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Thematische Bibliographien / Time delayed feedback control (TDFC) / Zeitschriftenartikel

Zeitschriftenartikel zum Thema „Time delayed feedback control (TDFC)“

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Veröffentlicht am 22. Juli 2024

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1

BANERJEE, TANMOY, und B. C. SARKAR. „CONVENTIONAL AND EXTENDED TIME-DELAYED FEEDBACK CONTROLLED ZERO-CROSSING DIGITAL PHASE LOCKED LOOP“. International Journal of Bifurcation and Chaos 22, Nr. 12 (Dezember 2012): 1230044. http://dx.doi.org/10.1142/s0218127412300443.

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This article investigates the effect of the conventional and extended time-delayed feedback control techniques of chaos control on a first-order positive zero-crossing digital phase locked loop (ZC1-DPLL) using local stability analysis, two-parameter bifurcation studies and two-parameter Lyapunov exponent spectrum. Starting from the nonlinear dynamics of a ZC1-DPLL, we at first explore the time-delayed feedback control (TDFC) algorithm on a ZC1-DPLL in the parameter space. A condition for the optimum value of the system control parameter is derived analytically for a TDFC based ZC1-DPLL. Next, the extended time-delayed feedback control (ETDFC) technique on a ZC1-DPLL is described. It is observed that the application of the delayed feedback control (DFC) technique on the sampled values of the incoming signal inside the loop finally results in the nonlinear DFC of the phase error dynamics. We prove that, for some suitably chosen control parameters, an ETDFC based ZC1-DPLL has a broader stability zone in comparison with a ZC1-DPLL and its TDFC version.

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2

ROBERT, B., H. H. C. IU und M. FEKI. „ADAPTIVE TIME-DELAYED FEEDBACK FOR CHAOS CONTROL IN A PWM SINGLE PHASE INVERTER“. Journal of Circuits, Systems and Computers 13, Nr. 03 (Juni 2004): 519–34. http://dx.doi.org/10.1142/s0218126604001568.

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Many power converters exhibit chaotic behaviors and bifurcations when conventional feedback corrector are badly tuned or when parameters vary. Time-Delayed Feedback Control (TDFC) can be used to stabilize them using a state feedback delayed by the period of the unstable orbit (UPO) to be stabilized. An obvious advantage of this method is the robustness because it does not require the knowledge of an accurate model but only the period of the target UPO. In this paper, TDFC is applied to a PWM current-programmed single phase inverter concurrently with a proportional corrector in order to avoid bifurcations and chaos and to stabilize the fundamental UPO over a widened range of application. Moreover an improvement of the dynamical performances is realized by defining an adaptive law for the TDFC.

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3

Erneux, T., G. Kozyreff und M. Tlidi. „Bifurcation to fronts due to delay“. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, Nr. 1911 (28.01.2010): 483–93. http://dx.doi.org/10.1098/rsta.2009.0228.

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The stability of a steady-state front (kink) subject to a time-delayed feedback control (TDFC) is examined in detail. TDFC is based on the use of the difference between system variables at the current moment of time and their values at some time in the past. We first show that there exists a bifurcation to a moving front. We then investigate the limit of large delays but weak feedback and obtain a global bifurcation diagram for the propagation speed. Finally, we examine the case of a two-dimensional front with radial symmetry and determine the critical radius above which propagation is possible.

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4

Sun, Xiuting, Yipeng Qu, Feng Wang und Jian Xu. „Effects of time-delayed vibration absorber on bandwidth of beam for low broadband vibration suppression“. Applied Mathematics and Mechanics 44, Nr. 10 (30.09.2023): 1629–50. http://dx.doi.org/10.1007/s10483-023-3038-6.

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AbstractThe effects of time-delayed vibration absorber (TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given, and the results show that the introduction of time-delayed feedback control (TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam, and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.

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5

ROBERT, B., M. FEKI und H. H. C. IU. „CONTROL OF A PWM INVERTER USING PROPORTIONAL PLUS EXTENDED TIME-DELAYED FEEDBACK“. International Journal of Bifurcation and Chaos 16, Nr. 01 (Januar 2006): 113–28. http://dx.doi.org/10.1142/s0218127406014629.

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Pulse width modulation (PWM) current-mode single phase inverters are known to exhibit bifurcations and chaos when parameters vary or if the gain of the proportional controller is arbitrarily increased. Our aim in this paper is to show, using control theory and numerical simulations, how to apply a method to stabilize the interesting periodic orbit for larger values of the proportional gain. To accomplish this aim, a time-delayed feedback controller (TDFC) is used in conjunction with the proportional controller in its simple form as well as in its extended form (ETDFC). The main advantages of those methods are the robustness and ease of construction because they do not require the knowledge of an accurate model but only the period of the target unstable periodic orbit (UPO). Moreover, to improve the dynamical performances, an optimal criterion and an adaptive law are defined to determine the control parameters.

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6

BANERJEE, TANMOY, BISHWAJIT PAUL und B. C. SARKAR. „BIFURCATION, CHAOS AND THEIR CONTROL IN A TIME-DELAY DIGITAL TANLOCK LOOP“. International Journal of Bifurcation and Chaos 23, Nr. 08 (August 2013): 1330029. http://dx.doi.org/10.1142/s0218127413300292.

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This paper reports the detailed parameter space study of the nonlinear dynamical behaviors and their control in a time-delay digital tanlock loop (TDTL). At first, we explore the nonlinear dynamics of the TDTL in parameter space and show that beyond a certain value of loop gain parameter the system manifests bifurcation and chaos. Next, we consider two variants of the delayed feedback control (DFC) technique, namely, the time-delayed feedback control (TDFC) technique, and its modified version, the extended time-delayed feedback control (ETDFC) technique. Stability analyses are carried out to find out the stable phase-locked zone of the system for both the controlled cases. We employ two-parameter bifurcation diagrams and the Lyapunov exponent spectrum to explore the dynamics of the system in the global parameter space. We establish that the control techniques can extend the stable phase-locked region of operation by controlling the occurrence of bifurcation and chaos. We also derive an estimate of the optimum parameter values for which the controlled system has the fastest convergence time even for a larger acquisition range. The present study provides a necessary detailed parameter space study that will enable one to design an improved TDTL system.

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7

Wang, Deli, Wei Xu, Zhicong Ren und Haiqing Pei. „Maximal Lyapunov Exponents and Steady-State Moments of a VI System based Upon TDFC and VED“. International Journal of Bifurcation and Chaos 29, Nr. 11 (Oktober 2019): 1950155. http://dx.doi.org/10.1142/s0218127419501554.

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This paper focuses on the investigation of a vibro-impact (VI) system based upon time-delayed feedback control (TDFC) and visco-elastic damping (VED) under bounded random excitations. A pretreatment for the TDFC and VED is necessary. A further simplification for the system is achieved by introducing the mirror image transformation. The averaging approach is adopted to analyze the above system relying on a parametric principal resonance consideration. By means of the first kind of a modified Bessel function, explicit asymptotic formulas for the maximal Lyapunov exponent (MLE) are given to examine the almost sure stability or instability of the trivial steady-state amplitude solution. Besides, the steady-state moments (SSM) of the nontrivial solutions of the system’s amplitude are derived by the application of the moment method and Itô’s calculus. Finally, the stability and its critical situations of the trivial solution are explored in detail through the important system parameters, i.e. embodying the TDFC parameters, the VED parameters, the restitution coefficient, the excitation amplitude and the random noise intensity. They are tested by numerical simulations. Additionally, the exploration of the steady-state moments involves the emergence of the general frequency response curve and the frequency island, discussions of conditions satisfied by the unstable boundary, and variations of the time-delayed island. Stochastic jumps and bifurcations are observed for the stationary joint transition probability density of the system’s trivial and nontrivial solutions based on parameter schemes of VED and TDFC.

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8

Xiao, Jianli, Hanli Xiao, Xinchang Zhang und Xiang You. „Stability, Bifurcation, and Chaos Control of Two-Sided Market Competition“. International Journal of Computer Games Technology 2022 (17.08.2022): 1–10. http://dx.doi.org/10.1155/2022/6006450.

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Benefitting from the popular uses of internet technologies, two-sided market has been playing an increasing prominent role in modern times. Users and developers can interact with each other through two-sided platforms. The two-sided market structure has been investigated profoundly. Through building a dynamics two-sided market model with bounded rational, stability conditions of the two-sided market competition system are presented. With the help of bifurcation diagram, Lyapunov exponent, and strange attractor, the stability of the two-sided market competition model is simulated. At last, we use the time-delayed feedback control (TDFC) method to control the chaos. Our main results are as follows: (1) when the adjustment speed of two-sided increases, the system becomes bifurcation, and chaos state happens finally. When the system is stable, the consumer fee is positive while developer fee is negative. (2) When the user externality increases, the stable area of the system increases, and the difference in user externality leads the whole system more stable. When the system is stable, the developer fee decreases. (3) The stable area becomes larger when developer externality increases; when the system is stable, the user fee becomes lower and developer fee becomes higher when developer externality increases. (4) The TDFC method is presented for controlling the chaos; we find that the system becomes more stable under the TDFC method.

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Arafa, Ayman A., Yong Xu und Gamal M. Mahmoud. „Chaos Suppression via Integrative Time Delay Control“. International Journal of Bifurcation and Chaos 30, Nr. 14 (November 2020): 2050208. http://dx.doi.org/10.1142/s0218127420502089.

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A general strategy for suppressing chaos in chaotic Burke–Shaw system using integrative time delay (ITD) control is proposed, as an example. The idea of ITD is that the feedback is integrated over a time interval. Physically, the chaotic system responds to the average information it receives from the feedback. The main feature of integrative is that the stability of the chaotic system occurs over a wider range of the space parameters. Controlling chaotic systems with ITD has not been discussed before as far as we know. Stability and the existence of Hopf bifurcation are studied which demonstrate that the switch stability occurs at critical values of the time delay. Employing the normal form theory and center manifold argument, an explicit formula is derived to determine the stability and the direction of the bifurcating periodic solutions. Numerically, the bifurcation diagram and the eigenvalues of the corresponding characteristic equations are computed to supply a clear interpretation for suppressing chaos via ITD. Furthermore, ITD method is compared with the time delayed feedback (TDF) control numerically. This comparison shows that the stability area with ITD is larger than TDF which demonstrates the feasibility and effectiveness of the ITD. Other examples of chaotic systems can be similarly investigated.

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10

Xiao, Jianli, und Hanli Xiao. „The Complexities in the R&D Competition Model with Spillover Effects in the Supply Chain“. Complexity 2024 (28.02.2024): 1–15. http://dx.doi.org/10.1155/2024/3152363.

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This study aims to investigate the research and development (R&D) competition within the supply chain, focusing on two aspects: R&D competition at the manufacturing level and competition in pricing strategies. This paper establishes a dynamic game model of R&D competition, comprising two manufacturers and two retailers, with both manufacturers exhibiting bounded rationality. The key findings are as follows: (1) an increase in the adjustment speed positively affects the chaotic nature of the R&D competition system, leading to a state of disorder. This chaotic state has adverse implications for manufacturing profitability. (2) The spillover effect exhibits a positive relationship with the level of chaos in the R&D competition system. A greater spillover effect contributes to a more turbulent environment, which subsequently impacts the profitability of manufacturers. (3) R&D cost parameters exert a positive influence on the stability of the R&D competition system. When the system reaches a state of equilibrium, an escalation in the R&D cost parameters poses a threat to manufacturer profitability. (4) Retailer costs play a detrimental role in the stability of the R&D competition system. As retailer costs increase, there is a decline in R&D levels, thereby diminishing manufacturer profitability. (5) To mitigate the chaotic state, we propose the implementation of the time-delayed feedback control (TDFC) method, which reflects a more stable state in the R&D competition system.

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11

Vasegh, Nastaran, und Ali Khaki Sedigh. „Chaos control via TDFC in time-delayed systems: The harmonic balance approach“. Physics Letters A 373, Nr. 3 (Januar 2009): 354–58. http://dx.doi.org/10.1016/j.physleta.2008.11.050.

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12

Zhang, Jinke, Xiaojie Wu, Lvshuai Xing, Chao Zhang, Herbert Iu und Tyrone Fernando. „Bifurcation Analysis of Five-Level Cascaded H-Bridge Inverter Using Proportional-Resonant Plus Time-Delayed Feedback“. International Journal of Bifurcation and Chaos 26, Nr. 11 (Oktober 2016): 1630031. http://dx.doi.org/10.1142/s0218127416300317.

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In this paper, a traditional five-level cascaded H-bridge inverter is studied and regulated by a proportional-resonant (PR) controller. In order to extend the range of the gain of PR controller, for the purpose of achieving a fast response, a time-delayed feedback controller (TDFC) is used. Similar to the pulse width modulation (PWM) current-mode single phase H-bridge inverter that exhibits bifurcation and chaos when parameters vary, we demonstrate for the first time that the cascaded H-bridge inverter also shows similar features. From the perspective of a discontinuous map, the cascaded H-bridge inverter generally displays extraordinary complexity. Moreover, a new virtual ergodic method (VEM) is proposed to establish the mathematical model of the whole system, which helps to understand the observed bifurcation phenomena. Simulation results are given to verify the analysis.

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13

Schöll, Eckehard, Judith Lehnert, Thomas Dahms, Anton Selivanov und Alexander L. Fradkov. „Adaptive time-delayed feedback control“. IEICE Proceeding Series 1 (17.03.2014): 674–77. http://dx.doi.org/10.15248/proc.1.674.

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14

Biggs, James D., und Colin R. McInnes. „Time-Delayed Feedback Control in Astrodynamics“. Journal of Guidance, Control, and Dynamics 32, Nr. 6 (November 2009): 1804–11. http://dx.doi.org/10.2514/1.43672.

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15

Just, Wolfram, Thomas Bernard, Matthias Ostheimer, Ekkehard Reibold und Hartmut Benner. „Mechanism of Time-Delayed Feedback Control“. Physical Review Letters 78, Nr. 2 (13.01.1997): 203–6. http://dx.doi.org/10.1103/physrevlett.78.203.

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16

Just, Wolfram, Ekkehard Reibold, Harmut Benner, Krzysztof Kacperski, Piotr Fronczak und Janusz Hołyst. „Limits of time-delayed feedback control“. Physics Letters A 254, Nr. 3-4 (April 1999): 158–64. http://dx.doi.org/10.1016/s0375-9601(99)00113-9.

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17

Mehendale, Charudatta S., und Karolos M. Grigoriadis. „CONTROL OF TIME-DELAYED LPV SYSTEMS USING DELAYED FEEDBACK“. IFAC Proceedings Volumes 38, Nr. 1 (2005): 249–54. http://dx.doi.org/10.3182/20050703-6-cz-1902.00612.

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18

Block, M., und E. Schöll. „Time delayed feedback control in growth phenomena“. Journal of Crystal Growth 303, Nr. 1 (Mai 2007): 30–33. http://dx.doi.org/10.1016/j.jcrysgro.2006.10.254.

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19

Sieber, J. „Generic stabilizability for time-delayed feedback control“. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, Nr. 2189 (Mai 2016): 20150593. http://dx.doi.org/10.1098/rspa.2015.0593.

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Time-delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current output and the output from a fixed time T ago. Thus, any periodic orbit of period T in the feedback-controlled system is also a periodic orbit of the uncontrolled system, independent of any modelling assumptions. It has been an open problem whether this approach can be successful in general, that is, under genericity conditions similar to those in linear control theory (controllability), or if there are fundamental restrictions to time-delayed feedback control. We show that, in principle, there are no restrictions. This paper proves the following: for every periodic orbit satisfying a genericity condition slightly stronger than classical linear controllability, one can find control gains that stabilize this orbit with extended time-delayed feedback control. While the paper’s techniques are based on linear stability analysis, they exploit the specific properties of linearizations near autonomous periodic orbits in nonlinear systems, and are, thus, mostly relevant for the analysis of nonlinear experiments.

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20

Lehnert, J., P. Hövel, V. Flunkert, P. Yu Guzenko, A. L. Fradkov und E. Schöll. „Adaptive tuning of feedback gain in time-delayed feedback control“. Chaos: An Interdisciplinary Journal of Nonlinear Science 21, Nr. 4 (Dezember 2011): 043111. http://dx.doi.org/10.1063/1.3647320.

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21

Pyragas, Kestutis. „Delayed feedback control of chaos“. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, Nr. 1846 (27.07.2006): 2309–34. http://dx.doi.org/10.1098/rsta.2006.1827.

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Time-delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. The method is based on applying feedback perturbation proportional to the deviation of the current state of the system from its state one period in the past, so that the control signal vanishes when the stabilization of the target orbit is attained. A brief review on experimental implementations, applications for theoretical models and most important modifications of the method is presented. Recent advancements in the theory, as well as an idea of using an unstable degree of freedom in a feedback loop to avoid a well-known topological limitation of the method, are described in detail.

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22

GUAN, XINPING, CAILIAN CHEN, HAIPENG PENG und ZHENGPING FAN. „TIME-DELAYED FEEDBACK CONTROL OF TIME-DELAY CHAOTIC SYSTEMS“. International Journal of Bifurcation and Chaos 13, Nr. 01 (Januar 2003): 193–205. http://dx.doi.org/10.1142/s021812740300642x.

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This paper addresses time-delayed feedback control (DFC) of time-delay chaotic systems. To extend the DFC approach to time-delay chaotic system, alter having been successfully used in chaotic systems without time-delays, the standard feedback control (SFC) method is firstly employed to show the main control technique in this paper based on one error control system. Then sufficient conditions for stabilization and tracking problems via DFC are derived from the results based on SFC. Also, the systematic and analytic controller design method can be obtained to stabilize the system to an unstable fixed point and to tracking an unstable periodic orbit, respectively. Some numerical examples are provided to demonstrate the effectiveness of the presented method.

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23

LI, P., Y. Z. LIU, K. L. HU, B. H. WANG und H. J. QUAN. „THE CHAOTIC CONTROL ON THE OCCASIONAL NONLINEAR TIME-DELAYED FEEDBACK“. International Journal of Modern Physics B 18, Nr. 17n19 (30.07.2004): 2680–85. http://dx.doi.org/10.1142/s0217979204025907.

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The method of controlling chaos by occasional nonlinear time-delayed feedback is proposed. Through the numerical analysis of bifurcation diagram and Lyapunov exponent, we found that the systematic chaos can be controlled effectively by the nonlinear time-delayed feedback as the form of u(xn,xn-k)=cxnxn-k. Under the proper feedback coefficient c, time-delayed coefficient k and occasional feedback period N, the system could be controlled from chaos to the steady periodic orbit, and also the steady period is the integral multiple of the occasional feedback period N.

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24

Guanrong Chen und Xinghuo Yu. „On time-delayed feedback control of chaotic systems“. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 46, Nr. 6 (Juni 1999): 767–72. http://dx.doi.org/10.1109/81.768837.

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25

Zakharova, Anna, Nadezhda Semenova, Vadim Anishchenko und Eckehard Schöll. „Time-delayed feedback control of coherence resonance chimeras“. Chaos: An Interdisciplinary Journal of Nonlinear Science 27, Nr. 11 (November 2017): 114320. http://dx.doi.org/10.1063/1.5008385.

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26

Chatterjee, S. „Time-delayed feedback control of friction-induced instability“. International Journal of Non-Linear Mechanics 42, Nr. 9 (November 2007): 1127–43. http://dx.doi.org/10.1016/j.ijnonlinmec.2007.08.002.

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27

Chatterjee, S. „Vibration control by recursive time-delayed acceleration feedback“. Journal of Sound and Vibration 317, Nr. 1-2 (Oktober 2008): 67–90. http://dx.doi.org/10.1016/j.jsv.2008.03.020.

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28

Fichtner, Andreas, Wolfram Just und Günter Radons. „Analytical investigation of modulated time-delayed feedback control“. Journal of Physics A: Mathematical and General 37, Nr. 10 (24.02.2004): 3385–91. http://dx.doi.org/10.1088/0305-4470/37/10/005.

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29

Just, Wolfram, Dirk Reckwerth, Ekkehard Reibold und Hartmut Benner. „Influence of control loop latency on time-delayed feedback control“. Physical Review E 59, Nr. 3 (01.03.1999): 2826–29. http://dx.doi.org/10.1103/physreve.59.2826.

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30

CHEN, GUANRONG, JIALIANG LU, BRENT NICHOLAS und SWATIPRAKASH M. RANGANATHAN. „BIFURCATION DYNAMICS IN CONTROL SYSTEMS“. International Journal of Bifurcation and Chaos 09, Nr. 01 (Januar 1999): 287–93. http://dx.doi.org/10.1142/s021812749900016x.

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This paper is to report the observation that when the popular time-delayed feedback strategy is used for control purpose, it may actually create unwanted bifurcations. Hopf bifurcation created by delayed feedback control is the main concern of this article, but some other types of bifurcations are also observed to exist in such delayed-feedback control systems. The observations are illustrated by computer simulations.

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31

Sipahi, Rifat, und Nejat Olgac. „Active Vibration Suppression With Time Delayed Feedback“. Journal of Vibration and Acoustics 125, Nr. 3 (18.06.2003): 384–88. http://dx.doi.org/10.1115/1.1569942.

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Various active vibration suppression techniques, which use feedback control, are implemented on the structures. In real application, time delay can not be avoided especially in the feedback line of the actively controlled systems. The effects of the delay have to be thoroughly understood from the perspective of system stability and the performance of the controlled system. Often used control laws are developed without taking the delay into account. They fulfill the design requirements when free of delay. As unavoidable delay appears, however, the performance of the control changes. This work addresses the stability analysis of such dynamics as the control law remains unchanged but carries the effect of feedback time-delay, which can be varied. For this stability analysis along the delay axis, we follow up a recent methodology of the authors, the Direct Method (DM), which offers a unique and unprecedented treatment of a general class of linear time invariant time delayed systems (LTI-TDS). We discuss the underlying features and the highlights of the method briefly. Over an example vibration suppression setting we declare the stability intervals of the dynamics in time delay space using the DM. Having assessed the stability, we then look at the frequency response characteristics of the system as performance indications.

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32

Peng, Jian, Mingjiao Xiang, Luxin Li, Hongxin Sun und Xiuyong Wang. „Time-Delayed Feedback Control of Piezoelectric Elastic Beams under Superharmonic and Subharmonic Excitations“. Applied Sciences 9, Nr. 8 (15.04.2019): 1557. http://dx.doi.org/10.3390/app9081557.

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The time-delayed displacement feedback control is provided to restrain the superharmonic and subharmonic response of the elastic support beams. The nonlinear equations of the controlled elastic beam are obtained with the help of the Euler–Bernoulli beam principle and time-delayed feedback control strategy. Based on Galerkin method, the discrete nonlinear time-delayed equations are derived. Using the multiscale method, the first-order approximate solutions and stability conditions of three superharmonic and 1/3 subharmonic resonance response on controlled beams are derived. The influence of time-delayed parameters and control gain are obtained. The results show that the time-delayed displacement feedback control can effectively suppress the superharmonic and subharmonic resonance response. Selecting reasonably the time-delayed quantity and control gain can avoid the resonance region and unstable multi-solutions and improve the efficiency of the vibration control. Furthermore, with the purpose of suppressing the amplitude peak and governing the resonance stability, appropriate feedback gain and time delay are derived.

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Su, Huan, und Jing Xu. „Time-Delayed Sampled-Data Feedback Control of Differential Systems Undergoing Hopf Bifurcation“. International Journal of Bifurcation and Chaos 31, Nr. 01 (Januar 2021): 2150004. http://dx.doi.org/10.1142/s0218127421500048.

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In this paper, time-delayed sampled-data feedback control technique is used to asymptotically stabilize a class of unstable delayed differential systems. Through the analysis for the distribution change of eigenvalues, an effective interval of the control parameter is obtained for a given sampling period. Here an indirect strategy is taken. Specifically, the system of continuous-time delayed feedback control is studied first by Hopf bifurcation theory. And then, the result and implicit function theorem are used to analyze the system of time-delayed sampled-data feedback control with a sufficiently small sampling period. Considering the practical criterion for the size of sampling period, the upper bound of sampling period is estimated. Finally, an application example, an unstable Mackey–Glass model, is asymptotically stabilized by introducing a blood transfusion item with time-delayed sampled-data feedback control. The blood transfusion speed and blood collection test period are derived from the main results. Some simulations and comparisons show the correctness and advantages of the main theoretical results.

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TIAN, YU-PING, XINGHUO YU und LEON O. CHUA. „TIME-DELAYED IMPULSIVE CONTROL OF CHAOTIC HYBRID SYSTEMS“. International Journal of Bifurcation and Chaos 14, Nr. 03 (März 2004): 1091–104. http://dx.doi.org/10.1142/s0218127404009612.

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This paper presents a time-delayed impulsive feedback approach to the problem of stabilization of periodic orbits in chaotic hybrid systems. The rigorous stability analysis of the proposed method is given. Using the time-delayed impulsive feedback method, we analyze the problem of detecting various periodic orbits in a special class of hybrid system, a switched arrival system, which is a prototype model of many manufacturing systems and computer systems where a large amount of work is processed in a unit time. We also consider the problem of stabilization of periodic orbits of chaotic piecewise affine systems, especially Chua's circuit, which is another important special class of hybrid systems.

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XU, XU, JIAWEI LUO und YUANTONG GU. „COLLECTIVE DYNAMICS AND CONTROL OF A 3-D SMALL-WORLD NETWORK WITH TIME DELAYS“. International Journal of Bifurcation and Chaos 22, Nr. 11 (November 2012): 1250281. http://dx.doi.org/10.1142/s0218127412502811.

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The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize the 3-D network system. And with properly chosen delay and gain in the delayed feedback path, the hybrid controlled model may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or complex stranger attractor from the period-doubling bifurcation. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are analyzed. The results are further extended to any "d" dimensional network. It shows that to stabilize a "d" dimensional delayed small-world network, at least a "d – 1" order completed differential feedback is needed. This work provides a constructive suggestion for the high dimensional delayed systems.

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Rezaie, Behrooz, und Mohammad-Reza Jahed Motlagh. „An adaptive delayed feedback control method for stabilizing chaotic time-delayed systems“. Nonlinear Dynamics 64, Nr. 1-2 (14.10.2010): 167–76. http://dx.doi.org/10.1007/s11071-010-9855-7.

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37

Schneider, Isabelle, und Matthias Bosewitz. „Eliminating restrictions of time-delayed feedback control using equivariance“. Discrete and Continuous Dynamical Systems 36, Nr. 1 (Juni 2015): 451–67. http://dx.doi.org/10.3934/dcds.2016.36.451.

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38

Semenov, V. V., T. E. Vadivasova, E. Schöll und A. S. Zakharova. „Time-delayed Feedback Control of Coherence Resonance. Experimental Study“. Series Physics 15, Nr. 3 (09.10.2015): 43–51. http://dx.doi.org/10.18500/1817-3020-2015-15-3-43-51.

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39

Schneider, F. W., R. Blittersdorf, A. Foerster, T. Hauck, D. Lebender und J. Mueller. „Continuous control of chemical chaos by time delayed feedback“. Journal of Physical Chemistry 97, Nr. 47 (November 1993): 12244–48. http://dx.doi.org/10.1021/j100149a025.

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40

Yang Ru und Zhang Bo. „Chaotification control of buck converter via time-delayed feedback“. Acta Physica Sinica 56, Nr. 7 (2007): 3789. http://dx.doi.org/10.7498/aps.56.3789.

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41

Wen, Shaofang, Yongjun Shen, Jiangchuan Niu und Yunfei Liu. „Dynamical Behavior of Fractional-Order Delayed Feedback Control on the Mathieu Equation by Incremental Harmonic Balance Method“. Shock and Vibration 2022 (19.07.2022): 1–13. http://dx.doi.org/10.1155/2022/7515080.

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In this study, the dynamical analysis of the Mathieu equation with multifrequency excitation under fractional-order delayed feedback control is investigated by the incremental harmonic balance method (IHBM). IHBM is applied to the fractional-order delayed feedback control system, and the general formulas of the first-order approximate periodic solution for the Mathieu equation are derived. Caputo’s definition is adopted to process the fractional-order delayed feedback term. The general formulas of this system are suitable for not only the weakly but also the strongly nonlinear fractional-order system. Through the analysis of the general formulas of this system, it shows that fractional-order delayed feedback control has two functions, which are velocity delayed feedback control and displacement delayed feedback control. Next, the numerical simulation of the system is carried out. The comparison between the approximate analytical solution and the numerical iterative result is made, and the accuracy of the approximate analytical result by IHBM is proved to be high. At last, the effects of the time delay, feedback coefficient, and fractional order are investigated, respectively. It is generally known that time delay is common and inevitable in the control system. But the fractional order can be used to adjust the influence caused by time delay in fractional-order delayed feedback control. Those new system characteristics will provide theoretical guidance to the design and the control of this kind system.

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Zhang, Shu, und Jian Xu. „Time-varying delayed feedback control for an internet congestion control model“. Discrete & Continuous Dynamical Systems - B 16, Nr. 2 (2011): 653–68. http://dx.doi.org/10.3934/dcdsb.2011.16.653.

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43

Zhu, Erxi. „Time-delayed feedback control for chaotic systems with coexisting attractors“. AIMS Mathematics 9, Nr. 1 (2023): 1088–102. http://dx.doi.org/10.3934/math.2024053.

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<abstract><p>This study investigated the Hopf bifurcation of the equilibrium point of chaotic systems with coexisting attractors under the time-delayed feedback control. First, the equilibrium point and Hopf bifurcation of chaotic systems with coexisting attractors were analyzed. Second, the chaotic systems were controlled by time-delayed feedback, the transversality condition of Hopf bifurcation at the equilibrium point was discussed, and the time-delayed value of Hopf bifurcation at the equilibrium point was obtained. Lastly, the correctness of the theoretical analysis was verified by using the numerical results.</p></abstract>

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WANG, ZAIHUA, und HAIYAN HU. „HOPF BIFURCATION CONTROL OF DELAYED SYSTEMS WITH WEAK NONLINEARITY VIA DELAYED STATE FEEDBACK“. International Journal of Bifurcation and Chaos 15, Nr. 05 (Mai 2005): 1787–99. http://dx.doi.org/10.1142/s0218127405012909.

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This paper presents a study on the problem of Hopf bifurcation control of time delayed systems with weak nonlinearity via delayed feedback control. It focusses on two control objectives: one is to annihilate the periodic solution, namely to perform a linear delayed feedback control so that the trivial equilibrium is asymptotically stable, and the other is to obtain an asymptotically stable periodic solution with given amplitude via linear or nonlinear delayed feedback control. On the basis of the averaging method and the center manifold reduction for delayed differential equations, an effective method is developed for this problem. It has been shown that a linear delayed feedback can always stabilize the unstable trivial equilibrium of the system, and a linear or nonlinear delayed feedback control can always achieve an asymptotically stable periodic solution with desired amplitude. The illustrative example shows that the theoretical prediction is in very good agreement with the simulation results, and that the method is valid with high accuracy not only for delayed systems with weak nonlinearity and via weak feedback control, but also for those when the nonlinearity and feedback control are not small.

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Ahn, Choon Ki. „Fuzzy delayed output feedback synchronization for time-delayed chaotic systems“. Nonlinear Analysis: Hybrid Systems 4, Nr. 1 (Februar 2010): 16–24. http://dx.doi.org/10.1016/j.nahs.2009.07.002.

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46

MORGÜL, ÖMER. „A NEW GENERALIZATION OF DELAYED FEEDBACK CONTROL“. International Journal of Bifurcation and Chaos 19, Nr. 01 (Januar 2009): 365–77. http://dx.doi.org/10.1142/s0218127409022920.

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In this paper, we consider the stabilization problem of unstable periodic orbits of one-dimensional discrete time chaotic systems. We propose a novel generalization of the classical delayed feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized by the proposed method; for higher order periods the proposed scheme possesses some inherent limitations. However, some more improvement over the classical delayed feedback scheme can be achieved with the proposed scheme. The stability proofs also give the possible feedback gains which achieve stabilization. We will also present some simulation results.

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Nestler, Peter, Eckehard Schöll und Fredi Tröltzsch. „Optimization of nonlocal time-delayed feedback controllers“. Computational Optimization and Applications 64, Nr. 1 (11.11.2015): 265–94. http://dx.doi.org/10.1007/s10589-015-9809-6.

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48

Wang, Huailei, und Guanrong Chen. „On the initial function space of time-delayed systems: A time-delayed feedback control perspective“. Journal of the Franklin Institute 352, Nr. 8 (August 2015): 3243–49. http://dx.doi.org/10.1016/j.jfranklin.2014.10.021.

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49

Guo, Yong, Yuh-Chung Hu und Chuan-Bo Ren. „An Optimization Algorithm of Time-Delayed Feedback Control Parameters for Quarter Vehicle Semiactive Suspension System“. Mathematical Problems in Engineering 2022 (30.04.2022): 1–9. http://dx.doi.org/10.1155/2022/2946091.

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Time-delayed feedback control is commonly used on the vehicle semiactive suspension system to improve ride comfort and safety. However, its performance on the suppression of road random excitation is less significant than that on the suppression of simple harmonic excitation. Therefore, this paper proposes a strategy of time-delayed feedback control with the vertical displacement of wheel and the method of optimizing its parameters based on equivalent harmonic excitation. The optimal parameters of the time-delayed feedback control are obtained in this way for the vehicle semiactive suspension system in its effective frequency band. The results of numerical simulation verify that the time-delayed feedback control with vertical wheel displacement and its parameter optimization based on equivalent harmonic excitation can significantly improve the ride comfort and stability. Its performance is much better than that of the passive suspension system.

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Vasegh, Nastaran, und Ali Khaki Sedigh. „Delayed feedback control of time-delayed chaotic systems: Analytical approach at Hopf bifurcation“. Physics Letters A 372, Nr. 31 (Juli 2008): 5110–14. http://dx.doi.org/10.1016/j.physleta.2008.06.023.

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