assignment (CMOMWTA) model is established in this paper. To solve this problem, three constraint-feature-guided multi-objective evolutionary algorithms (CFG-MOEAs) are proposed under three typical multi-objective evolutionary frameworks (i.e., NSGA-II, NSGA-III, and MOEA/D) to obtain various high-quality candidate decision schemes. Firstly, a constraint-feature-guided reproduction strategy incorporating crossover, mutation, and repair is developed to handle complex constraints. It extracts common row and column features from different linear constraints to generate the feasible offspring population. Then, a variable-length integer encoding method is adopted to concisely denote the decision schemes. Moreover, a hybrid initialization method incorporating both heuristic methods and random sampling is designed to better guide the population. Systemic experiments are conducted on three CFG-MOEAs to verify their effectiveness. The superior algorithm CFG-NSGA-II among three CFG-MOEAs is compared with two state-of-the-art CMOMWTA algorithms, and extensive experimental results demonstrate the effectiveness and superiority of CFG-NSGA-II.
  • ZHU Huijuan, ZHAO Yunbo, YAN Xiaohui, KANG Yu, LIU Binkun
    系统科学与复杂性(英文). 2025, 38(3): 1000-1020. https://doi.org/10.1007/s11424-025-4001-2
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    In this paper, a cross-sensor generative self-supervised learning network is proposed for fault detection of multi-sensor. By modeling the sensor signals in multiple dimensions to achieve correlation information mining between channels to deal with the pretext task, the shared features between multi-sensor data can be captured, and the gap between channel data features will be reduced. Meanwhile, in order to model fault features in the downstream task, the salience module is developed to optimize cross-sensor data features based on a small amount of labeled data to make warning feature information prominent for improving the separator accuracy. Finally, experimental results on the public datasets FEMTO-ST dataset and the private datasets SMT shock absorber dataset (SMT-SA dataset) show that the proposed method performs favorably against other STATE-of-the-art methods.
  • ZHONG Jiaqi, FENG Yan, WANG Kezhi, CHEN Yong
    系统科学与复杂性(英文). 2025, 38(3): 1021-1046. https://doi.org/10.1007/s11424-025-4120-9
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    This paper addresses the problem of achieving practical consensus in large-scale agent clusters governed by nonlinear reaction-diffusion equations, while considering actuator saturation and external disturbances. Different with the traditional consensus methods, the proposed observer-based boundary control relies on non-collocated and incomplete local measurements rather than idealistic global spatiotemporal dynamics. First, the discrete agents with a chain topology are regarded as a continuum, resulting in the derivation of a reaction-diffusion equation to replace the cumbersome ordinary differential equations (ODEs). Subsequently, an observer is constructed based on the non-collocated measurements to estimate the errors between the leader-following agent clusters. Then, a sufficient condition for the consensus controller is derived by improving the Lyapunov direct method, mean value theorem of integrals and a variation of Wirtinger's inequality. Furthermore, an optimization problem is proposed to effectively enhance the $H_\infty$ disturbance attenuation performance in the presence of actuator saturation. Finally, the comparison simulation is given to illustrate the superiority of proposed methodology.
  • XING Wei, ZHOU Xiaoyue, ZHANG Junfeng, JIA Xuan
    系统科学与复杂性(英文). 2025, 38(3): 1047-1071. https://doi.org/10.1007/s11424-025-4131-6
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    This paper presents a new proportional-integral-derivative control approach for positive switched systems based on a positive proportional-integral observer. First, a positive proportional-integral observer is constructed. By using the observer state, the proportional-integral-derivative control and the corresponding integral part are designed, respectively. Using 1-norm inequality, two dynamic event-triggering conditions are established for the proportional-integral observer and proportional-integral-derivative controller, respectively. A dynamic event-triggered proportional-integral observer-based dynamic event-triggered proportional-integral-derivative controller is proposed by combining the sample state and the integral of the weighted sample output estimation error. Under the designed event-triggering conditions, an interval system with upper and lower bounds is introduced. The positivity and $\ell_1$-gain stability are achieved by realizing the according properties of the lower and upper bound systems in terms of multiple copositive Lyapunov function, respectively. All gain matrices are designed by a matrix decomposition approach and the corresponding conditions are solved by linear programming. Finally, two examples are provided to illustrate the validity of the results.
  • GU Dake, GUO Xiaomeng, LIU Yindong
    系统科学与复杂性(英文). 2025, 38(3): 1072-1091. https://doi.org/10.1007/s11424-025-4230-4
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    In this paper, fully actuated system approaches are utilized to synthesize feedback linearizable nonlinear systems. First, a simple transformation is introduced to convert feedback linearizable nonlinear systems into fully actuated system models for both single-input and multi-input scenarios. Once the fully actuated system model is established, a nonlinear state feedback controller can be derived to achieve a constant linear closed-loop system with an assignable eigenstructure. All degrees of freedom present in the closed-loop system can be leveraged to enhance overall system performance. In comparison to feedback linearization, the proposed method places greater emphasis on the control variables, making it more convenient to address control challenges in dynamic systems. Finally, two numerical examples are presented to illustrate the design procedure for both single-input and multi-input cases, and to validate the effectiveness of the proposed approach.
  • NI Xuanming, ZHAO Qiaochu, HUANG Song, YU Lian
    系统科学与复杂性(英文). 2025, 38(3): 1092-1108. https://doi.org/10.1007/s11424-025-4261-x
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    In recent decades, significant advancements have been made in the rigorous runtime analysis of evolutionary algorithms (EAs). However, in the context of non-elitist EAs and the use of crossover, it is challenging to engage in any meaningful theoretical discussion due to the increasing complexity of the EA's population distribution as the EA runs. This paper aims to gain insight into the rigorous runtime analysis of the $(\mu,\lambda)$ EA with crossover, focusing on its optimization of the JUMP test function, by investigating the population distribution during the optimization process. It is proposed that, under typical circumstances, the population distribution will first reach a stable and fully-diverged state before attaining the global optimum. Consequently, the optimization process is divided into two parts, based on whether the population distribution has reached this state. By investigating this state, the authors are able to provide a better upper bound on the runtime of the EA. Furthermore, a series of experiments were conducted to validate our theoretical results, which also offered insights into the impact of different parameters on this state.
  • LI Dahai, DING Tao, LIANG Liang
    系统科学与复杂性(英文). 2025, 38(3): 1109-1135. https://doi.org/10.1007/s11424-025-3322-5
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    Leveraging the principal-agent theory, this study incorporates reputational capital into a continuous-time framework for analyzing venture capital exit decisions. The authors explore how the principal-agent relationships influence the decision to take capital public by synthesizing optimal incentive alignment and IPO timing within a unified model. The results uncover an intriguing aspect of reputational capital: Despite entrepreneurial efforts to augment this capital, its growth is not linear but tends to reach the highest level before the IPO event. Furthermore, the accumulation of reputational capital expedites the capital exit process and enhances the returns from such exits. Subsequently, as the exit timeline extends, the proportion of exit returns allocated to entrepreneurs escalates to a full share, imposing a constrained decision window for investors on exit timing. The findings suggest that the timing for maximizing investor returns at an IPO is later than the timing that maximizes company revenue. Moreover, excessive IPO costs further delay this exit decision for investors. These findings offer fresh insights into the languishing IPO market observed over the last two decades.
  • LI Yongwu, HUANG Wenchang, LI Jian, YAO Haixiang
    系统科学与复杂性(英文). 2025, 38(3): 1136-1161. https://doi.org/10.1007/s11424-025-4164-x
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    This paper investigates a dynamic mean variance investment decision problem with partial information, where the stock return is assumed to consist of an observable factor and an unobservable factor, which both follow mean reversion processes. Through the Bayesian learning mechanism, the unobservable components of stock returns can be learned by investors from available information, including stock prices and observable returns. Due to lack of time consistency in dynamic investment decision problem with mean-variance criterion, the authors solve this problem by using a game theory approach and characterize the equilibrium investment strategy through the extended Hamilton-Jacobi-Bellman equation (HJB) equations system. By solving the extended HJB equations system, the semi-analytical solutions of the equilibrium strategy and the corresponding value function are obtained. In addition, the influence of unobserved predictor and learning mechanism on the equilibrium investment strategy is also analyzed by utilizing numerical examples.
  • HE Baihua, SHI Hongwei, GUO Xu, ZOU Changliang, ZHU Lixing
    系统科学与复杂性(英文). 2025, 38(3): 1162-1185. https://doi.org/10.1007/s11424-024-3484-6
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    Simultaneously finding active predictors and controlling the false discovery rate (FDR) for high-dimensional survival data is an important but challenging statistical problem. In this paper, the authors propose a novel variable selection procedure with error rate control for the high-dimensional Cox model. By adopting a data-splitting strategy, the authors construct a series of symmetric statistics and then utilize the symmetry property to derive a data-driven threshold to achieve error rate control. The authors establish finite-sample and asymptotic FDR control results under some mild conditions. Simulation results as well as a real data application show that the proposed approach successfully controls FDR and is often more powerful than the competing approaches.
  • SUN Xiaowei, CHEN Jiaqi
    系统科学与复杂性(英文). 2025, 38(3): 1186-1205. https://doi.org/10.1007/s11424-025-4093-8
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    In clinical and observational research, multivariate recurrent event data are commonplace, as people may encounter several kinds of repeating occurrences. While event times are consistently recorded, there are instances where the corresponding event types might not be observed. For multivariate recurrent event data, the authors introduce a time-varying coefficients additive rate model which takes into consideration scenarios in which event types are missing at random (MAR). The authors employ an inverse probability-weighted estimating equation to derive inferences for the time-independent and time-dependent effects, with proofs for the estimators' asymptotic behavior. Moreover, the authors offer statistical tests to assess the temporal variation of covariate effects. The estimators' performance is evaluated by simulation experiments, and the authors apply this method to a platelet transfusion reactions dataset.
  • CHEN Shaoshi, DU Hao, GAO Yiman, LI Ziming
    系统科学与复杂性(英文). 2025, 38(3): 1206-1225. https://doi.org/10.1007/s11424-024-3325-7
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    The authors extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into one algorithm. As an application, the authors present an additive decomposition in rationally hyperexponential towers. The decomposition yields an alternative algorithm for computing elementary integrals over such towers. The alternative can find some elementary integrals that are unevaluated by the integrators in the latest versions of MAPLE and MATHEMATICA.
  • WANG Linpeng, MOU Chenqi
    系统科学与复杂性(英文). 2025, 38(3): 1226-1242. https://doi.org/10.1007/s11424-024-3419-2
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    Characteristic pairs consist of lexicographical Gröbner bases and the minimal triangular sets, called W-characteristic sets, contained in them, and they are good representations of multivariate polynomial ideals in terms of Gröbner bases and triangular sets simultaneously. In this paper, it is studied how to decompose a polynomial set of arbitrary dimensions into characteristic pairs with simple W-characteristic sets, and two algorithms are proposed over fields of characteristic zero and over finite fields respectively. Both of the algorithms rely on the concept of strong regular characteristic divisors, and the one for fields of characteristic zero also uses Lazard lemma to test whether an ideal is radical. Experimental results are presented to illustrate the effectiveness of the proposed algorithms
  • CHEN Hui, SHEN Liyong, MA Shaoqiang
    系统科学与复杂性(英文). 2025, 38(3): 1243-1258. https://doi.org/10.1007/s11424-025-4307-0
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    Direct modeling in CAD offers a promising avenue for model modification through direct interaction. However, a critical impediment to the advancement of direct modeling technology is the inconsistency between modified geometry and unaltered constraints. While several methods have been proposed to address this challenge, they often fail to provide effective solutions, particularly in contexts demanding high model precision. In this paper, the authors introduce a novel approach by integrating tolerance analysis into the constraint update system, followed by the proposal of a constraint update scheme utilizing the extreme value tolerance model and the probability tolerance model. This innovative tolerance-based scheme adeptly resolves the inconsistency problem prevalent in direct modeling while satisfying the requisites of high-precision modeling. A comparative analysis against established methodologies is conducted to demonstrate the advantages of the proposed approach.
  • CHEN Sheng, HU Haofei
    系统科学与复杂性(英文). 2025, 38(3): 1259-1280. https://doi.org/10.1007/s11424-024-3301-2
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    In this paper, the authors aim to study Kronecker canonical form theory for T-type digraphs, which can be used to construct trees by tensor product with some directed paths. Firstly, the authors show that some bicyclic digraphs and multicyclic digraphs are T-type digraphs. Secondly, the authors provide a characterization for T-type digraphs by their Kronecker canonical form. Moreover, the authors present an algorithm for computing the Kronecker canonical form, which can be used to determine whether or not a digraph is a T-type digraph. Lastly, for a class of T-type digraphs, the authors show that their incidence matrix pair can be transformed into Kronecker canonical form using unimodular matrices. The authors also present an algorithm related to finding such unimodular matrices.
  • ZHOU Pei, ZHU Chungang
    系统科学与复杂性(英文). 2025, 38(3): 1281-1311. https://doi.org/10.1007/s11424-024-3311-0
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    Isogeometric collocation method (IGC) shows high computational efficiency compared with isogeometric Galerkin method (IGG) when solving partial differential equations (PDEs). However, few studies about IGC have focused on multi-sided physical domains. In this paper, the authors propose a new IGC method based on toric parameterization (IGCT) for the multi-sided planar physical domains. Due to the high order continuity of toric basis functions, the IGCT method shows more accurate numerical approximation. Moreover, the authors generalize the adaptive $w$-refinement method into IGCT (IGCT-$w$), in which the weights of basis functions in physical domains are optimized independently for geometry representation. The numerical accuracy of IGCT-$w$ is significantly improved by an order of magnitude in comparison with IGCT method. To save the computational cost of IGCT-$w$, the authors devise a selection of weights scheme according to relative residuals. Finally, several numerical examples demonstrate the effectiveness and robustness of the proposed method.
  • CHEN Lingfan, YAO Shanshan
    系统科学与复杂性(英文). 2025, 38(3): 1312-1329. https://doi.org/10.1007/s11424-024-3306-x
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    The minimal basis of a univariate polynomial matrix $M(s)\in K[s]^{m\times n}$ is a basis of the syzygies of the polynomial matrix $M(s)$ with lowest possible degree, where $K[s]$ is the univariate polynomial ring over the field of $K$. It provides an efficient tool to compute the moving planes and moving quadratics of a rational parametric surface, which are employed to implicitize the parametric surface as a powerful implicitization method. In this paper, the authors develop two improved algorithms for computing the minimal bases of polynomial matrices. The algorithms are based on efficient methods to reduce the degrees of a set of univariate polynomial vectors. It is shown that the computational complexities of the two algorithms are $\mathcal{O}\big(m^{2}n^{3}d^2+d^2n^5-\big(2mn^4d^2-\frac{1}{6}m^3nd\big)\big)$, and $\mathcal{O}\big(m^2nd^2+(n-m)n^3d^2+\frac{m^2n^2d^2}{n-m}\big)$ respectively, where $m,n$ are the sizes of the polynomial matrix $M(s)$ and $d$ is the degree of each entry of the matrix. The new algorithms are faster than the state-of-the-art methods by experimental examples. Some properties about the degree of the minimal basis are also provided.
  • WANG Yiyang, SONG Xiaoliang
    系统科学与复杂性(英文). 2025, 38(3): 1330-1350. https://doi.org/10.1007/s11424-024-3568-3
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    The problem of nonconvex and nonsmooth optimization (NNO) has been extensively studied in the machine learning community, leading to the development of numerous fast and convergent numerical algorithms. Existing algorithms typically employ unified iteration schemes and require explicit solutions to subproblems for ensuring convergence. However, these inflexible iteration schemes overlook task-specific details and may encounter difficulties in providing explicit solutions to subproblems. In contrast, there is evidence suggesting that practical applications can benefit from approximately solving subproblems; however, many existing works fail to establish the theoretical validity of such approximations. In this paper, the authors propose a hybrid inexact proximal alternating method (hiPAM), which addresses a general NNO problem with coupled terms while overcoming all aforementioned challenges. The proposed hiPAM algorithm offers a flexible yet highly efficient approach by seamlessly integrating any efficient methods for approximate subproblem solving that cater to specificities. Additionally, the authors have devised a simple yet implementable stopping criterion that generates a Cauchy sequence and ultimately converges to a critical point of the original NNO problem. The proposed numerical experiments using both simulated and real data have demonstrated that hiPAM represents an exceedingly efficient and robust approach to NNO problems.
  • HU Huidan, CAO Zhenfu, DONG Xiaolei, LIN Changlu, LU Penghao
    系统科学与复杂性(英文). 2025, 38(3): 1351-1369. https://doi.org/10.1007/s11424-025-4490-z
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    Cloud computing has become prevalent in the sharing of outsourced data due to its strong computing power and storage capacity. Ensuring data security is vitally important when sharing data in the cloud. Recently, numerous broadcast proxy re-encryption (BPRE) schemes have been designed to address the data security issues of such applications. However, there are no any BPRE schemes that have been designed to address the issue of updating the re-encryption key in a dynamic cloud environment. Therefore, the authors propose a lightweight dynamic broadcast proxy re-encryption scheme (LD-BPRE) to address this issue in dynamic settings where the data owner can dynamically change the set of data users and does not need to update the re-encryption key for the new set of data users. In other words, the proxy can reset a re-encryption ciphertext for the new set of data users using the original re-encryption key. This is significant in a dynamic cloud setting and provides convenience for cloud users. The proposed LD-BPRE is lightweight for users with low-power devices as most of the computing overhead is offloaded to the cloud. The authors formally define the LD-BPRE scheme and prove its security under a decision $n$-BDHE assumption in the standard model. Finally, extensive comparisons and experiments indicate that LD-BPRE is efficient and practical.
  • LIU Jiang, WANG Tao, HOU Pingjing, NI Feng, ZHU Kun, ZHANG Leyi
    系统科学与复杂性(英文). 2025, 38(3): 1370-1387. https://doi.org/10.1007/s11424-025-3319-0
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    Riemman metric tensor (Rmt) plays a significant role in deducing basic formulas and equations arising in differential geometry and (pseudo-) Riemannian manifolds. It is a fundamental and challenging problem to determine the equivalence of indexed differential Rmt polynomials. This paper solves the problem by extending Gröbner basis theory and the previous work on the computational theory for indexed differentials. $L$-expansion of an indexed differential Rmt polynomial is defined. Then a decomposed form of the Gröbner basis of defining syzygies of the polynomial ring is presented, based on a partition of elementary indexed monomials. Meanwhile, the upper bound of the dummy index numbers of sim-monomials of the elements in each disjoint elementary indexed monomial subset is found. Finally, a DST-fundamental restricted ring is constructed, and the canonical form of a polynomial is confirmed to be the normal form with respect to the Gröbner basis in the DST-fundamental restricted ring.
  • WU Yansheng, MA Jin, YANG Shangdong
    系统科学与复杂性(英文). 2025, 38(3): 1388-1403. https://doi.org/10.1007/s11424-025-4313-2
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    Recently, linear complementary dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and ternary LCD codes leveraging curiosity-driven reinforcement learning (RL). By establishing reward and devising well-reasoned mappings from actions to states, it aims to facilitate the successful synthesis of binary or ternary LCD codes. Experimental results indicate that LCD codes constructed using RL exhibit slightly superior error-correction performance compared to those conventionally constructed LCD codes and those developed via standard RL methodologies. The paper introduces novel binary and ternary LCD codes with enhanced minimum distance bounds. Finally, it showcases how random network distillation aids agents in exploring beyond local optima, enhancing the overall performance of the models without compromising convergence.
  • GUO Wanming, ZHU Baoxuan
    系统科学与复杂性(英文). 2025, 38(3): 1404-1414. https://doi.org/10.1007/s11424-025-4302-5
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    Let $\beta$ be an integer and satisfy $0\leq\beta\leq5$. In this paper, the authors prove that the partition polynomial $$\prod_{k=1}^{n}[1+(2+\beta)q^k+q^{2k}]$$ is symmetric and unimodal for $n\geq1$.