中国科学院数学与系统科学研究院期刊网

25 April 2025, Volume 38 Issue 2
    

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  • CHEN Jie, CHEN Ben M., XIE Lihua, ZHANG Ji-Feng
    Journal of Systems Science & Complexity. 2025, 38(2): 511-512. https://doi.org/10.1007/s11424-025-5001-y
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  • ISIDORI Alberto
    Journal of Systems Science & Complexity. 2025, 38(2): 513-532. https://doi.org/10.1007/s11424-025-4590-9
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    This paper presents in organized form a number of results that have appeared in the literature in the last two decades, concerning the design of control laws for multi-input multi-output nonlinear systems, with emphasis on the problem of stabilizing an equilibrium, and addresses, at a broad level generality, systems that are invertible from an input-output viewpoint.
  • CHEN Zhixing, GUO Lei
    Journal of Systems Science & Complexity. 2025, 38(2): 533-546. https://doi.org/10.1007/s11424-025-4540-6
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    In this article, the authors investigate and derive adaptive strategies for the pursuit-evasion problem where both players lack knowledge of the opponent’s cost function parameters, which has rarely been investigated in the existing literature. To address this challenge, the authors consider a basic information structure that assumes that the evader will use an adaptive learning algorithm to estimate the unknown parameters and update its adaptive strategy piecewise, whereas the pursuer will adopt a strategy based on the opponent’s choices at each time instant. By employing methods of diminishing excitation and random switching, the authors establish certain excitation conditions for signals of the closed-loop game system to ensure the strong consistency of the parameter estimates. Moreover, the authors demonstrate that the adaptive game system can asymptotically reach the Nash equilibrium, which is the same equilibrium achieved in pursuit-evasion games when all game parameters are known.
  • CHENG Daizhan, QI Hongsheng, ZHANG Xiao, JI Zhengping
    Journal of Systems Science & Complexity. 2025, 38(2): 547-572. https://doi.org/10.1007/s11424-025-4411-1
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    For $k$-valued (control) networks, two types of (control) invariant subspaces are proposed, namely, the state-invariant and dual-invariant subspaces, which are subspaces of the state space and dual space, respectively. Algorithms are presented to check whether a dual subspace is dual-(control) invariant, and to construct state feedback controls}. The bearing space of $k$-valued (control) networks is introduced. Using the structure of the bearing space, the universal invariant subspace is presented, which is independent of the dynamics of particular networks. Finally, the relation between the state-invariant subspaces and the dual-invariant subspaces of a network is investigated. A duality property shows that if a dual subspace is invariant, then its perpendicular state subspace is also invariant, and vice versa.
  • ZHOU Xunkuai, CHEN Xi, CHEN Jie, CHEN Ben M.
    Journal of Systems Science & Complexity. 2025, 38(2): 573-596. https://doi.org/10.1007/s11424-025-4425-8
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    Visual-based defect detection efficiently monitors the health and quality of construction and industrial products. However, current defect detection methods often improve detection accuracy at the cost of lower inference speeds or more parameters, struggle with complex data representation, emphasize target features while neglecting environmental information importance, and utilize convolutional or max pooling operations for downsampling, leading to more feature loss. To address these issues, this work presents a low complexity, accurate defect detection network augmented by environmental information-assisted and flexible activation functions to enhance the neural network performance on complex data representation. Environmental information-assisted module is designed for defect detection tasks to assist in accurately locating and predicting defects. Moreover, this work restructure features post-downsampling to mitigate feature loss and design a simple feature module called deep-global fusion that integrates deep and global features to enhance detection performance. Extensive experiments validate the superiority of the proposed detection network. The deployment of the network on edge computing devices confirms its competitive advantage in portability and reliability.
  • XIE Kedi, LU Maobin, DENG Fang, SUN Jian, CHEN Jie
    Journal of Systems Science & Complexity. 2025, 38(2): 597-612. https://doi.org/10.1007/s11424-025-4535-3
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    This paper investigates the multi-player non-zero-sum game problem for unknown linear continuous-time systems with unmeasurable states. By only accessing the data information of input and output, a data-driven learning control approach is proposed to estimate $N$-tuple dynamic output feedback control policies which can form Nash equilibrium solution to the multi-player non-zero-sum game problem. In particular, the explicit form of dynamic output feedback Nash strategy is constructed by embedding the internal dynamics and solving coupled algebraic Riccati equations. The coupled policy-iteration based iterative learning equations are established to estimate the $N$-tuple feedback control gains without prior knowledge of system matrices. Finally, an example is used to illustrate the effectiveness of the proposed approach.
  • ZHANG Yizhong, LIAN Bosen, LEWIS Frank L.
    Journal of Systems Science & Complexity. 2025, 38(2): 613-632. https://doi.org/10.1007/s11424-025-4542-4
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    This article formulates interactive adversarial differential graphical games for synchronization control of multiagent systems (MASs) subject to adversarial inputs interacting with the systems through topology communications. Local control and interactive adversarial inputs affect each agent's local synchronization error via local networks. The distributed global Nash equilibrium (NE) solutions are guaranteed in the games by solving the optimal control input of each agent and the worst-case adversarial input based solely on local states and communications. The asymptotic stability of the local synchronization error dynamics and the NE are guaranteed. Furthermore, the authors devise a data-driven online reinforcement learning (RL) algorithm that only computes the distributed Nash control online using system trajectory data, eliminating the need for explicit system dynamics. A simulation-based example validates the game and algorithm.
  • BURTON Evan, NAKAMURA-ZIMMERER Tenavi, GONG Qi, KANG Wei
    Journal of Systems Science & Complexity. 2025, 38(2): 633-653. https://doi.org/10.1007/s11424-025-4529-1
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    Optimal feedback control of nonlinear system with free terminal time present many challenges including nonsmooth in the value function and control laws, and existence of multiple local or even global optimal trajectories. To mitigate these issues, the authors introduce an actor-critic method along with some enhancements. The authors demonstrate the algorithm's effectiveness on a prototypical example featuring each of the main pathological issues present in problems of this type as well as a higher dimensional example to show that the solution method presented can scale.
  • CAO Wenji, FENG Gang
    Journal of Systems Science & Complexity. 2025, 38(2): 654-670. https://doi.org/10.1007/s11424-025-4462-3
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    This paper investigates the output containment control problem of unknown heterogeneous non-minimum phase linear multi-agent systems over directed communication graphs. The dynamics of each follower are allowed to be unknown. A novel distributed adaptive pole placement control strategy is developed to address the output containment control problem of the concerned multi-agent system. It is shown that the proposed distributed adaptive control strategy guarantees the boundedness of all the signals in the resulting closed-loop system and the convergence of the followers' outputs to a convex hull spanned by the leaders' outputs. The efficacy of the proposed control strategy is demonstrated by two simulation examples.
  • ZHANG Liping, ZHANG Huanshui, XIE Lihua
    Journal of Systems Science & Complexity. 2025, 38(2): 671-690. https://doi.org/10.1007/s11424-025-4528-2
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    The distributed optimal output synchronization problem for the leaderless heterogeneous multi-agent system with a general global cost function is investigated for the first time by linear quadratic (LQ) optimal control theory. Conventional algorithms for heterogeneous systems are quite complex, requiring the design of a virtual reference generator and the solving of regulation equations. This paper presents a novel distributed asymptotically optimal controller by incorporating the design of distributed observer and feedforward controller. A general form of the distributed controller is obtained by solving an augmented algebraic Riccati equation, which is parallel to classical optimal control theory. The optimal topology is an arbitrary directed graph containing only a spanning tree. It is shown that the proposed algorithms outperform the traditional consensus methods in the convergence speed by selecting proper observer gain matrices, and eliminate the reliance on the nonzero eigenvalues of Laplacian matrix. Simulation example further demonstrates the effectiveness of the proposed scheme and a faster superlinear convergence speed than the existing algorithm.
  • NING Zepeng, FANG Xu, LI Yibei, XIE Lihua
    Journal of Systems Science & Complexity. 2025, 38(2): 691-716. https://doi.org/10.1007/s11424-025-4546-0
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    This paper proposes a data-driven learning-based approach to predictive control for switched nonlinear systems subject to state and control constraints and external stochastic disturbances. A switched Koopman modeling framework is developed, where a multi-mode neural network for state lifting is trained simultaneously with Koopman operators and state reconstruction matrices for all modes. This framework facilitates the construction of the switched linear Koopman model in a transformed space and effectively captures the dynamics of the original nonlinear system. A switched predictive control strategy is then designed to regulate the switched Koopman model with constrained states and control inputs against both the stochastic disturbances and the uncertainties introduced by the lifting neural network. The proposed control scheme ensures mean-square stability and guarantees boundedness during the online phase. Furthermore, boundedness analysis is performed to determine the bounded set of the original system state across all admissible switching sequences. The effectiveness of the proposed methodology is demonstrated through a case study of a gene regulatory network.
  • LIU Tong, LIU Tengfei, JIANG Zhong-Ping
    Journal of Systems Science & Complexity. 2025, 38(2): 717-738. https://doi.org/10.1007/s11424-025-4543-3
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    Feedback optimization aims at regulating the output of a dynamical system to a value that minimizes a cost function. This problem is beyond the reach of the traditional output regulation theory, because the desired value is generally unknown and the reference signal evolves according to a gradient flow using the system's real-time output. This paper complements the output regulation theory with the nonlinear small-gain theory to address this challenge. Specifically, the authors assume that the cost function is strongly convex and the nonlinear dynamical system is in lower triangular form and is subject to parametric uncertainties and a class of external disturbances. An internal model is used to compensate for the effects of the disturbances while the cyclic small-gain theorem is invoked to address the coupling between the reference signal, the compensators, and the physical system. The proposed solution can guarantee the boundedness of the closed-loop signals and regulate the output of the system towards the desired minimizer in a global sense. Two numerical examples illustrate the effectiveness of the proposed method.
  • ANWAR Junaid, RIZVI Syed Ali Asad, LIN Zongli
    Journal of Systems Science & Complexity. 2025, 38(2): 739-755. https://doi.org/10.1007/s11424-025-4589-2
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    Building heating, ventilating, and air conditioning (HVAC) systems have one of the largest energy footprint worldwide, which necessitates the design of intelligent control algorithms that improve the energy utilization while still providing thermal comfort. In this work, the authors formulate the HVAC equipment dynamics in the setting of a two-player non-zero-sum cooperative game, which enables two decision variables (mass flow rate and supply air temperature) to perform joint optimization of the control utilization and thermal setpoint tracking by simultaneously exchanging their policies. The HVAC zone serves as a game environment for these two decision variables that act as two players in a game. It is assumed that dynamic models of HVAC equipment are not available. Furthermore, neither the state nor any estimates of HVAC disturbance (heat gains, outside variations, etc.) are accessible, but only the measurement of the zone temperature is available for feedback. Under these constraints, the authors develop a new data-driven Q-learning scheme employing policy iteration and value iteration with a bias compensation mechanism that accounts for unmeasurable disturbances and circumvents the need of full-state measurement. The proposed algorithms are shown to converge to the optimal solution corresponding to the generalized algebraic Riccati equations (GAREs) in dynamic games.
  • XU Yuchun, ZHANG Yanjun, ZHANG Ji-Feng
    Journal of Systems Science & Complexity. 2025, 38(2): 756-781. https://doi.org/10.1007/s11424-025-5088-1
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    This paper studies the leader-following adaptive tracking control problem for multi-agent systems comprising a leader agent and $N$ follower agents with uncertain nonlinear dynamics. Specifically, a novel event-triggered communication based adaptive distributed observer is developed to enable each follower agent to estimate the leader's information. Then, new forms of adaptive control law and parameter update law are designed with the estimated leader's signals. The developed distributed adaptive control strategy has several characteristics: (i) With the introduced time-varying observer gain, the designed adaptive distributed observer eliminates the need for global graph information but ensures convergence of the estimates; (ii) By appropriately designing the event-triggered mechanism, the communication frequency among follower agents is reduced in the sense that the communication rate decays over time; (iii) The newly designed adaptive control law ensures a linear estimation error equation, facilitating the development of a stable parameter update law without requiring prior knowledge of uncertain system parameters. The stability of closed-loop system and leader-following asymptotical tracking are achieved. Simulation study demonstrates the theoretical results.
  • GENG Fan, DONG Yi, HONG Yiguang
    Journal of Systems Science & Complexity. 2025, 38(2): 782-804. https://doi.org/10.1007/s11424-025-4487-7
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    This paper considers the practical fixed-time tracking control problem for a state constrained pure-feedback nonlinear system. A new barrier function is first proposed to handle various asymmetric time-varying constraints and unify the cases with and without state constraints. Then a low-cost neural network based adaptive fixed-time controller is constructed by further combining the dynamic surface control, which overcomes the technical problems of overparametrization and singularity in the backstepping procedure. The proposed design guarantees that the tracking error converges to a small neighbourhood of zero in a fixed time while satisfying the state constraints as a priority task without imposing feasibility conditions on the virtual controllers. Simulation results validate the effectiveness of the proposed adaptive fixed-time tracking control strategy.
  • ZHENG Liwen, XU Shengyuan
    Journal of Systems Science & Complexity. 2025, 38(2): 805-820. https://doi.org/10.1007/s11424-025-4477-9
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    In this paper, the authors address the bounded leader-following consensus problem for linear multi-agent systems connected via undirected graphs, specifically in the presence of non-consistent time-varying communication delays. The periodic event-triggered scheme is proposed to mitigate the adverse effects of these delays, which ensures discrete data transmission only occurs at specific event instants. By leveraging the nature of periodic event-triggered schemes, Zeno-freeness can be guaranteed by discretely event-checking. Additionally, the appropriate design of the threshold range prevents the event-triggered consensus from degrading into sampled-data consensus. The numerical simulation is presented in the end to show the effectiveness of the provided approach.
  • LI Xuehui, ZHENG Zhou, DONG Hairong, SUN Zhendong
    Journal of Systems Science & Complexity. 2025, 38(2): 821-836. https://doi.org/10.1007/s11424-025-4536-2
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    In this paper, the authors propose an approach to properly aggregate a reversible discrete-time switched linear system and prove that, for any $n$-dimensional exponentially stabilizable switched system, the authors could design up to $n$ linear gain matrices, such that the extended system is also exponentially stabilizable as a switched autonomous system. By utilizing the pathwise state feedback switching strategy of the switched autonomous system, the original system is aggregated into a piecewise linear system that is step-wise norm contractive and exponentially stable. The authors also develop a robust switching design mechanism that simultaneously achieves exponential stability, structural stability, and input-to-state stability for the closed-loop system. A numerical example is presented to demonstrate the effectiveness of the proposed design scheme.
  • CONG Siming, GU Nan, WANG Haoliang, WANG Dan, PENG Zhouhua
    Journal of Systems Science & Complexity. 2025, 38(2): 837-856. https://doi.org/10.1007/s11424-025-4494-8
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    This paper investigates the path-guided distributed formation control of networked autonomous surface vehicles (ASVs) subject to model uncertainties and environmental disturbances. A safety-certified path-guided coordinated control method is proposed for multiple ASVs to achieve a distributed formation in obstacle environments. Specifically, a neural predictor with a high-order tuner is presented to approximate unknown nonlinearities with accelerated learning performance. Subsequently, %a kinematic control law is designed by unifying control Lyapunov functions (CLFs) and control barrier functions (CBFs). %The path-guided coordinated control objectives are described using CLFs, while safety considerations are addressed through CBFs. control Lyapunov functions (CLFs) and control barrier functions (CBFs) are constructed for mapping stability constraints and safety constraints on states to control inputs. A quadratic optimization problem is constructed with the norm of control inputs as the objective function, CLFs and CBFs as constraints. Neurodynamic optimization is used to deal with the quadratic programming problem and generate the optimal kinetic control signals, thereby attaining the desired safe formation. Unlike the high-order CBF, a CBF backstepping method is proposed to establish safety constraints such that repeated time derivatives of system nonlinearities can be avoided. The multi-ASVs system is ensured to be input-to-state safe irrespective of high-order relative degree. Through the Lyapunov theory, the multi-ASVs system is proven to be input-to-state stable. Finally, simulation results are presented to validate the efficacy of the presented safety-certified distributed formation control for networked ASVs.
  • DEHGHANI AGHBOLAGH Hassan, CHEN Zhiyong, SERON Maria
    Journal of Systems Science & Complexity. 2025, 38(2): 857-873. https://doi.org/10.1007/s11424-025-4356-4
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    With advances in network control systems, new applications such as the analysis of opinion dynamics have emerged. Using mathematical tools, various dynamic models have been developed to study how people change opinions in social settings. One such model is the DeGroot-Friedkin model, a two-stage approach for sequential discussion of multiple issues. For each issue, the classical DeGroot model, closely related to the consensus problem, is used to analyze opinion dynamics. This model incorporates the theory of self-appraisal to study the evolution of an individual's self-esteem, where individuals evaluate their contributions to the issues being discussed. However, the question “How does the social network affect one's self-esteem?” remains unaddressed. In this paper, the authors propose a new self-esteem evolution model that examines the effects of social relationships on individuals' self-esteem by considering changes in opinion as an indicator of the social network's impact. The authors also introduce a convergence criterion for the new model and provide analytical proofs of the results.
  • SUN Chao, CHEN Bo, WANG Jianzheng, HU Guoqiang
    Journal of Systems Science & Complexity. 2025, 38(2): 874-901. https://doi.org/10.1007/s11424-025-4486-8
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    This study aims to solve the Nash equilibrium (NE) seeking problem for monotone $N$-coalition games. The authors assume that the gradient mapping of the game is monotone but not necessarily strictly or strongly monotone. Such a merely monotone assumption presents significant challenges to NE seeking, since the basic gradient descent method may fail to converge. The authors start with a regularization-based projected gradient dynamical system in a general non-cooperative game framework and analyze the convergence of the dynamics under different scenarios. Then, the authors develop NE seeking algorithms for monotone $N$-coalition games with undirected and connected inner-coalition communication graphs. Asymptotic convergence to the least-norm NE is proven. The convergence rate of the algorithm for an analytic mapping is provided. Furthermore, the authors propose a novel regularization-based dynamical system that allows different parameters among the coalitions. Rigorous analysis and a numerical example are provided to illustrate the effectiveness of the proposed method.
  • WANG Lu, LIU Lu
    Journal of Systems Science & Complexity. 2025, 38(2): 902-918. https://doi.org/10.1007/s11424-025-4538-0
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    This paper first proposes a distributed continuous-time Newton-Raphson algorithm for heterogeneous linear multi-agent systems over unbalanced digraphs. Then this approach extends to cases where the local cost functions and Hessian matrices are unknown. While local exponential stability of the inverse Hessian matrix estimator has been established for single-agent systems, this paper proves local exponential stability in multi-agent systems, ensuring the stability of the proposed distributed Newton-Raphson extremum seeking algorithm. A numerical example demonstrates the effectiveness of the proposed algorithms.
  • XU Dabo
    Journal of Systems Science & Complexity. 2025, 38(2): 919-952. https://doi.org/10.1007/s11424-025-4549-x
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    This paper presents a global robust nonlinear output regulation (GROR) design for nonlinear systems that do not necessarily exhibit hyperbolic zero dynamics. The hyperbolic condition has been predominantly required in existing literature on GROR, particularly for smooth global asymptotic stabilization in various scenarios. This limitation has motivated the current investigation to relevant global regulation control problems. Building on the paradigm of “reduction of the plant dynamics and augmentation of the exosystem” (termed Reduction-Augmentation) proposed in Huang, 1995, the author shall develop an internal model-based Lyapunov approach to achieving GROR through smooth error-output feedback under mild conditions. Notably, the author establishes a smooth global stabilizer by means of a Lyapunov's direct method for the augmented system using the tool of input-to-state stability (ISS) with respect to a compact zero-invariant set. As an interesting outcome, the proposed method applies to nonlinear systems under strictly relaxed conditions than previous studies.