Article
Mathematics
Molan Li, Da Li, Junxing Zhang, Xuanlu Xiang, Di Zhao
Summary: By discussing the dynamical properties of optimal cue integration with time-varying delay, we find that it is asymptotically stable and leads to a unique insect home direction. These results provide a theoretical basis for further research on insect homing behaviors and the establishment of autonomous robots that mimic insect navigation mechanisms in the future.
Article
Computer Science, Artificial Intelligence
Kai Wu, Jigui Jian
Summary: This article focuses on the global robust exponential dissipativity (GRED) of uncertain second-order BAM neural networks with mixed time-varying delays. New differential inequalities and Lyapunov-Krasovskii functionals are established to present new GRED criteria in the form of linear matrix inequalities. The correctness of the theoretical results is verified through simulation experiments.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2021)
Article
Engineering, Electrical & Electronic
G. Nagamani, A. Karnan, G. Soundararajan
Summary: This paper addresses the state estimation problem for bidirectional associative memory cellular neural networks with multi-proportional delays, aiming to achieve global asymptotic stability of the estimation error system. Sufficient conditions in the form of LMIs are obtained by utilizing Lyapunov stability theory, and numerical illustrations are provided to demonstrate the applicability and advantages of the proposed theoretical results.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Mathematics, Applied
Xiao Ge, Chenyang Shi, SeakWeng Vong
Summary: In this article, exponential stability of time-varying delay systems is investigated by introducing intermediate polynomials and slack variables to develop intermediate polynomial-based weighted functions (IPWFs). An exponential stability criterion in terms of linear matrix inequalities is obtained by selecting an appropriate Lyapunov-Krasovskii functional and novel techniques on IPWFs. Numerical results demonstrate that the criterion derived in this study is less conservative than some previous results.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Engineering, Mechanical
G. Nagamani, B. Adhira, G. Soundararajan
Summary: This paper discusses the design of a non-fragile state estimator for a class of discrete-time neural networks, including uncertainties and time-varying delay components, to study a robust extended dissipativity criterion. The proposed approach involves constructing a Lyapunov-Krasovskii functional and expressing theoretical results in terms of linear matrix inequalities. Numerical examples, such as a quadruple tank process system model, have been used to illustrate the applicability and effectiveness of the proposed theoretical results.
NONLINEAR DYNAMICS
(2021)
Article
Computer Science, Artificial Intelligence
Mengying Yan, Jigui Jian, Sheng Zheng
Summary: This paper investigates the passivity of uncertain BAM inertial neural networks with time-varying delays, proposing new Lyapunov functionals and delay-dependent criteria based on linear matrix inequalities to ensure the passivity of the systems. Numerical simulations demonstrate the effectiveness of the proposed approach.
Article
Mathematics
Shenping Xiao, Jin Yu, Simon X. Yang, Yongfeng Qiu
Summary: This article studies the stability problem of linear systems with time-varying delays. A new negative condition is established for a class of quadratic functions within a closed set. Based on this condition, stability criteria for the system are derived by constructing an appropriate Lyapunov-Krasovskii functional. Two numerical examples demonstrate that these criteria are efficient and outperform existing methods.
Article
Computer Science, Interdisciplinary Applications
M. Shafiya, G. Nagamani, D. Dafik
Summary: This paper investigates the global synchronization problem for a class of uncertain fractional-order bidirectional associative memory neural networks with constant time delay. Stability conditions are established based on linear matrix inequalities and fractional-order integral inequalities. Global synchronization criteria are developed using a new Lyapunov-Krasovskii functional and improved fractional-order inequalities, extending the results to uncertain networks. A numerical example is presented to demonstrate the feasibility and effectiveness of the proposed theoretical results.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Computer Science, Artificial Intelligence
Qiao Chen, Xinge Liu, Xuemei Li
Summary: This paper presents an improved approach for the exponential stability of neural networks with time-varying delay, establishing a less conservative stability criterion by combining various inequalities. The effectiveness and benefits of the proposed method are illustrated through several numerical examples.
NEURAL COMPUTING & APPLICATIONS
(2022)
Article
Mathematics, Applied
M. Manikandan, K. Ratnavelu, P. Balasubramaniam, S. H. Ong
Summary: This paper investigates the synchronization problem of BAM CGFCNNs with discrete time-varying and unbounded distributed delays, and obtains sufficient conditions using Lyapunov-Krasovskii (LK) functional and Linear matrix inequality (LMI) approach to guarantee the synchronization of the system under parametric uncertainty. Numerical examples with simulations are provided to demonstrate the effectiveness of the derived results in ensuring global asymptotic stability of the error dynamics.
IRANIAN JOURNAL OF FUZZY SYSTEMS
(2021)
Article
Mathematics, Interdisciplinary Applications
Feifei Du, Jun-Guo Lu
Summary: This article investigates the finite-time stability of fractional-order bidirectional associative memory neural networks with discrete and distributed delays. Novel fractional order delayed Gronwall inequalities are developed, along with FTS criteria for the networks.Examples are provided to illustrate the effectiveness and less conservativeness of the proposed methods.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Jose J. Oliveira
Summary: This paper provides sufficient conditions for the global asymptotic stability of a general n-dimensional nonautonomous and nonlinear differential equation with infinite delay. The main stability criterion depends on the delay size on the linear part and the dominance of linear terms over nonlinear terms. The obtained theoretical stability results are applied to answer open problems and generalize a bidirectional associative memory neural network model with delays. A numerical example is given to illustrate the novelty of the results.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematical & Computational Biology
S. Othmani, N. -E. Tatar, A. Khemmoudj
Summary: This paper examines a neural network model with distributed delays and proves an exponential stability result when the standard Lipschitz continuity condition is violated. The study deals with activation functions that may not be Lipschitz continuous, and a nonlinear version of the Halanay inequality is used to overcome difficulties. The obtained differential inequality for exponential stability is 'state dependent,' with the usual constant depending on the state itself.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
(2021)
Article
Computer Science, Interdisciplinary Applications
G. Rajchakit, R. Sriraman, C. P. Lim, B. Unyong
Summary: This paper analyzes the global asymptotic stability and global exponential stability of Clifford-valued neutral-type neural network models with time delays. By considering the neutral term, a Clifford-valued neural network model with time delays is formulated, encompassing real-valued, complex-valued, and quaternion-valued neural network models as special cases. With the decomposition of the n-dimensional Clifford-valued neural network model into 2mn-dimensional real-valued models, a proper function is constructed to handle the neutral term and prove the existence of the equilibrium point. By utilizing homeomorphism theory, linear matrix inequality, and Lyapunov functional methods, sufficient conditions for the existence, uniqueness, and global asymptotic stability of the equilibrium point for the Clifford-valued neutral-type neural network model are derived. Numerical examples are provided to demonstrate the effectiveness of the results, and the simulation results are analyzed and discussed.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
M. Hymavathi, G. Muhiuddin, M. Syed Ali, Jehad F. Al-Amri, Nallappan Gunasekaran, R. Vadivel
Summary: This paper investigates the global exponential stability of fractional order complex-valued neural networks with leakage delay and mixed time varying delays. Sufficient conditions for global exponential stability are established by constructing a proper Lyapunov-functional. The stability conditions are expressed in terms of linear matrix inequalities and the effectiveness of the obtained results is illustrated through two numerical examples.
FRACTAL AND FRACTIONAL
(2022)
Article
Automation & Control Systems
Rathinasamy Sakthivel, Sargunan Priyanka, Oh-Min Kwon, Saminathan Mohanapriya
Summary: This article focuses on the concerns of tracking control and active disturbance rejection for nonlinear switched systems. It employs the Takagi-Sugeno fuzzy framework, state-dependent nonlinear perturbations, actuator saturations, and disturbances. Nonlinear equivalent-input-disturbance technique and modified repetitive control are used to improve system stability and tracking precision. Fuzzy membership functions are utilized to ensure exponential stability of the investigated system.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Computer Science, Artificial Intelligence
Yunfei Qiu, Ju H. H. Park, Changchun Hua, Xijuan Wang
Summary: This article investigates the stability of Takagi-Sugeno (T-S) fuzzy systems with time-varying delay. Firstly, a novel Lyapunov-Krasovskii functional (LKF) is proposed by fully utilizing single integral polynomial-delay-product terms and membership-function-dependent matrices, considering more delay information. Secondly, by introducing negative integral estimation inequalities and polynomial inequality, the estimation gap of derivatives is further decreased. As a result, a less conservative criterion is presented. Finally, examples are used to verify the validity of the stability approach.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Automation & Control Systems
Fang Fang, Jiayu Li, Yajuan Liu, Ju H. Park
Summary: In this article, a resilient distributed sampled-data control scheme is proposed for multiagent systems. The scheme introduces novel logic processors to obtain information on DoS attacks and develops resilient distributed controllers using derived criteria. Two examples are provided to demonstrate the efficiency of the proposed scheme.
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS
(2023)
Article
Automation & Control Systems
Dong Ding, Ze Tang, Ju H. Park, Yan Wang, Zhicheng Ji
Summary: This article investigates the synchronization of complex networks with nonlinear couplings and distributed time-varying delays. It analyzes a leader-following quasisynchronization issue using impulsive control due to the mismatched parameters of individual systems. A dynamic self-triggered impulsive controller is proposed to predict the available instants of impulsive inputs. The synchronization conditions within a specific bound are derived using the Lyapunov stability theorem and the comparison method.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Automation & Control Systems
Guopin Liu, Ju H. Park, Changchun Hua, Yafeng Li
Summary: This article considers the load frequency control problem for power systems using the dynamic event-triggered control approach. A model-based feedback controller is designed to compensate for errors between plant states and feedback data. A dynamic event-triggered mechanism is proposed to exclude Zeno behavior by regularizing the triggering interval. A hybrid model is established to describe the dynamics of the power system under DoS attacks. The stability of the power system can be preserved if the attacks frequency and duration are within a certain range.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Automation & Control Systems
M. J. Park, S. H. Lee, B. Kaviarasan, O. M. Kwon
Summary: A synchronization method for complex dynamical networks (CDNs) with time-varying delay feedback control is proposed in this article to ensure secure communication between the command system and each node of CDNs. The original information signal transmitted from the command system is encrypted using N-shift cipher and public key techniques to enhance communication security. Through Lyapunov stability sense and linear matrix inequality (LMI) framework, a new delay-dependent synchronization criterion is established to restore the original information signal on each node of the CDN and ensure stable synchronization for secure communication among all nodes of the command system and CDN. The validity of the proposed method is verified through numerical simulation.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics, Applied
Boomipalagan Kaviarasan, Oh-Min Kwon, Myeong Jin Park, Rathinasamy Sakthivel
Summary: This paper presents a mode-dependent reduced-order filtering problem for semi-Markovian jump systems with time-varying delay and external disturbance, where the measurement output is susceptible to randomly occurring false data injection attacks. The attacks are described by a nonlinear function satisfying Lipschitz continuity and the possible attack scenarios are represented by a stochastic parameter following the Bernoulli distribution. By using Lyapunov-Krasovskii stability theory and stochastic analysis, a convex optimization problem is formulated, and the filter gain matrices are efficiently obtained to ensure the stochastic stability and strict (Q, S, R) - gamma-dissipativity of the augmented filtering system. Numerical examples demonstrate the advantages and effectiveness of the proposed theoretical findings.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Information Systems
Hao Shen, Yu-An Liu, Kaibo Shi, Ju H. Park, Jing Wang
Summary: This article introduces a more general semi-Markov process to describe the switching of communication topology among distributed generations in a microgrid. A distributed resilient secondary control method is proposed considering network constraints, network security, communication burden, and transmission delay. The method reduces communication numbers and transmission rate while achieving frequency restoration and accurate real power sharing of the microgrid.
IEEE SYSTEMS JOURNAL
(2023)
Article
Engineering, Electrical & Electronic
Bo Zhang, Chunxia Dou, Dong Yue, Ju H. Park, Yusheng Xue, Zhanqiang Zhang, Yudi Zhang, Xiaohua Ding
Summary: In this study, a hierarchical multi-mode management strategy is proposed for restoring the balance of supply and demand in a severely disturbed microgrid. The strategy includes predicting and fitting the support capacity of neighbor microgrids, managing local source-storage-load, and establishing mathematical models for analyzing system stability. The effectiveness of the proposed methods is verified through case studies.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2023)
Article
Engineering, Electrical & Electronic
Xiao Cai, Kaibo Shi, Kun She, Poogyeon Park, Shouming Zhong, Ohmin Kwon, Yue Yu
Summary: This article focuses on the event-triggered strategy design of a two-degree-of-freedom helicopter system with denial-of-service attacks. The attack characteristics of DoS are introduced, and the DoS attacks on the system are considered. A new first-order weight-sampling control method is developed, and novel-looped functionals are constructed. Furthermore, a new event-triggered controller is designed under DoS attacks to ensure the stability of the system.
IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION
(2023)
Article
Automation & Control Systems
Deqiang Zeng, Liping Yang, Ruimei Zhang, Ju H. Park, Zhilin Pu, Xiangpeng Xie
Summary: This article studies the synchronization in probability of reaction-diffusion neural networks (RDNNs) with stochastic sampling. A new switching system protocol is proposed by introducing a stochastic switching parameter for stochastic sampling control systems, effectively improving existing methods. A stochastic switching sampled-data controller is designed using the protocol, transforming the considered system into a switching system. New synchronization in probability criteria are established for RDNNs by constructing a new stochastic switching Lyapunov-Krasovskii functional (LKF) and utilizing the law of large numbers and the Lagrange mean value theorem. The effectiveness of the proposed results is verified by two numerical examples.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Automation & Control Systems
Xiangze Lin, Jingxin Huang, Ju H. H. Park
Summary: This article investigates the problem of adaptive nonsmooth state-feedback stabilization for uncertain output-constrained cascade switched systems. To solve the problem of adaptive control, some mild assumptions have been imposed on the subsystems, such as zero dynamics with input-to-state stability, nonlinear terms with a growth condition, and well-known small signal conditions. State-feedback control laws are designed and an adaptive law is constructed using the adding a power integrator (AAPI) technique. A common Lyapunov function is constructed to cope with output constraints. The proposed method can handle adaptive stabilization of switched systems with uncertain cascade switched systems with/without output constraints.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Computer Science, Information Systems
Xiaozhen Pan, Jinjie Huang, Sangmoon Lee
Summary: This paper investigates the non-static error tracking control issue for the networked control system. It establishes unstable modes of the external disturbance signal and the output signal of the reference system to form a new series system with controlled objects. An internal model compensation controller is proposed to achieve non-static tracking error, and an adaptive event triggering mechanism is introduced to improve network resource utilization. By formulating the tracking control problem as the stabilization problem of a time-varying time-delay system, a sufficient condition for asymptotic stability and H-infinity output tracking performance is derived. Simulation examples demonstrate the feasibility and effectiveness of the approach.
Article
Automation & Control Systems
M. S. Mekala, Gaurav Dhiman, Ju H. Park, Ho-Youl Jung, Wattana Viriyasitavat
Summary: This article introduces a method for improving service reliability and quality in edge computing, which optimizes service execution error rate through the node-centric Lyapunov method and distributed Markov mechanism. Furthermore, a nonlinear programming multi-tenancy heuristic method is used to enhance resource utilization.
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS
(2023)
Article
Automation & Control Systems
Wenhui Dou, Shihong Ding, Ju H. Park
Summary: This article proposes a novel event-triggered second-order sliding mode (SOSM) control algorithm using the small-gain theorems. The algorithm has a global event property in terms of the triggering time intervals. It first designs an SOSM controller related to the sampling error of states and proves the finite-time input-to-state stability (FTISS) of the closed-loop system with the sampling error using the small-gain theorems. Then, a new triggering mechanism is proposed based on the sampling error by designing the appropriate FTISS gain condition. The practical finite-time stability of the closed-loop system is verified, showing that the minimum triggering time interval is always positive in the whole state space. Finally, simulation results demonstrate the effectiveness of the developed control method.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
