Article
Mathematics, Applied
Mohammadreza Askari Sepestanaki, Mohammad Soofi, Mojtaba Hadi Barhaghtalab, Hamidreza Bahmani, Saleh Mobayen, Abolfazl Jalilvand
Summary: This study proposes an adaptive continuous barrier function as a fractional-order control system to stabilize chaotic systems with unknown uncertainties using the terminal sliding mode control technique with chattering-free property. The greater flexibility of the fractional-order controller compared to the integer-order controller is the main reason for its usage. Applying an adaptive approach and Lyapunov's stability theory, the study presents an adaptive continuous barrier fractional-order chattering-free finite-time controller for chaotic systems with unknown uncertainties and external disturbances. The suggested controller can effectively stabilize the chaotic system with a continuous and smooth control law, even without knowledge of the system boundaries, and in the presence of unknown disturbances caused by model uncertainties. MATLAB simulation results confirm the high efficiency of the proposed control technique in controlling chaotic systems with unknown perturbations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Hua Zhang
Summary: This paper presents an adaptive controller for MIMO chaotic systems with system uncertainties and unknown control direction. Matrix decomposition theory and Nussbaum-type function are used to handle the unknown control direction, and a proportional integral (PI) law is proposed to update the parameters of the fuzzy system. The stability of the controlled system is strictly proven, and simulation results are provided.
Article
Mathematics, Applied
Honglei Yin, Bo Meng, Zhen Wang
Summary: This article addresses the synchronization control problem of a class of chaotic systems with unknown uncertainties and outside perturbation by using an innovative adaptive sliding mode controller constructed using a disturbance observer. The disturbance observer can approximate the unknown external disturbances well by choosing the appropriate gain matrix. Then, a continuous adaptive sliding mode controller based on the disturbance observer's output is designed using adaptive techniques and the system dimensional expansion method. The efficiency of the suggested strategy is finally tested numerically using the Duffing-Holmes chaotic system.
Article
Mathematics, Applied
Hui Fu, Yonggui Kao
Summary: This paper proposes two adaptive sliding mode control (ASMC) strategies for achieving finite-time synchronization of uncertain general fractional unified chaotic systems (UGFUCSs) in the presence of uncertainty and external disturbance. The general fractional unified chaotic system (GFUCS) is first developed, which can be transitioned from the general Lorenz system to the general Chen system using a general kernel function. Two ASMC methods are then employed to achieve finite-time synchronization of UGFUCSs, where the system states reach the sliding surfaces within a finite time. The first ASMC approach uses three sliding mode controllers for synchronization between chaotic systems, while the second ASMC method only requires one sliding mode controller. The effectiveness of the proposed ASMC approaches is verified through numerical simulations.
Article
Mathematics, Applied
Hao Wen, Zixuan Liang, Hexiong Zhou, Xinyang Li, Baoheng Yao, Zhihua Mao, Lian Lian
Summary: Sliding Mode Control is a type of robust control method, and this study proposes a new adaptive sliding mode control method that can handle the control problem for unknown uncertain non-linear systems without prior knowledge. The method can also ensure state error convergence at the same boundary for different systems. Two illustrative examples are presented to demonstrate the main features and applicability of the proposed method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Automation & Control Systems
Xiaowei Yang, Yaowen Ge, Wenxiang Deng, Jianyong Yao
Summary: This paper investigates an asymptotic adaptive dynamic surface tracking control strategy for uncertain full-state constrained nonlinear systems subject to parametric uncertainties and external disturbances. A novel disturbance estimator (DE) is used to compensate for external disturbances, while the parametric uncertainties are handled with a synthesized adaptive law. The backstepping design framework employs a novel adaptive-gain nonlinear filter, avoiding complexity explosion and conservatism of filter gain selection. The theoretical analysis confirms the assured asymptotic tracking performance with the proposed controller. Simulation cases demonstrate the validity of the proposed controller.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Ke Shao
Summary: This paper introduces a nested adaptive integral terminal sliding mode control scheme for high-order uncertain nonlinear systems, which eliminates the reaching phase and stabilizes the system in finite time. The proposed method achieves finite-time origin convergence without reaching phase, nonoverestimation, nonsingular and chattering-free control signal, providing advantages over conventional methods.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2021)
Article
Computer Science, Information Systems
Yufei Liang, Dong Zhang, Guodong Li, Tao Wu
Summary: This paper proposes a novel controller for the trajectory tracking problem with unknown uncertainties utilizing PIDSM and a variable gain hyperbolic reaching law. The control effect is significantly improved by introducing a PID-type sliding mode surface and a variable gain hyperbolic approach law. The simultaneous redesign of the sliding mode surface and reaching law ensures the robustness and tracking accuracy of the uncertain system. The combination of adaptive estimation and sliding mode control further enhances the tracking accuracy and robustness of the system.
Article
Computer Science, Interdisciplinary Applications
Hocine Takhi, Karim Kemih, Lazaros Moysis, Christos Volos
Summary: Passivity-based sliding mode control is applied to a unified chaotic system with uncertainties and perturbations. By combining sliding mode and passivity method, a switching surface is designed for stability. The proposed design is effective for stabilizing uncertain perturbed systems and synchronizing chaotic systems with uncertainties.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Automation & Control Systems
Anbang Zhai, Jin Wang, Haiyun Zhang, Guodong Lu, Howard Li
Summary: This paper investigates the cooperative robotic manipulators under uncertain base coordinate and proposes an adaptive robust controller to solve the problem. Mathematical proof and numerical experiments are conducted to demonstrate its effectiveness.
Article
Engineering, Mechanical
Yana Yang, Xiaoshuang Zhou, Junpeng Li
Summary: This article aims to design a fixed-time control scheme for a class of uncertain bridge crane systems. A novel two-layer adaptive disturbance observer (TADO) based on the principle of equivalent control is designed to handle unknown external disturbances in the complex environment. A novel continuous nonsingular terminal sliding mode (CNTSM) controller is proposed to achieve the control objective of bridge crane system in fixed time based on the estimated disturbances.
NONLINEAR DYNAMICS
(2023)
Article
Automation & Control Systems
Ke Shao, Jinchuan Zheng, Rongchuan Tang, Xiu Li, Zhihong Man, Bin Liang
Summary: This article presents a barrier function based adaptive sliding mode control scheme for uncertain nonlinear systems with actuator saturation. The proposed method can adapt to time-varying disturbances and does not require the upper bound information of disturbance.
IEEE-ASME TRANSACTIONS ON MECHATRONICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Alfredo Roldan-Caballero, J. Humberto Perez-Cruz, Eduardo Hernandez-Marquez, Jose Rafael Garcia-Sanchez, Mario Ponce-Silva, Jose de Jesus Rubio, Miguel Gabriel Villarreal-Cervantes, Jesus Martinez-Martinez, Enrique Garcia-Trinidad, Alejandro Mendoza-Chegue
Summary: This paper presents the design of an adaptive controller to solve the synchronization control problem of two identical Nwachioma chaotic systems in a master-slave configuration. The closed-loop stability is guaranteed by a Lyapunov-like analysis. Numerical simulations comparing the proposed approach with an active control algorithm are conducted to verify feasibility and performance. Experimental testing of the master-slave Nwachioma chaotic system using two personal computers and two low-cost Arduino UNO boards demonstrates both the effectiveness of the adaptive control and the suitability of Arduino UNO boards for the experimental setup.
Article
Multidisciplinary Sciences
Xiaopei Liu, Lin Sun
Summary: In this research, an adaptive control strategy based on fuzzy sliding mode control is developed and applied to chaotic vibration control of a multi-dimension nonlinear dynamic system of a laminated composite cantilever beam. The study reveals the importance of considering the multi-dimensional nonlinear dynamic system of the cantilever beam for accurate vibration estimation.
SCIENTIFIC REPORTS
(2023)
Article
Automation & Control Systems
Qingdong Sun, Junchao Ren, Yuqi Guo
Summary: This paper investigates the issue of dynamic event-triggered sliding mode control for uncertain discrete-time systems with disturbances based on the reaching law. It proposes a dynamic event-triggered mechanism to enhance the data utilization rate and introduces an observer accordingly. The paper also designs an observer-based linear sliding surface and a sliding mode controller based on a chattering-free reaching law to ensure the reachability of the sliding region.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(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)