中国科学院数学与系统科学研究院期刊网

2023年, 第36卷, 第4期 刊出日期:2023-08-25
  

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  • GUO Chaoqun, HU Jiangping
    系统科学与复杂性(英文版). 2023, 36(4): 1351-1372. https://doi.org/10.1007/s11424-023-2370-y
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    This paper is devoted to stabilizing the high-order uncertain nonlinear system in a fixed time by output feedback control. First, a novel settling time solution method is proposed by establishing an indirect double system and using the comparison principle. Then a fixed-time observer and a neural networked based adaptive law are constructed to estimate the state and the unknown disturbance for the high-order uncertain nonlinear system. Furthermore, a fixed-time output feedback controller is proposed via the homogeneity technique. The upper bound of the settling time is analyzed for the closed-loop system under the proposed output feedback control. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.
  • LI Zixuan, SHI Jingtao
    系统科学与复杂性(英文版). 2023, 36(4): 1373-1406. https://doi.org/10.1007/s11424-023-1261-6
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    In this paper, a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost functionals. The coefficients in the state equation and the weighting matrices in the cost functionals are all deterministic. Closed-loop strategies are introduced, which require to be independent of initial states; and such a nature makes it very useful and convenient in applications. The follower first solves a stochastic linear quadratic optimal control problem, and his optimal closed-loop strategy is characterized by a Riccati equation, together with an adapted solution to a linear backward stochastic differential equation. Then the leader turns to solve a stochastic linear quadratic optimal control problem of a forward-backward stochastic differential equation, necessary conditions for the existence of the optimal closed-loop strategy for the leader is given by a Riccati equation. Some examples are also given.
  • PANG Zhonghua, FU Yuan, GUO Haibin, SUN Jian
    系统科学与复杂性(英文版). 2023, 36(4): 1407-1422. https://doi.org/10.1007/s11424-022-2120-6
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    This paper mainly investigates the security problem of a networked control system based on a Kalman filter. A false data injection attack scheme is proposed to only tamper the measurement output, and its stealthiness and effects on system performance are analyzed under three cases of system knowledge held by an attacker and a defender. Firstly, it is derived that the proposed attack scheme is stealthy for a residual-based detector when the attacker and the defender hold the same accurate system knowledge. Secondly, it is proven that the proposed attack scheme is still stealthy even if the defender actively modifies the Kalman filter gain so as to make it different from that of the attacker. Thirdly, the stealthiness condition of the proposed attack scheme based on an inaccurate model is given. Furthermore, for each case, the instability conditions of the closed-loop system under attack are derived. Finally, simulation results are provided to test the proposed attack scheme.
  • HU Jun, HU Zhibin, DONG Hongli, LIU Hongjian
    系统科学与复杂性(英文版). 2023, 36(4): 1423-1442. https://doi.org/10.1007/s11424-023-2183-z
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    This paper is concerned with the distributed resilient fusion filtering (DRFF) problem for a class of time-varying multi-sensor nonlinear stochastic systems (MNSSs) with random sensor delays (RSDs). The phenomenon of the RSDs is modeled by a set of random variables with certain statistical features. In addition, the nonlinear function is handled via Taylor expansion in order to deal with the nonlinear fusion filtering problem. The aim of the addressed issue is to propose a DRFF scheme for MNSSs such that, for both RSDs and estimator gain perturbations, certain upper bounds of estimation error covariance (EEC) are given and locally minimized at every sample time. In the light of the obtained local filters, a new DRFF algorithm is developed via the matrix-weighted fusion method. Furthermore, a sufficient condition is presented, which can guarantee that the local upper bound of the EEC is bounded. Finally, a numerical example is provided, which can show the usefulness of the developed DRFF approach.
  • LIU Chuang, WU Jinxia, YANG Weidong
    系统科学与复杂性(英文版). 2023, 36(4): 1443-1462. https://doi.org/10.1007/s11424-023-2215-8
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    This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy discrete systems with input delays and cyber attacks. The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties. By considering the influences of input delays and stochastic cyber attacks, a newly fuzzy robust controller is established. Afterward, the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional. Afterward, a solving algorithm for obtaining the controller gains is given. Finally, the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.
  • WANG Shitong, WU Zheng-Guang, WU Zhaojing
    系统科学与复杂性(英文版). 2023, 36(4): 1463-1479. https://doi.org/10.1007/s11424-023-2157-1
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    The output regulation control problem for the Markovian jump systems with colored-noise is proposed in this paper. Since the modes mismatch problem often exists in the Markovian switching system, the authors design a modes asynchronous controller with an internal model form, which can not only deal with external disturbance, but also reduce the influence of stochastic noise on the system, such that the mean square of the regulation error can be made arbitrarily small by turning the designed parameters. Meanwhile, a criterion of the m-th moment noise-to-state exponential stability is presented for continuous-time Markovian jump systems under the asynchronous control.
  • LIU Ping, CHEN Seng, XUE Wenchao, LI Wenbo
    系统科学与复杂性(英文版). 2023, 36(4): 1480-1497. https://doi.org/10.1007/s11424-023-1399-2
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    The attitude control and momentum management (ACMM) problem is quite fundamental for many spacecrafts including space stations, sky laboratories and etc. Instead of single attitude control problem, ACMM problem has to take account of both disturbance rejection and energy optimization. This paper studies the ACMM problem for general spacecraft. A practical active disturbance rejection control architecture is proposed with hierarchical compensation to different kinds of uncertain dynamics or disturbances. In particular, by integrating RLS into ESO, the constant and sinusoidal disturbance terms to be compensated are reconstructed. Also, the LQR law is implemented to achieve the desired performance of control systems after disturbance compensation. Furthermore, quantitative performances of the generalized ESO, the RLS algorithm and the closed-loop tracking system are rigorously analyzed. Finally, the results under 9-DOF semi-physical test environment show the effectiveness of our control method.
  • QI Wei, JI Zhijian, LIU Yungang, LIN Chong
    系统科学与复杂性(英文版). 2023, 36(4): 1498-1518. https://doi.org/10.1007/s11424-023-1516-2
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    In this paper, the strong structural controllability of the leader-follower framework is discussed. Firstly, the authors analyze different edge augmentation methods to preserve the strong structural controllability of the path-bud topology. The following four cases are considered: Adding edges from the path to the bud; adding edges from the bud to the path; adding the reverse or forward edges to the path or bud; and adding both the reverse and forward edges to the path or bud. Then sufficient conditions are derived for the strong structural controllability of the new topologies which are generated by adding different edges. In addition, it is proved that rank[A B] = n is a necessary condition for the strong structural controllability. Finally, three examples are given to verify the effectiveness of the main results.
  • LIN Yaning, ZHANG Weihai
    系统科学与复杂性(英文版). 2023, 36(4): 1519-1539. https://doi.org/10.1007/s11424-023-1145-9
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    This paper discusses feedback Stackelberg strategies for the continuous-time mean-field type stochastic systems with multiple followers in infinite horizon. First, optimal control problems of the followers are studied in the sense of Nash equilibrium. With the help of a set of generalized algebraic Riccati equations (GAREs), sufficient conditions for the solvability are put forward. Then, the leader faces a constrained optimal control problem by transforming the cost functional into a trace criterion. Employing the Karush-Kuhn-Tucker (KKT) conditions, necessary conditions are presented in term of the solvability of the cross-coupled stochastic algebraic equations (CSAEs). Moreover, feedback Stackelberg strategies are obtained based on the solutions of the CSAEs. In addition, an iterative scheme is introduced to obtain efficiently the solutions of the CSAEs. Finally, an example is given to shed light on the effectiveness of the proposed results.
  • WANG Yanqing
    系统科学与复杂性(英文版). 2023, 36(4): 1540-1559. https://doi.org/10.1007/s11424-023-1102-7
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    In this work, the author proposes a discretization for stochastic linear quadratic control problems (SLQ problems) subject to stochastic differential equations. The author firstly makes temporal discretization and obtains SLQ problems governed by stochastic difference equations. Then the author derives the convergence rates for this discretization relying on stochastic differential/difference Riccati equations. Finally an algorithm is presented. Compared with the existing results relying on stochastic Pontryagin-type maximum principle, the proposed scheme avoids solving backward stochastic differential equations and/or conditional expectations.
  • XIAO Ke, LI Shuyong
    系统科学与复杂性(英文版). 2023, 36(4): 1560-1582. https://doi.org/10.1007/s11424-023-1332-8
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    The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching. Under the influence of impulsive disturbance, the solution for the system is discontinuous. By using the Razumikhin technique and stochastic analysis approaches, as well as combining the idea of mathematical induction and classification discussion, some sufficient conditions for the pth moment exponential stability and almost exponential stability of the systems are obtained. The stability conclusion is full time-delay. The results show that impulse, the point distance of impulse and Markovain switching affect the stability for the system. Finally, two examples are provided to illustrate the effectiveness of the results proposed.
  • LIU Yifa, CHENG Long
    系统科学与复杂性(英文版). 2023, 36(4): 1583-1608. https://doi.org/10.1007/s11424-023-2256-z
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    Networked cyber-physical systems are facing serious security threats from malicious attacks. It is noted that the networked cyber-physical system should take defense measures into account at the beginning of its construction. From the conservative defensive perspective, this paper proposes a robust optimal defense resource allocation strategy to reduce the maximum possible losses of the networked cyber-physical system caused by potential attacks. Then, based on the robust optimal allocation strategy, it can be proved that the topology of the networked cyber-physical system has a great influence on the loss function. In order to further improve security, the effects of adding redundant connections are investigated. Furthermore, by taking geographical knowledge into account, a hexagonal construction scheme is proposed for providing a geographically-feasible and economically-viable solution for building networked cyber-physical systems, where the loss function has a cubic decay.
  • YAO Yaqiong, ZOU Jiahui, WANG Haiying
    系统科学与复杂性(英文版). 2023, 36(4): 1609-1625. https://doi.org/10.1007/s11424-023-1179-z
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    Softmax regression, which is also called multinomial logistic regression, is widely used in various fields for modeling the relationship between covariates and categorical responses with multiple levels. The increasing volumes of data bring new challenges for parameter estimation in softmax regression, and the optimal subsampling method is an effective way to solve them. However, optimal subsampling with replacement requires to access all the sampling probabilities simultaneously to draw a subsample, and the resultant subsample could contain duplicate observations. In this paper, the authors consider Poisson subsampling for its higher estimation accuracy and applicability in the scenario that the data exceed the memory limit. The authors derive the asymptotic properties of the general Poisson subsampling estimator and obtain optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under both A- and L- optimality criteria. The optimal subsampling probabilities contain unknown quantities from the full dataset, so the authors suggest an approximately optimal Poisson subsampling algorithm which contains two sampling steps, with the first step as a pilot phase. The authors demonstrate the performance of our optimal Poisson subsampling algorithm through numerical simulations and real data examples.
  • LI Zhenpeng, TANG Xijin
    系统科学与复杂性(英文版). 2023, 36(4): 1626-1640. https://doi.org/10.1007/s11424-023-1482-8
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    In this paper, the authors consider both the nodes’ opinions dynamics and signed network edges’ evolution. Simulated Annealing Algorithm is applied for searching the minimal global energy function, and bounded confidence model is used for nodes’ opinions updating. The authors find that the local and global level of balance of signed network is consistent with collective opinions 2-polarization. This property is explainable in terms of the structure balance of the sign distributions on the nodes and edges. The level of balance and the final opinions polarization pattern are achieved depends on the initial density of signed network, and the percentage of initial positive edges. Numerical simulations of the proposed model display a rich and intuitive behavior of the opinions polarization processes. In particular, the authors show that opinions persistent fluctuations is consistent with minimal global the energy function. This work verify that signed social networks are indeed limited balanced, could be used to explain ubiquitous binary polarization phenomenon of real world.
  • CAO Zhongwei, MU Xiaojie, JIANG Daqing
    系统科学与复杂性(英文版). 2023, 36(4): 1641-1657. https://doi.org/10.1007/s11424-023-1199-8
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    Due to many uncertain factors, parameter values in many microorganism cultivation systems are affected to a greater or lesser extent by environmental fluctuation. In this paper, the authors develop a stochastic turbidostat model that considers white noise, formulate and analyze dynamical behavior for the stochastic model. The authors obtain the existence and uniqueness of globally positive equilibrium. Sufficient conditions of the extinction for the system are established. Since the uniformly elliptic condition can fail to satisfy, the existence of the stationary distribution of the system is proved by using Markov semigroups theory. Biologically speaking, the existence of stationary distribution suggests that microorganism will exist for a long time. The analytical results are tested and verified by numerical simulations, which evaluate the influence of white noise on the dynamics of microorganism.
  • CHENG Bing, BAO Qin, ZHENG Yangyang, LI Yuze, WANG Shouyang, WU Peixin, YANG Tao
    系统科学与复杂性(英文版). 2023, 36(4): 1658-1679. https://doi.org/10.1007/s11424-023-1214-0
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    Statistical analysis of COVID-19 mortality is challenging due to its non-stationarity and cross-sectional instability. In this paper, the authors introduce a unified method to evaluate the fatality rate of COVID-19 across countries, whose method provides more reliable information for cross-country comparison than the traditional case-fatality rate (CFR). It emerges that the new method, the blockwise case-fatality rate (BCFR), varies for different countries and in different periods. The authors also decompose the COVID-19 fatality data by three factors: 1) The virus infection dynamics over population in different countries, 2) pure distribution and evolution of instantaneous death rate attributed to different individual’s physical characteristics such as age and health, and 3) individual countries’ variations affecting interactions between the virus infection and the instantaneous mortality due to individual’s physical characteristics. Based on the new three-factor model, the authors obtain six key findings of the COVID-19 fatality rate. Our study suggests that, on average, the estimated instantaneous fatality rate contributes about 57.0% to the global BCFR while the time-varying weight contributes about 41.5% in December 2020. The country-specific contribution of instantaneous fatality rate is significantly higher than that of the time-varying weight. Besides, the country-specific characteristics in demographical, social, and economic aspects would affect the relative severity of the disease.
  • WANG Jinjuan, JIANG Zhenzhen, LIU Hongzhi, MENG Zhen
    系统科学与复杂性(英文版). 2023, 36(4): 1680-1696. https://doi.org/10.1007/s11424-023-1168-2
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    Multiple response regression model is commonly employed to investigate the relationship between multiple outcomes and a set of potential predictors, where single-response analysis and multivariate analysis of variance (MANOVA) are two frequently used methods for association analysis. However, both methods have their own limitations. The basis of the former method is independence of multiple responses and the latter one assumes that multiple responses are normally distributed. In this work, the authors propose a test statistic for multiple response association analysis in high-dimensional situations based on F statistic. It is free of normal distribution assumption and the asymptotic normal distribution is obtained under some regular conditions. Extensive computer simulations and four real data applications show its superiority over single-response analysis and MANOVA methods.
  • YANG Bin, CHEN Min, ZHOU Jianjun
    系统科学与复杂性(英文版). 2023, 36(4): 1697-1716. https://doi.org/10.1007/s11424-023-1431-6
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    Existing methods for analyzing semi-functional linear models usually assumed that random errors are not serially correlated or serially correlated with the known order. However, in some applications, these assumptions on random errors may be unreasonable or questionable. To this end, this paper aims at testing error correlation in a semi-functional linear model (SFLM). Based on the empirical likelihood approach, the authors construct an empirical likelihood ratio statistic to test the serial correlation of random errors and identify the order of autocorrelation if the serial correlation holds. The proposed test statistic does not need to estimate the variance as it is data adaptive and possesses the nonparametric version of Wilks’ theorem. Simulation studies are conducted to investigate the performance of the proposed test procedure. Two real examples are illustrated by the proposed test method.
  • SUN Yang, FANG Xiangzhong
    系统科学与复杂性(英文版). 2023, 36(4): 1717-1737. https://doi.org/10.1007/s11424-023-1456-x
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    Recently, uncertainty quantification is getting more and more attention, especially for computer model calibration. However, most of the existing papers assume the errors follow a Gaussian or sub-Gaussian distribution, which would not be satisfied in practice. To overcome the limitation of the traditional calibration procedures, the authors develop a robust calibration procedure based on Huber loss, which can deal with responses with outliers and heavy-tail errors efficiently. The authors propose two different estimators of the calibration parameters based on ordinary least estimator and L2 calibration respectively, and investigate the nonasymptotic and asymptotic properties of the proposed estimators under certain conditions. Some numerical simulations and a real example are conducted, which verifies good performance of the proposed calibration procedure.
  • XIE Xiaofeng, TIAN Tian
    系统科学与复杂性(英文版). 2023, 36(4): 1738-1756. https://doi.org/10.1007/s11424-023-1452-1
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    In EUROCRYPT 2017, a new structure-difference property, say “a-multiple-of-8” was proposed on 5-round AES. Inspired by the idea, yoyo attacks and mixture differential attacks were proposed yielding new records on data and computational complexities for key-recovery attacks against 5-round AES. In this paper, the authors attempt to apply the idea of mixture differential cryptanalysis to Midori64. Midori is a lightweight block cipher proposed at ASIACRYPT 2015. Although the structure of Midori is similar to AES, the MixColumn matrix of Midori is not MDS. Based on this observation, the authors present a class of deterministic differential trails on 2-round Midori. Then combined with the yoyo trick, a new type of 4-round retracing boomerang distinguishers is obtained on Midori. Based on the new 4-round distinguishers, a key-recovery attack on 6-round Midori64 is given that requires only 227 computational complexity, 229 chosen plaintexts, 220 adaptively chosen ciphertexts. The key-recovery attack has been experimentally verified.
  • SHI Minjia, LI Shitao, KIM Jon-Lark, SOLÉ Patrick
    系统科学与复杂性(英文版). 2023, 36(4): 1757-1768. https://doi.org/10.1007/s11424-023-1518-0
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    The authors study the binary codes spanned by the adjacency matrices of the strongly regular graphs (SRGs) on at most two hundred vertices whose existence is unknown. The authors show that in length less than one hundred they cannot be cyclic, except for the exceptions of the SRGs of parameters (85, 42, 20, 21) and (96, 60, 38, 36). In particular, the adjacency code of a (85, 42, 20, 21) is the zero-sum code. In the range [100, 200] the authors find 29 SRGs that could possibly have a cyclic adjacency code.
  • MITTERAMSKOGLER Johann Josef, WINKLER Franz
    系统科学与复杂性(英文版). 2023, 36(4): 1769-1788. https://doi.org/10.1007/s11424-023-1427-2
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    If a first-order algebraic ODE is defined over a certain differential field, then the most elementary solution class, in which one can hope to find a general solution, is given by the adjunction of a single arbitrary constant to this field. Solutions of this type give rise to a particular kind of generic point—a rational parametrization—of an algebraic curve which is associated in a natural way to the ODE’s defining polynomial. As for the opposite direction, we show that a suitable rational parametrization of the associated curve can be extended to a general solution of the ODE if and only if one can find a certain automorphism of the solution field. These automorphisms are determined by linear rational functions, i.e., Möbius transformations. Intrinsic properties of rational parametrizations, in combination with the particular shape of such automorphisms, lead to a number of necessary conditions on the existence of general solutions in this solution class. Furthermore, the desired linear rational function can be determined by solving a comparatively simple differential system over the ODE’s field of definition. These results hold for arbitrary differential fields of characteristic zero.