中国科学院数学与系统科学研究院期刊网

29 July 2025, Volume 38 Issue 5
    

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  • LI Xin, LIU Guochen, SONG Kang, ZHAO Yanlong
    Journal of Systems Science & Complexity. 2025, 38(5): 1833-1852. https://doi.org/10.1007/s11424-025-4408-9
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    This paper considers the real-time estimation problem of vehicle mass, which has a significant impact on driving comfort and safety. A bilinear parameter identification algorithm is proposed for a type of nonlinear identification problems, which encompass vehicle mass estimation. The feature of this nonlinear model is that two parameters to be estimated are multiplied together, which brings great difficulties to identification compared to linear models. The main idea proposed in the algorithm design is to transform the original nonlinear model into two mutually dependent linear models, which are identified by the recursive algorithms. By constructing a combined Lyapunov function, it is theoretically proved that the algorithm converges under the input excitation condition, and the convergence rate $O(1/t)$ is achieved based on some extra mild conditions. Finally, the algorithm is verified through practical experiments, with the estimated vehicle mass error of $1.06%$ on average, which shows the feasibility of the algorithm.
  • ZHAO Xiaoxiao, LEI Jinlong, LI Li, BUSONIU Lucian, XU Jia
    Journal of Systems Science & Complexity. 2025, 38(5): 1853-1886. https://doi.org/10.1007/s11424-025-4426-7
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    This paper studies a distributed policy gradient in collaborative multi-agent reinforcement learning (MARL), where agents communicating over a network aim to find an optimal policy that maximizes the average of all the agents' local returns. To address the challenges of high variance and bias in stochastic policy gradients for MARL, this paper proposes a distributed policy gradient method with variance reduction, combined with gradient tracking to correct the bias resulting from the difference between local and global gradients. The authors also utilize importance sampling to solve the distribution shift problem in the sampling process. The authors then show that the proposed algorithm finds an $\epsilon$-approximate stationary point, where the convergence depends on the number of iterations, the mini-batch size, the epoch size, the problem parameters, and the network topology. The authors further establish the sample and communication complexity to obtain an $\epsilon$-approximate stationary point. Finally, numerical experiments are performed to validate the effectiveness of the proposed algorithm.
  • ZHANG Yuan, LIU Shujun
    Journal of Systems Science & Complexity. 2025, 38(5): 1887-1908. https://doi.org/10.1007/s11424-025-4550-4
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    This paper focuses on solving the distributed optimization problem with binary-valued intermittent measurements of local objective functions. In this paper, a binary-valued measurement represents whether the measured value is smaller than a fixed threshold. Meanwhile, the ``intermittent’’ scenario arises when there is a non-zero probability of not detecting each local function value during the measuring process. Using this kind of coarse measurement, the authors propose a discrete-time stochastic extremum seeking-based algorithm for distributed optimization over a directed graph. As is well-known, many existing distributed optimization algorithms require a doubly-stochastic weight matrix to ensure the average consensus of agents. However, in practical engineering, achieving double-stochasticity, especially for directed graphs, is not always feasible or desirable. To overcome this limitation, the authors design a row-stochastic matrix and a column-stochastic matrix as weight matrices in the proposed algorithm instead of relying on doubly-stochasticity. Under some mild conditions, the authors rigorously prove that agents can reach the average consensus and ultimately find the optimal solution. Finally, the authors provide a numerical example to illustrate the effectiveness of the algorithm.
  • WANG Xianghan, ZHONG Jianghua, LIN Dongdai
    Journal of Systems Science & Complexity. 2025, 38(5): 1909-1935. https://doi.org/10.1007/s11424-025-4215-3
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    Nonlinear feedback shift registers (NFSRs) are used in many stream ciphers as their main building blocks. An NFSR is said to be observable if any two distinct initial states are distinguishable from their resulting output sequences, and it is said to be nonsingular if its state diagram contains only cycles. To avoid weak key attacks, stream ciphers must use nonsingular and observable NFSRs. With condition that NFSRs only output their first bits, Fibonacci NFSRs are clearly observable, but Galois NFSRs' observability is more complex and is little studied. This paper continues the research on the observability of Galois NFSRs with relaxation of their output restriction. Resorting to the semi-tensor product based Boolean network theory, the paper first reveals the observability index's lower bound for general Galois NFSRs and its upper bound for singular and nonsingular Galois NFSRs and further for nonsingular (sub)maximum-cycle Galois NFSRs. It then gives some necessary and/or sufficient conditions for the observability of general Galois NFSRs. Based on the disclosure of the characterizations of distinguishable initial states on a cycle, the paper finally provides some necessary and/or sufficient conditions for the observability of nonsingular (sub)maximum-cycle Galois NFSRs, helpful to the design of stream ciphers.
  • CONG Wenyu, SHI Jingtao
    Journal of Systems Science & Complexity. 2025, 38(5): 1936-1949. https://doi.org/10.1007/s11424-025-4415-x
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    This paper addresses an indefinite linear-quadratic mean field games for stochastic large-population system, where the individual diffusion coefficients may depend on both the state and the control of the agents. Moreover, the control weights in the cost functionals could be indefinite. The authors employ a direct approach to derive the $\epsilon$-Nash equilibrium strategy. First, the authors formally solve an $N$-player game problem within a vast but finite population setting. Subsequently, by introducing two Riccati equations, the authors decouple or reduce the high-dimensional systems to yield centralized strategies, which depend on the state of a specific player and the average state of the population. As the population size $N$ goes infinity, the construction of decentralized strategies becomes feasible. Then, the authors demonstrate that these strategies constitute an $\epsilon$-Nash equilibrium. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed strategies
  • ZHENG Zuohuan, XU Pengcheng
    Journal of Systems Science & Complexity. 2025, 38(5): 1950-1970. https://doi.org/10.1007/s11424-025-4300-7
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    A weighted and an un-weighted transition network are built and applied to analyze the characteristics of a chaotic time series. The topological entropy, the correlation entropy, the correlation dimension and the maximal Lyapunov exponents of the chaotic time series are estimated by the transition network. The analysis reveals the relationship between the chaotic time series and its corresponding transition network. By estimating those characteristics for two artificial chaotic time series, it concludes that the transition network is a useful tool to analyze a chaotic time series.
  • YAO Jiaye, LIU Jingmei, XU Juanjuan
    Journal of Systems Science & Complexity. 2025, 38(5): 1971-1986. https://doi.org/10.1007/s11424-025-4407-x
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    In this paper, the authors consider a class of linear quadratic optimal control problems of backward stochastic differential equations under partial information with initial value constraint. The main contribution is to obtain an explicitly optimal controller by using a Riccati equation and an optimal parameter characterized by a matrix equation. The key technique is to introduce Lagrange multiplier to transform the problem with initial value constraint into unconstrained optimal control problem and optimal parameter calculation problem, and solve the optimal parameter calculation by using the exact controllability of the system.
  • TAN Shaolin
    Journal of Systems Science & Complexity. 2025, 38(5): 1987-2006. https://doi.org/10.1007/s11424-025-4353-7
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    In this paper, the author is concerned with the problem of achieving Nash equilibrium in noncooperative games over networks. The author proposes two types of distributed projected gradient dynamics with accelerated convergence rates. The first type is a variant of the commonly-known consensus-based gradient dynamics, where the consensual terms for determining the actions of each player are discarded to accelerate the learning process. The second type is formulated by introducing the Nesterov's accelerated method into the distributed projected gradient dynamics. The author proves convergence of both algorithms with at least linear rates under the common assumption of Lipschitz continuity and strongly monotonicity. Simulation examples are presented to validate the outperformance of the proposed algorithms over the well-known consensus-based approach and augmented game based approach. It is shown that the required number of iterations to reach the Nash equilibrium is greatly reduced in the proposed algorithms. These results could be helpful to address the issue of long convergence time in partial-information Nash equilibrium seeking algorithms.
  • BI Wenshan, ZHAO Luyao, SUI Shuai, ZHAO Zhihong, CHEN C. L. Philip
    Journal of Systems Science & Complexity. 2025, 38(5): 2007-2027. https://doi.org/10.1007/s11424-025-4327-9
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    This paper investigates an innovative predefined time output feedback adaptive fuzzy consensus control method for fractional-order nonlinear multi-agent systems (FONMASs). The controlled system includes unmeasurable states and unknown nonlinear functions. The fuzzy state observer is built to evaluate unmeasurable state variables, unknown nonlinear functions are addressed through fuzzy logic system approximation. Combining with fractional-order dynamic surface control (DSC) and the theory of stability of predefined time, the control method is raised. By employing FODSC techniques, the computational explosion problem can be avoided. The stability of the closed-loop system is analyzed using the Lyapunov function, demonstrating that FONMAS achieves semi-global practical predefined time stability (SGPPTS). Eventually, the validity of the prescribed control strategy is verified by a simulation case.
  • ZHANG Tong, HAO Jianghao, ZHANG Yajing
    Journal of Systems Science & Complexity. 2025, 38(5): 2028-2045. https://doi.org/10.1007/s11424-025-4332-z
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    In this paper, the authors consider a wave-plate transmission system on Riemannian manifold with boundary controls on the plate equation. This model arises from the noise control and is extended to the broader context of the Riemannian manifold. By employing the semigroup method, the authors obtain the well-posedness of the system. Subsequently, under certain geometric conditions, the authors establish a polynomial energy decay estimate of type $t^{-1}$ by using the geometric multiplier method in which the conclusion proposed by Guo and Yao (2006) plays a crucial role in the obtained proof. It effectively addresses the challenge posed by curvature on the Riemannian manifold. Moreover, by employing the higher-order energy method, the authors overcome the technical difficulties caused by higher-order terms in boundary controls, which generalizes the results in the literature.
  • YANG Junqi, WANG Shangkun, CHEN Yantao, LI Zhiqiang
    Journal of Systems Science & Complexity. 2025, 38(5): 2046-2065. https://doi.org/10.1007/s11424-025-4270-9
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    In this paper, the issues of both reconstructibility analysis and state estimation are investigated for locally reconstructible Boolean networks (BNs), where the pinning control is employed to design a special control sequence. First, this paper will focus on dealing with state unreconstructible cycle based on state set-estimation theory, and the concept of set-to-set reachability is proposed. Second, the locally reconstructible BNs are transformed to Boolean control networks (BCNs) by pinning control technique, where a logical matrix is designed by a special algorithm such that all states in the unreconstructible initial state set can evolve into the reconstructible state set, simultaneously. Third, a sufficient condition for the existence of a free Boolean control sequence is obtained, which guarantees that a locally reconstructible BN can be transformed into a reconstructible one. Besides, an optimization control algorithm is proposed to generate pinning control sequence and further optimize the reconstructibility of BNs. A kind of pinning control-based state estimation method is also developed. Finally, an example is provided to show the feasibility of the proposed methods.
  • ZHANG Mengyue, ZHAO Shishun, XU Da, HU Tao, SUN Jianguo
    Journal of Systems Science & Complexity. 2025, 38(5): 2066-2083. https://doi.org/10.1007/s11424-024-3474-8
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    The paper discusses the regression analysis of current status data, which is common in various fields such as tumorigenic research and demographic studies. Analyzing this type of data poses a significant challenge and has recently gained considerable interest. Furthermore, the authors consider an even more difficult scenario where, apart from censoring, one also faces left-truncation and informative censoring, meaning that there is a potential correlation between the examination time and the failure time of interest. The authors propose a sieve maximum likelihood estimation (MLE) method and in the proposed method for inference, a copula-based procedure is applied to depict the informative censoring. Additionally, the authors utilise the splines to estimate the unknown nonparametric functions in the model, and the asymptotic properties of the proposed estimator are established. The simulation results indicate that the developed approach is effective in practice, and it has been successfully applied to a set of real data.
  • QIAN Chengde, JIANG Haiyan, LIANG Decai
    Journal of Systems Science & Complexity. 2025, 38(5): 2084-2107. https://doi.org/10.1007/s11424-024-3543-z
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    In many applications involving data streams, the sequences of data arise from highly dynamic and often unstable real-life processes, rendering untenable the standard assumption that current and future data come from the same distribution. In response, new methodologies, such as dynamic online learning, have been proposed in order to account for the nonstationary features in the data-generating process. Motivated by the stability and statistical efficiency of the notable stochastic approximation method, average stochastic gradient descent (ASGD) in time-invariant systems, the authors propose an exponentially weighted moving average (EWMA)-based stochastic gradient descent (SGD) which accommodates the dynamic structure by introducing a forgetting factor and replacing the simple averaging step in ASGD with an EWMA step. Provided that the dynamic drift is Lipschitz continuous, the mean squared tracking error rate of the proposed method achieves the optimal rate in the nonparametric statistical paradigm. The proposed framework also allows us to derive the dynamic regret bound and asymptotic normality with a path variation constraint in a natural manner. Numerical analysis has been conducted to verify the performance of the proposed method. In particular, the proposed method is much more robust to the selection of learning rates compared with the ordinary SGD method.
  • WANG Yeshunying, MENG Hui, LIAO Pu
    Journal of Systems Science & Complexity. 2025, 38(5): 2108-2124. https://doi.org/10.1007/s11424-024-3199-8
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    In this paper, the authors investigate the optimal per-claim reinsurance problem under the continuous-time framework to minimize the insurer's ruin probability based on the Lundberg exponent. Considering reinsurance participants' diversified risk preferences, the authors assume that the reinsurance premium is calculated by a combined premium principle, including the expected value premium principle and upper moment premium principle. Then, the authors derive the insurer's optimal reinsurance strategy satisfying the principle of indemnity and the incentive compatibility condition in an infinite reinsurance space based on the point-wise optimization approach. Besides, the proposed work emphasizes the optimality and admissibility of the combination of the excess of loss reinsurance and its dual form when a piecewise reinsurance premium principle is considered. As a special case, the optimal reinsurance strategy under the expected value premium principle reduces to the classic result. Furthermore, the numerical analyses are provided to illustrate the effects of the main parameters on the maximal Lundberg exponent and the optimal reinsurance strategy.
  • XU Yitai, YUAN Jianbo, ZHOU Wen, YU Miao, SUN Xiaomin, ZHU Kun
    Journal of Systems Science & Complexity. 2025, 38(5): 2125-2146. https://doi.org/10.1007/s11424-025-3397-z
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    The Russia-Ukraine situation has become a notable international issue, with the resulting changes in global diplomatic relations gaining considerable attention. To examine the evolving diplomatic strategies of the countries involved, the authors apply the theories and methodologies of complex network games. First, the authors incorporate overflow payoff theory from economic and trade cooperation networks to summarise the spillover income phenomenon in diplomatic games and to facilitate modelling. Drawing on the classic Fermi rule in network game theory, the authors introduce belief and the same-strategy factors to propose an evolutionary game rule driven by interests, beliefs, and neighbouring strategies. Using numerical simulations, the authors examine the factors that affect the evolutionarily stable strategies of various nations. The authors also conduct comparative experiments to validate the scientific credibility of the method proposed in this paper.
  • HAN Xiaoxue, HAN Bing, ZHAO Peng, CHEN Jianbin
    Journal of Systems Science & Complexity. 2025, 38(5): 2147-2163. https://doi.org/10.1007/s11424-025-4197-1
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    The factorial design within a conditional model is utilized when the effects of one factor in a factorial experiment hold greater significance under each fixed level of another factor. This paper investigates the generalized minimum aberration $(N,s^p)$-design, where each factor is $s$-level, with $s$ being any prime or prime power. Via utilizing the method of complementary designs, the authors explore the design with a pair of conditional and conditioning factors. The proposed approach applies not only to regular designs but also to nonregular designs. Additionally, the findings can be extrapolated to encompass designs under the two pairs conditional model. The findings presented in this paper not only strengthen but also generalize the existing knowledge in this field.
  • CAI Tingting, HU Tao
    Journal of Systems Science & Complexity. 2025, 38(5): 2164-2184. https://doi.org/10.1007/s11424-025-4469-9
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    In the analysis of censored survival data, it is crucial to consider the heterogeneity of treatment effects in order to avoid biased inferences. The deep neural network-based heterogeneous partially linear Cox model offers a flexible and robust solution by incorporating both heterogeneous linear and homogeneous nonlinear components. The authors propose a novel approach to subgroup detection for this model under right-censoring, using deep neural networks to approximate nonlinear effects. To simultaneously estimate parameters and identify subgroups, the authors employ a concave pairwise penalty and the alternating direction method of multipliers (ADMM) algorithm. Furthermore, the authors demonstrate that the proposed estimator possesses oracle properties and achieves model selection consistency. Through simulation studies and empirical data analysis on breast cancer, the authors illustrate the effectiveness of the proposed method.
  • QU Wenxin, LIANG Beiting, WANG Guochang
    Journal of Systems Science & Complexity. 2025, 38(5): 2185-2203. https://doi.org/10.1007/s11424-024-3571-8
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    For functional data, the most popular dimension reduction methods are functional sliced inverse regression (FSIR) and functional sliced average variance estimation (FSAVE). Both FSIR and FSAVE methods are based on the slice approach to estimate the conditional expectation $E[x(t)|y]$. While sliced-based methods are effective for scalar responses, they often perform poorly or even lead to failure for multivariate responses and small sample sizes as the so-called ``curse of dimensionality". To avoid this problem, this study proposes a projective resampling method that first projects the multivariate response into a scalar-response and then uses SDR method for the univariate response to estimate the effective dimension reduction space (e.d.r space). The proposed projective resampling method is insensitive to the number of slices and the dimensionality of the response variable. In theory, the proposed resampling method can fully recover the effective dimension reduction space. Furthermore, this study investigates the performance of the proposed method through simulation studies and one real data analysis and compares the proposed method with other methods.
  • YANG Kai, CHEN Xiaoman, LI Han, XIA Chao, WANG Xinyang
    Journal of Systems Science & Complexity. 2025, 38(5): 2204-2225. https://doi.org/10.1007/s11424-024-4027-x
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    This paper introduces a bivariate hysteretic integer-valued autoregressive (INAR) process driven by a bivariate Poisson innovation. It deals well with the buffered or hysteretic characteristics of the data. Model properties such as sationarity and ergodicity are studied in detail. Parameter estimation problem is also well address via methods of two-step conditional least squares (CLS) and conditional maximum likelihood (CML). The boundary parameters are estimated via triangular grid searching algorithm. The estimation effect is verified through simulations based on three scenarios. Finally, the new model is applied to the offence counts in New South Wales (NSW), Australia.
  • SUN Zhi-Wei
    Journal of Systems Science & Complexity. 2025, 38(5): 2226-2251. https://doi.org/10.1007/s11424-024-4159-z
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    In this paper, the author first reviews the history of Hilbert's Tenth Problem, and then study mixed quantifier prefixes over Diophantine equations with integer variables. For example, the author proves that $\forall^2\exists^4$ over $\mathbb Z$ is undecidable, that is, there is no algorithm to determine for any $P(x_1,\cdots,x_6)\in\mathbb Z[x_1,\cdots,x_6]$ whether $$\forall x_1\forall x_2\exists x_3\exists x_4\exists x_5\exists x_6(P(x_1,\cdots,x_6)=0),$$ where $x_1,\cdots,x_6$ are integer variables. The author also has some similar undecidable results with universal quantifies bounded, for example, $\exists^2\forall^2\exists^2$ over $\mathbb Z$ with $\forall$ bounded is undecidable. The author conjectures that $\forall^2\exists^2$ over $\mathbb Z$ is undecidable.
  • QI Niuniu, DEHBI Lydia, LIU Banglong, YANG Zhengfeng, ZENG Zhenbing
    Journal of Systems Science & Complexity. 2025, 38(5): 2252-2271. https://doi.org/10.1007/s11424-024-3366-y
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    This paper primarily focuses on solving the Heilbronn problem of convex polygons, which involves minimizing the area of a convex polygon $P_1P_2\cdots P_n$ while satisfying the condition that the areas of all triangles formed by consecutive vertices are equal to $\frac{1}{2}$. The problem is reformulated as a polynomial optimization problem with a bilinear objective function and bilinear constraints. A new method is presented to verify the upper and lower bounds for the optimization problem. The upper bound is obtained by the affine regular decagon. Then Bilinear Matrix Inequalities (BMI) theory and the branch-and-bound technique are used to verify the lower bound of the problem. The paper concludes by proving that the lower bound for the area minimization problem of a convex polygon with 10 vertices is 13.076548. The relative error compared to the global optimum is 0.104%.
  • SUN Jiawei, LI Biao
    Journal of Systems Science & Complexity. 2025, 38(5): 2272-2290. https://doi.org/10.1007/s11424-024-3418-3
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    In this paper, by modifying loss function MSE (adding the mean square error of the complex conjugate term to the loss function) and training area of the physics-informed neural network (PINN), the authors proposed two neural network models: Mix-training PINN and prior information mix-training PINN. The authors demonstrated the advantages of these models by simulating rogue waves in the nonlocal $\mathcal{PT}$-symmetric Schrödinger equation. Numerical experiments showed that the proposed models not only simulate first-order rogue waves, but also significantly improve the simulation capability. Compared with original PINN, the prediction accuracy of the first-order rouge waves are improved by one to three orders of magnitude. By testing the inverse problem of first-order rogue waves, it is also proved that these models have good performance.