Article
Computer Science, Artificial Intelligence
Xia Wang, Bin Xu, Peng Shi, Shuai Li
Summary: This paper investigates the synchronization control problem for a class of fractional-order chaotic systems with unknown dynamics and disturbance. A new design scheme is proposed to achieve higher synchronization accuracy and better estimation performance. The controller is constructed using neural approximation and disturbance estimation, and the simulation results demonstrate the effectiveness of the proposed approach.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Mathematics, Interdisciplinary Applications
Ali Durdu, Yilmaz Uyaroglu
Summary: The performance of two popular synchronization methods, active control and P-C methods, for secure communication application were compared in this study. It was found that the P-C method had a shorter synchronization time and was more suitable for secure communication applications.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Fei Qi, Jianfeng Qu, Yi Chai, Liping Chen, Antonio M. Lopes
Summary: This paper investigates the synchronization of incommensurate fractional-order (FO) chaotic systems and proposes a sufficient condition for achieving synchronization using linear matrix inequalities (LMIs). The effectiveness and feasibility of the method are demonstrated through examples involving two typical FO chaotic systems.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Joel Perez Padron, Jose P. Perez, Jose Javier Perez Diaz, Carlos Astengo-Noguez
Summary: In this research, time-delay adaptive synchronization and adaptive anti-synchronization of chaotic fractional order systems are analyzed using the Caputo fractional derivative. The problem of synchronization and anti-synchronization of chaotic systems with variable fractional order is solved using the fractional order PID control law, adaptive laws of variable-order fractional calculus, and a control law derived from Lyapunov's theory extended to systems of time-delay variable-order fractional calculus. This research solves two important problems in the control area: synchronization of chaotic systems with adaptive fractional order and time delay using the fractional order PID control law and adaptive laws, and anti-synchronization of chaotic systems with adaptive fractional order and time delay using the fractional order PID control law and adaptive laws.
FRACTAL AND FRACTIONAL
(2023)
Article
Automation & Control Systems
Sanjay Kumar, Ahmed E. Matouk, Harindri Chaudhary, Shashi Kant
Summary: This article introduces the basic concepts of fractional calculus and control, discussing the existence and uniqueness solutions of fractional-order satellite system and studying the local stability of the system at equilibrium points. Through the use of fractional dynamics and computational simulation, the lowest dimension of chaotic attractor of satellite system is determined. Chaos control and synchronization of two identical noninteger order chaotic satellite systems are achieved through feedback control method and adaptive control methodology, respectively.
INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING
(2021)
Article
Computer Science, Information Systems
Madini O. Alassafi, Shumin Ha, Fawaz E. Alsaadi, Adil M. Ahmad, Jinde Cao
Summary: An adaptive command filtered fuzzy synchronization approach is implemented for strict feedback fractional-order chaotic systems, solving computational explosion in backstepping using a fractional-order command filter and error compensation mechanism, ensuring stability of synchronization errors.
INFORMATION SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Yanbin Zhang, Ping Lin, Weigang Sun
Summary: This paper investigates circuit implementation and anti-synchronization in coupled nonidentical fractional-order chaotic systems. A fractance module is introduced to approximate the fractional derivative. A nonlinear coupling strategy is designed and proved by stability theory to achieve anti-synchronization in the fractional-order Rucklidge chaotic systems. Circuit experiments are conducted to validate the theoretical results and suggest potential applications in secure communication and data encryption.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics
Runlong Peng, Cuimei Jiang, Rongwei Guo
Summary: This paper investigates the partial anti-synchronization problem of fractional-order chaotic systems through dynamic feedback control method. Necessary and sufficient conditions are proposed and an algorithm is given to obtain all solutions. The designed single-input controllers are used to realize the partial anti-synchronization problem, which is verified through numerical simulations in two illustrative examples.
Article
Mathematics
Joel Perez Padron, Jose Paz Perez, Jose Javier Perez Diaz, Atilano Martinez Huerta
Summary: In this research paper, the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations is solved using PID control theory and Lyapunov-Krasovskii stability theory. The results obtained through simulation with examples demonstrate satisfactory outcomes in achieving synchronization and anti-synchronization of chaotic systems of a variable fractional order with discrete time delay.
Article
Mathematics
Masoumeh Firouzjahi, Bashir Naderi, Yousef Edrisi Tabriz
Summary: This paper focuses on the adaptive consensus problem of incommensurate chaotic fractional order multiagent systems. The paper introduces the fractional-order derivative in the sense of Caputo and the classical stability theorem of linear fractional order systems. It also presents algebraic graph theory and sufficient conditions for ensuring consensus in fractional multiagent systems. Furthermore, the paper designs adaptive protocols using local information for each agent and provides a detailed analysis of the leader-following consensus. Numerical simulation examples are given to demonstrate the effectiveness of the proposed results.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Nanxiang Yu, Wei Zhu
Summary: This paper investigates the synchronization of fractional-order differential chaotic systems using event-triggered impulsive control, combining the advantages of impulsive control and event-triggered control. By reducing the update frequency of the controller, the consumption of communication bandwidth and computing resources can be further reduced, while excluding Zeno-behavior of the impulsive sequence. The theoretical results are validated through a numerical example with simulation.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Interdisciplinary Applications
J. L. Echenausia-Monroy, C. A. Rodriguez-Martine, L. J. Ontanon-Garcia, J. Alvarez, J. Pena Ramirez
Summary: This study examines the effectiveness of dynamic coupling as a synchronization strategy for fractional chaotic systems, identifying regions where complete synchronization occurs in the coupled systems. The integration order is considered a key parameter, with statistical metrics and linearized error dynamics used to study the local stability of synchronous solutions. Results show that the integration order affects not only the onset of full synchronization but also the individual dynamic behavior of uncoupled systems.
Article
Computer Science, Artificial Intelligence
Kayode S. Ojo, Samuel T. Ogunjo, Ibiyinka A. Fuwape
Summary: The paper investigates a new hybrid synchronization method called modified hybrid synchronization (MHS) using the active control technique. Stable controllers were derived to achieve the coexistence of complete synchronization and anti-synchronization in four identical fractional order chaotic systems. Numerical simulations were conducted to confirm the effectiveness of the proposed technique.
Article
Mathematics, Interdisciplinary Applications
Runzi Luo, Shuai Liu, Zijun Song, Fang Zhang
Summary: This paper investigates the fixed-time control of a class of fractional-order systems via the backstepping method. A new fractional-order fixed-time stability theorem, which is a generalization of the integer order stability theorem, is presented. By using the proposed stability theorem, the fixed-time control problem of a class of fractional-order chaotic systems is investigated. Some fixed-time convergence criteria which have some pretty properties such as no singularity and no chattering are presented via backstepping method. Simulation results are given to show the effectiveness of the presented results.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Electrical & Electronic
Xin Meng, Zhengtian Wu, Cunchen Gao, Baoping Jiang, Hamid Reza Karimi
Summary: This brief introduces a method for addressing the problem of finite-time projective synchronization of variable-order fractional chaotic systems using sliding mode control. The method involves designing novel sliding surfaces and control strategies to ensure system stability and obtaining a criterion for finite-time stability.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Physics, Multidisciplinary
Vijay K. Yadav, Rakesh Kumar, A. Y. T. Leung, Subir Das
CHINESE JOURNAL OF PHYSICS
(2019)
Article
Computer Science, Interdisciplinary Applications
Shubham Jaiswal, Manish Chopra, S. Das
MATHEMATICS AND COMPUTERS IN SIMULATION
(2019)
Article
Computer Science, Artificial Intelligence
Rakesh Kumar, Subir Das
NEURAL COMPUTING & APPLICATIONS
(2020)
Article
Mathematics, Interdisciplinary Applications
Vijay K. Yadav, Vijay K. Shukla, Subir Das
CHAOS SOLITONS & FRACTALS
(2019)
Article
Mechanics
A. Singh, S. Das, E-M Craciun
MECHANICS OF COMPOSITE MATERIALS
(2019)
Article
Physics, Multidisciplinary
Prashant Pandey, Sachin Kumar, Subir Das
EUROPEAN PHYSICAL JOURNAL PLUS
(2019)
Article
Mathematics, Applied
Sachin Kumar, Prashant Pandey, Subir Das
COMPUTATIONAL & APPLIED MATHEMATICS
(2019)
Article
Mathematics, Applied
Rakesh Kumar, Subir Das
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2020)
Article
Mechanics
E. M. Craciun, A. Rabaea, S. Das
JOURNAL OF MECHANICS
(2020)
Article
Computer Science, Artificial Intelligence
Rakesh Kumar, Subir Das, Yang Cao
Article
Mathematics, Applied
A. Singh, S. Das, H. Altenbach, E. -M. Craciun
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2020)
Article
Thermodynamics
Anup Singh, S. Das
JOURNAL OF POROUS MEDIA
(2019)
Article
Engineering, Mechanical
Anup Singh, S. Das, S. H. Ong, H. Jafari
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2019)
Article
Engineering, Multidisciplinary
Vijay K. Yadav, Vijay K. Shukla, Mayank Srivastava, Subir Das
JOURNAL OF APPLIED NONLINEAR DYNAMICS
(2020)
Article
Engineering, Mechanical
Vijay K. Yadav, S. Das
NONLINEAR ENGINEERING - MODELING AND APPLICATION
(2019)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
