Article
Mathematics, Applied
Yanxia Zhang, Yanfei Jin, Yang Li
Summary: This study investigates the effects of time-delayed feedback control on a vibration energy harvester mounted on a rotating automobile tire, showing that time delay can either enhance or weaken stochastic resonance behavior.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Automation & Control Systems
Eli Gershon, Uri Shaked
Summary: This article introduces a descriptor method for designing static output-feedback controllers for linear, continuous-time, retarded, stochastic systems with a prescribed H-infinity performance. A design solution is obtained for the uncertain case, where the parameters of the system matrices reside in a given polytope. The theory is also extended to the gain-scheduling case and demonstrated through two examples.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Automation & Control Systems
Feng Wang, Xiuting Sun, Hao Meng, Jian Xu
Summary: This article studies the vibration absorption performances of a vibration absorber with time-delayed feedback control for a low frequency primary system. The stiffness of the absorber is designed as an adjustable parameter to extend its effective working frequency band. Two parameter design principles based on the antiresonance frequency and optimum condition are proposed for controlling the vibration amplitude of low-frequency nonlinear primary systems.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2021)
Article
Automation & Control Systems
Bin Zhou, Zhe Zhang, Wim Michiels
Summary: This paper addresses the prescribed-time output feedback stabilization problem for linear systems using a functional observer and a dual observer. The proposed feedback achieves prescribed-time convergence of the state to zero and is more efficient compared to existing periodic control methods.
Article
Physics, Multidisciplinary
Mei Liu, Binglong Lu, Zhanfeng Li, Haijun Jiang, Cheng Hu
Summary: This paper investigates the fixed-time synchronization problem for delayed dynamical complex networks and proposes new results and methods to achieve fixed-time synchronization. By designing adaptive controllers and discontinuous feedback controllers, fixed-time synchronization can be achieved by adjusting the main control parameters. The introduction of a new theorem aims to reduce conservatism in existing work, including conditions and synchronization time estimates.
Article
Automation & Control Systems
Lucas T. F. de Souza, Marcia L. C. Peixoto, Reinaldo M. Palhares
Summary: This paper investigates stability and state-feedback control design for linear parameter-varying systems with time-varying delays. The new conditions for stability and control design are based on Lyapunov theory and Linear Matrix Inequalities. The proposed methodology employs a parameter-dependent Lyapunov-Krasovskii functional and handles the time-derivative using integral inequalities for quadratic functions. The main results include a novel stability condition for delay-dependent systems and a new condition for designing gain-scheduled state-feedback controllers. An example based on a real-world problem is provided to demonstrate the effectiveness of the proposed method.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Yunfei Dai, Yujuan Wang, Chao Wang
Summary: This article investigates the problem of finite-time tracking control for a class of nonlinear pure-feedback systems with both time-varying state delays and control input delays, proposing a new performance function and a novel construction of the Lyapunov-Krasovskii (LK) function. In addition, a continuous package function is introduced to handle the unknown nonlinear terms arising from uncertain perturbation and the derivation of the LK function. Simulation examples demonstrate the effectiveness of the proposed approach.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Engineering, Mechanical
Gao Hong, Deng Zhongmin, Zhao Yanlin, Yan Hongbo, Zhang Xinjie, Meng Lingzi, Luo Qi
Summary: In this study, a time-delayed displacement and velocity feedback controller was designed to improve the nonlinear dynamic characteristics and stability of a giant magnetostrictive actuator system. The results showed that the velocity feedback gain and time delay parameters had a significant impact on the stability of the primary resonance, chaotic motion, and limit cycle amplitude.
NONLINEAR DYNAMICS
(2022)
Article
Automation & Control Systems
Fatemeh Shojaei, Jafar Zarei, Mehrdad Saif
Summary: This paper proposes an adaptive dynamic surface controller for uncertain time-delay non-strict nonlinear systems with unknown control direction and unknown dead zone. The uncertainty in nonlinear terms is managed by using a fuzzy logic and an adaptive approach. A specific observer is designed to approximate the immeasurable states. The stability of the closed-loop system is ensured and the effectiveness of the proposed controller is validated through a practical simulation.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Mechanical
Haojie Liu, Xiumin Gao
Summary: This study investigates the time-delayed feedback control for a rectangular prism undergoing galloping under wind excitation. By using mathematical models and stability analysis, it is found that delayed acceleration feedback can achieve multiple control objectives and change bifurcation behavior.
NONLINEAR DYNAMICS
(2021)
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
Automation & Control Systems
Xin Yu, Wei Zhao, Jianwei Xia, Xiangyong Chen, Hao Shen
Summary: This paper investigates the fixed-time tracking control issue for a class of high-order nonlinear delayed systems subject to mismatched disturbances. The fuzzy logic system is applied to handle the nonlinear functions and the power integrator technique is introduced to address the high-order terms. Different from conventional methods, the adaptive backstepping method is utilized in this paper to cope with the delayed terms. The main objective is to design a suitable adaptive fuzzy fixed-time controller to ensure stability and boundedness of the closed-loop system in a fixed-time interval.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Jianpeng Ding, Youming Lei
Summary: The time-delayed feedback control method is a popular method for chaos control, but it faces challenges in choosing the feedback gain and overcoming the odd number limitation. Fortunately, deep reinforcement learning offers a solution by learning the controlled environment and providing a time-varying feedback gain. This data-driven method expands the operating range while maintaining the noninvasive property of the time-delayed feedback control.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Engineering, Civil
Weiqi Bai, Hairong Dong, Zixuan Zhang, Yidong Li
Summary: This study systematically investigates the coordinated control problem for a multiple high-speed train system subject to unknown communication delays. By constructing a nonlinear control model and designing distributed control laws, faster convergence rate during the train status adjustment process is achieved.
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
(2022)
Article
Automation & Control Systems
Zhen-Guo Liu, Hongli Dong, Weixing Chen, Weidong Zhang
Summary: This article investigates the adaptive regulation problem of uncertain delayed nonlinear systems and presents two unified adaptive control methods to achieve global asymptotic stability by introducing dynamic gain transformation and using homogeneous domination method.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Physics, Fluids & Plasmas
Isabelle Schneider, Marie Kapeller, Sarah Loos, Anna Zakharova, Bernold Fiedler, Eckehard Schoell
Article
Mathematics, Applied
Andre Roehm, Kathy Luedge, Isabelle Schneider
Article
Physics, Multidisciplinary
A. Zakharova, I. Schneider, Y. N. Kyrychko, K. B. Blyuss, A. Koseska, B. Fiedler, E. Schoell
Article
Multidisciplinary Sciences
Isabelle Schneider
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2013)
Article
Mathematics
Bernold Fiedler, Alejandro Lopez Nieto, Richard H. Rand, Si Mohamed Sah, Isabelle Schneider, Babette de Wolff
JOURNAL OF DIFFERENTIAL EQUATIONS
(2020)
Article
Mathematics, Applied
B. de Wolff, I Schneider
Summary: By studying the failure of Pyragas control on periodic orbits and equilibria, a fundamental observation on the invariance of the geometric multiplicity of the trivial Floquet multiplier was derived, leading to a clear understanding of the odd-number limitation. The study also revealed a necessary condition for successful control based on the geometric invariance of the determining center. Interestingly, the application of Pyragas control on equilibria showed a geometric invariance not only on the determining center but also on centers resonating with the time delay, resulting in the formulation of odd- and any-number limitations for different eigenvalue pairs and time delays.
Article
Mathematics, Applied
Isabelle Schneider, Babette de Wolff, Jia-Yuan Dai
Summary: In this article, certain significant classes of unstable spiral waves within circular and spherical geometries are selectively stabilized for the first time using the symmetry-breaking control triple method. This results in the obtaining of stable spiral waves with an arbitrary number of arms.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2022)
Article
Mathematics, Applied
I. Schneider, J. Y. Dai
Summary: Reaction-diffusion equations are widely used in various scientific domains, but observing unstable patterns can be challenging. In this study, we propose a new noninvasive feedback control method based on symmetry groupoids to selectively stabilize unstable equilibria. Unlike traditional reflection-based control schemes, our approach incorporates additional symmetries and designs new convolution controls, providing a new tool for investigating and controlling systems with unstable patterns.
Article
Mathematics, Applied
Bernold Fiedler, Isabelle Schneider
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2020)
Proceedings Paper
Physics, Applied
Isabelle Schneider, Bernold Fiedler
CONTROL OF SELF-ORGANIZING NONLINEAR SYSTEMS
(2016)
Article
Mathematics, Applied
Quanqing Li, Wenming Zou
Summary: In this paper, we investigate the existence of normalized ground state solutions to the Sobolev critical nonlinear Schrödinger equation. By using the Pohozaev manifold and the concentration-compactness principle, we obtain a couple of normalized solutions to the equation. Our main contribution is extending the previous results and answering an open problem raised by N. Soave.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2024)
Article
Mathematics, Applied
Rong Dong, Dongsheng Li
Summary: The paper discusses the regularity of elliptic equations in non-divergence form with homogenization. We establish uniform interior and boundary C-1,C-1 estimates in bounded C-2,C-Dini domains, provided that the coefficients and inhomogeneous terms of the equations are Dini continuous, and the boundary data are of C-2,C-Dini, which weakens the assumptions of some existence results.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2024)
Article
Mathematics, Applied
Jose A. Carrillo, Yingping Peng, Zhaoyin Xiang
Summary: This paper investigates a chemotaxis-fluid system with stronger and more nonlinear coupling than most studied models. The author establishes extensibility criteria and global existence of solutions based on a new entropy functional inequality. Decay estimates are also obtained. The work seems to be the first to address the global well-posedness and decay property of solutions to the self-consistent chemotaxis-fluid system.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2024)
Article
Mathematics, Applied
Benedetta Ferrario, Margherita Zanella
Summary: This study establishes the uniqueness and asymptotic stability of the invariant measure for the two-dimensional Navier-Stokes equations driven by multiplicative noise with various growth conditions. By utilizing the generalized asymptotic coupling techniques, the paper demonstrates the flexibility of these methods in dealing with multiplicative noise.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2024)
Article
Mathematics, Applied
Mumtaz Hussain, Bixuan Li, Nikita Shulga
Summary: In this study, we present a detailed analysis of the Hausdorff dimension of a set of real numbers where the product of consecutive partial quotients in their continued fraction expansion grows at a certain rate while the growth of the single partial quotient is at a different rate. We introduce the concept of two different types of probability measures supported on a suitably constructed Cantor type subset, and utilize the classical mass distribution principle to obtain surprising results, including the emptiness of the set for certain non-trivial choices of functions. Our findings contribute to the metrical theory of continued fractions and extend several known results.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2024)
