In recent decades,studies on delayed system dynamics have attracted increasing attention and advances have been achieved in stability,nonlinearity,delay identification, delay elimination and application.However,most o...In recent decades,studies on delayed system dynamics have attracted increasing attention and advances have been achieved in stability,nonlinearity,delay identification, delay elimination and application.However,most of the existing work is on the theoretical basis and little is on the experiment.This paper presents our experimental studies on delayed feedback control conducted in recent years with the focus on the discussion of a DSP-based delayed experiment system.Some phenomena in our delay experiments are discussed and a few topics of interest for further research are brought forward.展开更多
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-ba...We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.展开更多
This paper introduces the basic idea and provides the mathematical formulation of the delayed feedback control （DFC） methodology, which has been widely used in chaos control. Stability analysis including the well-kn...This paper introduces the basic idea and provides the mathematical formulation of the delayed feedback control （DFC） methodology, which has been widely used in chaos control. Stability analysis including the well-known odd number linfitation of the DFC is reviewed. Some new developments in characterizing the limitation of the DFC are presented. Various modified DFC methods, which are developed in order to overcome the odd number limitation, are also described. Finally, some open problems in this research field are discussed.展开更多
The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are...The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality （LMI）. A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.展开更多
This work explores the function of the noisy direct delayed feedback(NDDF)control strategy in suppressing the pathological oscillations in the basal ganglia(BG)with Parkinson’s disease(PD).Deep brain stimulation(DBS)...This work explores the function of the noisy direct delayed feedback(NDDF)control strategy in suppressing the pathological oscillations in the basal ganglia(BG)with Parkinson’s disease(PD).Deep brain stimulation(DBS)alleviates the PD state fantastically.However,due to its unclear mechanism and open-loop characteristic,it is challenging to further improve its effects with lower energy expenditure.The noise stimulus performs competitively in alleviating the PD state theoretically,but it cannot adapt to the neural condition timely and automatically due to its open-loop control scheme.The direct delayed feedback(DDF)control strategy is able to disturb excessive synchronous effectively.Therefore,the NDDF control strategy is proposed and researched based on a BG computational model,which can reflect the intrinsic properties of the BG neurons and their connections with thalamic neurons.Simulation results show that the NDDF control strategy with optimal parameters is effective in removing the pathological beta oscillations.By comparison,we find the NDDF control strategy performs more excellent than DDF in alleviating PD state.Additionally,we define the multiple-NDDF control strategy and find that the multiple-NDDF with appropriate parameters performs better than NDDF.The obtained results contribute to the cure for PD symptoms by optimizing the noise-induced improvement of the BG dysfunction.展开更多
This paper investigates the dynamical behaviour of the Liu system with time delayed feedback. Two typical situations are considered and the effect of time-delay parameter on the dynamics of the system is discussed. It...This paper investigates the dynamical behaviour of the Liu system with time delayed feedback. Two typical situations are considered and the effect of time-delay parameter on the dynamics of the system is discussed. It is shown that the Liu system with time delayed feedback may exhibit interesting and extremely rich dynamical behaviour. The evolution of the dynamics is shown to be complex with varying time-delay parameter. Moreover, the strange attractor like ‘wormhole＇ is detected via numerical simulations.展开更多
In neurodegenerative disorders such as Parkinson＇s disease （PD）, deep brain stimulation （DBS） is a desirable approach when the medication is less effective for treating the symptoms. DBS incorporates transferring...In neurodegenerative disorders such as Parkinson＇s disease （PD）, deep brain stimulation （DBS） is a desirable approach when the medication is less effective for treating the symptoms. DBS incorporates transferring electrical pulses to a specific tissue of the central nervous system, obtaining therapeutic results by modulating the neuronal activity of that region. DBS has certain advantages such as reversibility and adjustability features over medication, since the neuronal firing patterns can be recorded and used to alter the parameters of the DBS signal （Benabid et al., 2009）. One of the DBS indications is its ability to suppress the abnormal neuronal activity to treat symptoms like tremor, akinesia and dystonia.展开更多
A time-delayed feedback ratchet consisting of two Brownian particles interacting through the elastic spring is consid ered. The model describes the directed transport of coupled Brownian particles in an asymmetric two...A time-delayed feedback ratchet consisting of two Brownian particles interacting through the elastic spring is consid ered. The model describes the directed transport of coupled Brownian particles in an asymmetric two-well ratchet potential which can be calculated theoretically and implemented experimentally. We explore how the centre-of-mass velocity is af fected by the time delay, natural length of the spring, amplitude strength, angular frequency, external force, and the structure of the potential. It is found that the enhancement of the current can be obtained by varying the coupling strength of the delayed feedback system. When the thermal fluctuation and the harmonic potential match appropriately, directed current evolves periodically with the natural length of the spring and can achieve a higher transport coherence. Moreover, the external force and the amplitude strength can enhance the directed transport of coupled Brownian particles under certain conditions. It is expected that the polymer of large biological molecules may demonstrate a variety of novel cooperative effects in real propelling devices.展开更多
We study the transport of overdamped Brownian particles in a symmetricaJly periodic potential in the presence of an asymmetrically ac driving force and a time-delayed feedback. It is found that for low frequencies, th...We study the transport of overdamped Brownian particles in a symmetricaJly periodic potential in the presence of an asymmetrically ac driving force and a time-delayed feedback. It is found that for low frequencies, the average velocity can be negative by changing the driving amplitude, for high frequencies, there exists an optimized driving amplitude at which the average velocity takes its maximum value. Additionally, there is a threshold value of driving amplitude below which no directed transport can be obtained for high frequencies. For the large value of the delay time, the average velocity is independent of the delay time.展开更多
The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with t...The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance, it is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node （SN） or Hopf bifurcation （HB） as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.展开更多
The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. First, the time-delayed feedback control force is expressed ap...The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged It? stochastic differential equations for the system are derived by using the stochastic averaging method. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of the first-passage time are established. Finally, the conditional reliability function, the conditional probability density and moments of the first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. The effects of time delay in feedback control force on the conditional reliability function, conditional probability density and moments of the first-passage time are analyzed. The validity of the proposed method is confirmed by digital simulation.展开更多
The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented ba...The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.展开更多
The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and com...The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.展开更多
Recently, some researches indicate that positive feedback can benefit the control if appropriate time delay is intentionally introduced into control system. However, most work is theoretical one but few are experiment...Recently, some researches indicate that positive feedback can benefit the control if appropriate time delay is intentionally introduced into control system. However, most work is theoretical one but few are experimental. This paper presents theoretical and experimental studies of delayed positive feedback control technique using a flexible beam as research object. The positive feedback weighting coefficient is designed by using the optimal control method. The available time delay is determined by analyzing the maximal real part of characteristic roots of the system. A DSP-based experiment system is introduced. Simulation and experimental results indicate that the delayed positive feedback control may effectively reduce the beam vibration if time delay is appropriately selected.展开更多
This paper concerns with the master-slave exponential synchronization analysis for a class of general Lur'esystems with time delay.Different from the previous methods based on the differential inequality technique...This paper concerns with the master-slave exponential synchronization analysis for a class of general Lur'esystems with time delay.Different from the previous methods based on the differential inequality technique, a newapproach is proposed to derive some new exponential synchronization criteria.The restriction that the control widthhas to be larger than the time delay is removed.This leads to a larger application scope for our method.Moreover, notranscendental equation is involved in the obtained result, which reduces the computational burden.Two examples aregiven to validate the theoretical results.展开更多
On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally, the influences of the time delay, the coupling constant, and the asymmetric parameter of the pote...On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally, the influences of the time delay, the coupling constant, and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated. The centre-of-mass velocity of two coupled Brownian particles, the average effective diffusion coefficient, and the Pe number are calculated. It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential. It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case. It is expected that the results obtained here may be observed in some physical and biological systems.展开更多
Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,where the resulting nonlinearities critically influence subh...Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,where the resulting nonlinearities critically influence subharmonic resonance phenomena,yet comprehensive investigations remain limited.This study employs the generalized harmonic balance(HB)method to conduct an analytical investigation of the subharmonic resonance behavior in asymmetric stiffness nonlinear systems with time delay.To further examine the switching behavior between primary and subharmonic resonances,a numerical continuation approach combining the shooting method and the parameter continuation algorithm is developed.The analytical and numerical continuation solutions are validated through direct numerical integration.Subsequently,the switching behavior and associated bifurcation points are analyzed by means of the numerical continuation results in conjunction with the Floquet theory.Finally,the effects of delay parameters on the existence range of subharmonic responses are discussed in detail,and the influence of initial conditions on system dynamics is explored with basin of attraction plots.This work establishes a comprehensive framework for the analytical and numerical study on time-delayed nonlinear systems with asymmetric stiffness,providing valuable theoretical insights into the stability management of such dynamic systems.展开更多
Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding o...Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, Hopf bifurcation in the circuit is analysed using the Hopf bifurcation theory and the central manifold theorem in this paper. Bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodical orbit （oscillation） in Chen circuit with direct time delay feedback. Bifurcation boundaries are derived using the Hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit.展开更多
It is a fact that the feedback delay actually arises in digital control systems. It is necessary to modify the structure of digital control systems and develop new control algorithms, which is done in this paper. A gr...It is a fact that the feedback delay actually arises in digital control systems. It is necessary to modify the structure of digital control systems and develop new control algorithms, which is done in this paper. A great number of digital computer simulation experiments have shown the obvious advantage of the new algorithms.展开更多
The feedback delay can severely affect the quality of the channel state information at the transmitter(CSIT)which is fed back from the receiver.The outdated CSIT will cause large performance loss in the transmit beamf...The feedback delay can severely affect the quality of the channel state information at the transmitter(CSIT)which is fed back from the receiver.The outdated CSIT will cause large performance loss in the transmit beamforming systems.The effect of variable feedback delay on the capacity of transmit beamforming systems over Rayleigh fading channels is studied.First,the case of fixed feedback delay is considered and a closed-form expression of system capacity is derived.Based on the results of fixed delay,the delay following certain distributions in variable delay case is assumed and the closed-form expressions of capacities are derived.The closed-form expressions show that the capacity is significantly affected by the statistical characteristics of the feedback delay.The obtained results provide an analytical insight into the effects caused by variable delay on the system capacity.展开更多
基金supported by the Science Foundation of China (11072146,11002087,10772112)the Key Scientific Project of Shanghai Municipal Education Commission(09ZZ17)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China (20070248032)the Research Project of State Key Laboratory of Ocean Engineering of China(GKZD010807).
文摘In recent decades,studies on delayed system dynamics have attracted increasing attention and advances have been achieved in stability,nonlinearity,delay identification, delay elimination and application.However,most of the existing work is on the theoretical basis and little is on the experiment.This paper presents our experimental studies on delayed feedback control conducted in recent years with the focus on the discussion of a DSP-based delayed experiment system.Some phenomena in our delay experiments are discussed and a few topics of interest for further research are brought forward.
基金Project supported by the National Natural Science Foundation of China(Nos.10772159 and 10802030)the Research Fund for Doctoral Program of Higher Education of China(No.20060335125)
文摘We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.
文摘This paper introduces the basic idea and provides the mathematical formulation of the delayed feedback control （DFC） methodology, which has been widely used in chaos control. Stability analysis including the well-known odd number linfitation of the DFC is reviewed. Some new developments in characterizing the limitation of the DFC are presented. Various modified DFC methods, which are developed in order to overcome the odd number limitation, are also described. Finally, some open problems in this research field are discussed.
基金supported by National Natural Science Foundation of China (No.60674092)
文摘The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality （LMI）. A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.
基金Project supported by Tianjin Natural Science Foundation,China(Grant No.19JCYBJC18800)Tangshan Science and Technology Project,China(Grant No.18130208A)Hebei Science and Technology Project,China(Grant No.18277773D).
文摘This work explores the function of the noisy direct delayed feedback(NDDF)control strategy in suppressing the pathological oscillations in the basal ganglia(BG)with Parkinson’s disease(PD).Deep brain stimulation(DBS)alleviates the PD state fantastically.However,due to its unclear mechanism and open-loop characteristic,it is challenging to further improve its effects with lower energy expenditure.The noise stimulus performs competitively in alleviating the PD state theoretically,but it cannot adapt to the neural condition timely and automatically due to its open-loop control scheme.The direct delayed feedback(DDF)control strategy is able to disturb excessive synchronous effectively.Therefore,the NDDF control strategy is proposed and researched based on a BG computational model,which can reflect the intrinsic properties of the BG neurons and their connections with thalamic neurons.Simulation results show that the NDDF control strategy with optimal parameters is effective in removing the pathological beta oscillations.By comparison,we find the NDDF control strategy performs more excellent than DDF in alleviating PD state.Additionally,we define the multiple-NDDF control strategy and find that the multiple-NDDF with appropriate parameters performs better than NDDF.The obtained results contribute to the cure for PD symptoms by optimizing the noise-induced improvement of the BG dysfunction.
基金Project supported by the Science Foundation of Huazhong University of Science and Technology (Grant No 2006Q003B)
文摘This paper investigates the dynamical behaviour of the Liu system with time delayed feedback. Two typical situations are considered and the effect of time-delay parameter on the dynamics of the system is discussed. It is shown that the Liu system with time delayed feedback may exhibit interesting and extremely rich dynamical behaviour. The evolution of the dynamics is shown to be complex with varying time-delay parameter. Moreover, the strange attractor like ‘wormhole＇ is detected via numerical simulations.
文摘In neurodegenerative disorders such as Parkinson＇s disease （PD）, deep brain stimulation （DBS） is a desirable approach when the medication is less effective for treating the symptoms. DBS incorporates transferring electrical pulses to a specific tissue of the central nervous system, obtaining therapeutic results by modulating the neuronal activity of that region. DBS has certain advantages such as reversibility and adjustability features over medication, since the neuronal firing patterns can be recorded and used to alter the parameters of the DBS signal （Benabid et al., 2009）. One of the DBS indications is its ability to suppress the abnormal neuronal activity to treat symptoms like tremor, akinesia and dystonia.
基金supported by the National Natural Science Foundation of China(Grant No.11075016)the Fundamental Research Funds for the Central Universities,China(Grant No.201001)+1 种基金the Research Fund for the Doctoral Program of Higher Education,China(Grant No.20100003110007)the Science Foundation of the Educational Department of Liaoning Province,China(Grant No.L2012386)
文摘A time-delayed feedback ratchet consisting of two Brownian particles interacting through the elastic spring is consid ered. The model describes the directed transport of coupled Brownian particles in an asymmetric two-well ratchet potential which can be calculated theoretically and implemented experimentally. We explore how the centre-of-mass velocity is af fected by the time delay, natural length of the spring, amplitude strength, angular frequency, external force, and the structure of the potential. It is found that the enhancement of the current can be obtained by varying the coupling strength of the delayed feedback system. When the thermal fluctuation and the harmonic potential match appropriately, directed current evolves periodically with the natural length of the spring and can achieve a higher transport coherence. Moreover, the external force and the amplitude strength can enhance the directed transport of coupled Brownian particles under certain conditions. It is expected that the polymer of large biological molecules may demonstrate a variety of novel cooperative effects in real propelling devices.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 61072029 and 11175067the Guangdong Provincial Natural Science Foundation under Grant Nos. 10151063101000025 and S2011010003323
文摘We study the transport of overdamped Brownian particles in a symmetricaJly periodic potential in the presence of an asymmetrically ac driving force and a time-delayed feedback. It is found that for low frequencies, the average velocity can be negative by changing the driving amplitude, for high frequencies, there exists an optimized driving amplitude at which the average velocity takes its maximum value. Additionally, there is a threshold value of driving amplitude below which no directed transport can be obtained for high frequencies. For the large value of the delay time, the average velocity is independent of the delay time.
基金Project supported by the Scientific Research Foundation for Returned Overseas Chinese Scholar of Ministry of Eduction, China (No.2006-331)
文摘The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance, it is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node （SN） or Hopf bifurcation （HB） as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10932009, 11072212 and 50905051)Key Discipline of the Ocean Mechatronic Equipments Technology Foundation
文摘The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged It? stochastic differential equations for the system are derived by using the stochastic averaging method. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of the first-passage time are established. Finally, the conditional reliability function, the conditional probability density and moments of the first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. The effects of time delay in feedback control force on the conditional reliability function, conditional probability density and moments of the first-passage time are analyzed. The validity of the proposed method is confirmed by digital simulation.
文摘The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.
基金supported by the National Natural Science Foundation of China(10971232)the Natural Science Foundation of Guangdong Province(101510090010000398351009001000002)
文摘The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.
基金supported by the Key Project (11132001)the General Projects of the National Natural Science Foundation of China (11072146, 11002087)
文摘Recently, some researches indicate that positive feedback can benefit the control if appropriate time delay is intentionally introduced into control system. However, most work is theoretical one but few are experimental. This paper presents theoretical and experimental studies of delayed positive feedback control technique using a flexible beam as research object. The positive feedback weighting coefficient is designed by using the optimal control method. The available time delay is determined by analyzing the maximal real part of characteristic roots of the system. A DSP-based experiment system is introduced. Simulation and experimental results indicate that the delayed positive feedback control may effectively reduce the beam vibration if time delay is appropriately selected.
基金Supported by the National Natural Science Foundation of China under Grant Nos.60774039,60974024,and 61074089CityU Research Enhancement Fund 9360127,CityU SRG 7002355
文摘This paper concerns with the master-slave exponential synchronization analysis for a class of general Lur'esystems with time delay.Different from the previous methods based on the differential inequality technique, a newapproach is proposed to derive some new exponential synchronization criteria.The restriction that the control widthhas to be larger than the time delay is removed.This leads to a larger application scope for our method.Moreover, notranscendental equation is involved in the obtained result, which reduces the computational burden.Two examples aregiven to validate the theoretical results.
基金supported by the Foundation for the Doctoral Research Project of Shenyang Normal University,China (Grant No.054-55440107021)the Science Foundation of the Educational Department of Liaoning Province,China (Grant No.2009A646)
文摘On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally, the influences of the time delay, the coupling constant, and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated. The centre-of-mass velocity of two coupled Brownian particles, the average effective diffusion coefficient, and the Pe number are calculated. It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential. It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case. It is expected that the results obtained here may be observed in some physical and biological systems.
基金Project supported by the National Natural Science Foundation of China(Nos.U24B2062,520754285247051087)+1 种基金the Two-chain Fusion High-end Machine Tool Project of Shaanxi Province of China(No.2021LLRh-01-02)the Youth Fund of the National Natural Science Foundation of China(No.52205281)。
文摘Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,where the resulting nonlinearities critically influence subharmonic resonance phenomena,yet comprehensive investigations remain limited.This study employs the generalized harmonic balance(HB)method to conduct an analytical investigation of the subharmonic resonance behavior in asymmetric stiffness nonlinear systems with time delay.To further examine the switching behavior between primary and subharmonic resonances,a numerical continuation approach combining the shooting method and the parameter continuation algorithm is developed.The analytical and numerical continuation solutions are validated through direct numerical integration.Subsequently,the switching behavior and associated bifurcation points are analyzed by means of the numerical continuation results in conjunction with the Floquet theory.Finally,the effects of delay parameters on the existence range of subharmonic responses are discussed in detail,and the influence of initial conditions on system dynamics is explored with basin of attraction plots.This work establishes a comprehensive framework for the analytical and numerical study on time-delayed nonlinear systems with asymmetric stiffness,providing valuable theoretical insights into the stability management of such dynamic systems.
基金Project supported in part by the National Natural Science Foundation of China (Grant No. 60804040)Fok Ying-Tong Education Foundation for Young Teacher (Grant No. 111065)
文摘Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, Hopf bifurcation in the circuit is analysed using the Hopf bifurcation theory and the central manifold theorem in this paper. Bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodical orbit （oscillation） in Chen circuit with direct time delay feedback. Bifurcation boundaries are derived using the Hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit.
文摘It is a fact that the feedback delay actually arises in digital control systems. It is necessary to modify the structure of digital control systems and develop new control algorithms, which is done in this paper. A great number of digital computer simulation experiments have shown the obvious advantage of the new algorithms.
基金supported by the Natural Science Foundation of Shanghai(09ZR1430500)the Chinese National Science and Technology Major Project(2011ZX03003-001-01,2009ZX03002-003-004)
文摘The feedback delay can severely affect the quality of the channel state information at the transmitter(CSIT)which is fed back from the receiver.The outdated CSIT will cause large performance loss in the transmit beamforming systems.The effect of variable feedback delay on the capacity of transmit beamforming systems over Rayleigh fading channels is studied.First,the case of fixed feedback delay is considered and a closed-form expression of system capacity is derived.Based on the results of fixed delay,the delay following certain distributions in variable delay case is assumed and the closed-form expressions of capacities are derived.The closed-form expressions show that the capacity is significantly affected by the statistical characteristics of the feedback delay.The obtained results provide an analytical insight into the effects caused by variable delay on the system capacity.
