The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requ...The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.展开更多
The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, ...The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.展开更多
This paper discusses the design of event-triggered output-feedback controller for a class of nonlinear time-delay systems with multiple uncertainties. In sharp contrast to previous works, the considered systems posses...This paper discusses the design of event-triggered output-feedback controller for a class of nonlinear time-delay systems with multiple uncertainties. In sharp contrast to previous works, the considered systems possess two important characteristics: (i) The uncertain nonlinear terms meet the linearly unmeasurable-states dependent growth with the growth rate being an unknown function of the input and output. (ii) There exist input matching uncertainty and unknown measurement sensitivity. By introducing a single dynamic gain and employing a cleverly devised event-triggering mechanism (ETM), we design a new gain-based event-triggered output-feedback controller, which globally regulates all states of the considered systems and maintains global boundedness of the closed-loop system. Furthermore, the estimation of input matching uncertainty achieves convergence towards its actual value, and Zeno behavior does not happen. Two simulation examples including a practical one show that the proposed approach is effective.展开更多
This study investigates the nonlinear resonance responses of suspended cables subjected to multi-frequency excitations and time-delayed feedback.Two specific combinations and simultaneous resonances are selected for d...This study investigates the nonlinear resonance responses of suspended cables subjected to multi-frequency excitations and time-delayed feedback.Two specific combinations and simultaneous resonances are selected for detailed examination.Initially,utilizing Hamilton’s variational principle,a nonlinear vibration control model of suspended cables under multi-frequency excitations and longitudinal time-delayed velocity feedback is developed,and the Galerkin method is employed to obtain the discrete model.Subsequently,focusing solely on single-mode discretization,analytical solutions for the two simultaneous resonances are derived using the method of multiple scales.The frequency response equations are derived,and the stability analysis is presented for two simultaneous resonance cases.The results demonstrate that suspended cables exhibit complex nonlinearity under multi-frequency excitations.Multiple solutions under multi-frequency excitation can be distinguished through the frequency–response and the detuning-phase curves.By adjusting the control gain and time delay,the resonance range,response amplitude,and phase of suspended cables can be modified.展开更多
In this paper,a pair of dynamic high-gain observer and output feedback controller is proposed for nonlinear systems with multiple unknown time delays.By constructing Lyapunov-Krasovskii functionals,it shows that globa...In this paper,a pair of dynamic high-gain observer and output feedback controller is proposed for nonlinear systems with multiple unknown time delays.By constructing Lyapunov-Krasovskii functionals,it shows that global state asymptotic regulation can be ensured by introducing a single dynamic gain;furthermore,global asymptotic stabilization can be achieved by choosing a sufficiently large static scaling gain when the upper bounds of all system parameters are known.Especially,the output coefficient is allowed to be non-differentiable with unknown upper bound.This paper proposes a generalized Lyapunov matrix inequality based dynamic-gain scaling method,which significantly simplifies the design computational complexity by comparing with the classic backstepping method.展开更多
This paper studies global stabilization via predictor-based sampled-data output feedback for a class of feedforward nonlinear time-delay systems.Note that the traditional sampled-data observer via zero-order holder ma...This paper studies global stabilization via predictor-based sampled-data output feedback for a class of feedforward nonlinear time-delay systems.Note that the traditional sampled-data observer via zero-order holder may result in the performance degradation of the observer.In this paper,an improved predictor-based observer is designed to compensate for the influence of the unmeasurable states,sampling errors and output delay.In addition,a sampled-data output-feedback controller is also constructed using the gain scaling technique.By the Lyapunov-Krasovskii functional method,the global exponential stability of the resulting closed-loop system can be guaranteed under some sufficient conditions.The simulation results are provided to demonstrate the main results.展开更多
Dear Editor,to This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities.By constructing reduced-order obs...Dear Editor,to This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities.By constructing reduced-order observer,based on homogeneous domination theory together with the adding a power integrator method,an output feedback controller is developed guarantee the equilibrium of the closed system globally uniformly asymptotically stable.展开更多
A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dyn...A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dynamic absorbers with different structural and control parameters as examples, the effects of third-order nonlinear coefficients, time-delay control parameters, and negative stiffness coefficients on reducing the replication of the main system were discussed. The nonlinear dynamic absorber has a very good vibration reduction effect at the resonance point of the main system and a nearby area, and when 1 increases to a certain level, the stable region of the system continues to increase. The amplitude curve of the main system of a nonlinear dynamic absorber will generate Hop bifurcation and saddle node bifurcation in the region far from the resonance point, resulting in almost periodic motion and jumping phenomena in the system. For nonlinear dynamic absorbers with determined structural parameters, time-delay feedback control can be adopted to control the amplitude of the main system. For different negative stiffness coefficients, there exists a minimum damping point for the amplitude of the main system under the determined system structural parameters and time-delay feedback control parameters.展开更多
This paper discusses the problem of global state regulation via output feedback for a class of feedforward nonlinear time-delay systems with unknown measurement sensitivity. Different from previous works, the nonlinea...This paper discusses the problem of global state regulation via output feedback for a class of feedforward nonlinear time-delay systems with unknown measurement sensitivity. Different from previous works, the nonlinear terms are dominated by upper triangular linear unmeasured (delayed) states multiplied by unknown growth rate. The unknown growth rate is composed of an unknown constant, a power function of output, and an input function. Furthermore, due to the measurement uncertainty of the system output, it is more difficult to solve this problem. It is proved that the presented output feedback controller can globally regulate all states of the nonlinear systems using the dynamic gain scaling technique and choosing the appropriate Lyapunov–Krasovskii functionals.展开更多
A composite anti-disturbance predictive control strategy employing a Multi-dimensional Taylor Network(MTN)is presented for unmanned systems subject to time-delay and multi-source disturbances.First,the multi-source di...A composite anti-disturbance predictive control strategy employing a Multi-dimensional Taylor Network(MTN)is presented for unmanned systems subject to time-delay and multi-source disturbances.First,the multi-source disturbances are addressed according to their specific characteristics as follows:(A)an MTN data-driven model,which is used for uncertainty description,is designed accompanied with the mechanism model to represent the unmanned systems;(B)an adaptive MTN filter is used to remove the influence of the internal disturbance;(C)an MTN disturbance observer is constructed to estimate and compensate for the influence of the external disturbance;(D)the Extended Kalman Filter(EKF)algorithm is utilized as the learning mechanism for MTNs.Second,to address the time-delay effect,a recursiveτstep-ahead MTN predictive model is designed utilizing recursive technology,aiming to mitigate the impact of time-delay,and the EKF algorithm is employed as its learning mechanism.Then,the MTN predictive control law is designed based on the quadratic performance index.By implementing the proposed composite controller to unmanned systems,simultaneous feedforward compensation and feedback suppression to the multi-source disturbances are conducted.Finally,the convergence of the MTN and the stability of the closed-loop system are established utilizing the Lyapunov theorem.Two exemplary applications of unmanned systems involving unmanned vehicle and rigid spacecraft are presented to validate the effectiveness of the proposed approach.展开更多
A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and...A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.展开更多
Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coup...Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
In the modal analysis and control of nonlinear dynamical systems,participation factors(PFs)of state variables with respect to a critical or selected mode serve as a pivotal tool for simplifying stability studies by fo...In the modal analysis and control of nonlinear dynamical systems,participation factors(PFs)of state variables with respect to a critical or selected mode serve as a pivotal tool for simplifying stability studies by focusing on a subset of highly influential state variables.For linear systems,PFs are uniquely determined by the mode’s composition and shape,which are defined by the system’s left and right eigenvectors,respectively.However,the uniqueness of other types of PFs has not been thoroughly addressed in literatures.This paper establishes sufficient conditions for the uniqueness of nonlinear PFs and five other PF variants,taking into account uncertain scaling factors in a mode’s shape and composition.These scaling factors arise from variations in the choice of physical units,which depend on the value ranges of real-world state variables.Understanding these sufficient conditions is essential for the correct application of PFs in practical stability analysis and control design.展开更多
Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this cha...Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.展开更多
In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigatio...In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigation but also monitor the optical power and dispersion profile over multi-span links.The link status information can be extracted by the characteristics of the learned optical fiber parameters without any other measuring instruments.The efficiency and feasibility of this method have been investigated in different fiber link conditions,including various launch power,transmission distance,and the location and the amount of the abnormal losses.A good monitoring performance can be obtained while the launch optical power is 2 dBm which does not affect the normal operation of the optical communication system and the step size of DBP is 20 km which can provide a better distance resolution.This scheme successfully detects the location of single or multiple optical attenuators in long-distance multi-span fiber links,including different abnormal losses of 2 dB,4 dB,and 6 dB in 360 km and serval combinations of abnormal losses of(1 dB,5 dB),(3 dB,3 dB),(5 dB,1 dB)in 360 km and 760 km.Meanwhile,the transfer relationship of the estimated coefficient values with different step sizes is further investigated to reduce the complexity of the fiber nonlinear damage compensation.These results provide an attractive approach for precisely sensing the optical fiber link status information and making correct strategies timely to ensure optical communication system operations.展开更多
Herein,we report the synthesis and third-order nonlinear optical(NLO)properties of a novel cage-based 2D metal-organic framework constructed from Ti_(4)L_(6)(L4-=embonate)cage combined with Mg^(2+)and tris[4-(1H-imida...Herein,we report the synthesis and third-order nonlinear optical(NLO)properties of a novel cage-based 2D metal-organic framework constructed from Ti_(4)L_(6)(L4-=embonate)cage combined with Mg^(2+)and tris[4-(1H-imidazol-1-yl)phenyl]amine(tipa)ligand,whose molecular formula is(Me_(2)CH_(2))_(2)[Mg_(3)(Ti_(4)L_(6))(tipa)(H_(2)O)_(12)](PTC‑378).The Ti_(4)L_(6)tetrahedral cages serve as robust building units,while the Mg^(2+)ions and tipa ligands provide structural stability and tunable optical properties.The resulting PTC‑378 film exhibited intriguing third-order NLO property,which was systematically investigated using Z-scan techniques.Our results demonstrate that the synergistic interaction between Ti_(4)L_(6)cages andπ-conjugated ligands significantly enhances the NLO performance of the materials.CCDC:2453909.展开更多
Resonant linear and nonlinear properties in terahertz range of 2D materials graphene and silicene placed into a bias magnetic field are investigated theoretically on the base of the quasi-classical kinetic theory. Whe...Resonant linear and nonlinear properties in terahertz range of 2D materials graphene and silicene placed into a bias magnetic field are investigated theoretically on the base of the quasi-classical kinetic theory. When the electromagnetic frequency is close to the cyclotron one, the linear conductivity increases two orders. Under the resonant frequencies nonlinearity becomes essential at low magnitudes of terahertz electric fields. In absence of a bias magnetic field the nonlinear dependences of the surface electric currents on terahertz electric field are practically the same simulated from kinetics and electron hydrodynamics with nonzero “kinetic” electron effective mass. Graphene possesses higher values of nonlinearity of the resonant conductivity, whereas in absence of a bias magnetic field, the electron nonlinearity is higher in silicene.展开更多
With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixe...With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.展开更多
基金supported in part by the National Natural Science Foundation of China (62103093)the National Key Research and Development Program of China (2022YFB3305905)+6 种基金the Xingliao Talent Program of Liaoning Province of China (XLYC2203130)the Fundamental Research Funds for the Central Universities of China (N2108003)the Natural Science Foundation of Liaoning Province (2023-MS-087)the BNU Talent Seed Fund,UIC Start-Up Fund (R72021115)the Guangdong Key Laboratory of AI and MM Data Processing (2020KSYS007)the Guangdong Provincial Key Laboratory IRADS for Data Science (2022B1212010006)the Guangdong Higher Education Upgrading Plan 2021–2025 of “Rushing to the Top,Making Up Shortcomings and Strengthening Special Features” with UIC Research,China (R0400001-22,R0400025-21)。
文摘The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.
基金Supported by the "973" Project of P. R. China (G1998020300)
文摘The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.
基金supported by the fund of Beijing Municipal Commission of Education(KM202210017001 and 22019821001)the Natural Science Foundation of Henan Province(222300420253).
文摘This paper discusses the design of event-triggered output-feedback controller for a class of nonlinear time-delay systems with multiple uncertainties. In sharp contrast to previous works, the considered systems possess two important characteristics: (i) The uncertain nonlinear terms meet the linearly unmeasurable-states dependent growth with the growth rate being an unknown function of the input and output. (ii) There exist input matching uncertainty and unknown measurement sensitivity. By introducing a single dynamic gain and employing a cleverly devised event-triggering mechanism (ETM), we design a new gain-based event-triggered output-feedback controller, which globally regulates all states of the considered systems and maintains global boundedness of the closed-loop system. Furthermore, the estimation of input matching uncertainty achieves convergence towards its actual value, and Zeno behavior does not happen. Two simulation examples including a practical one show that the proposed approach is effective.
基金supported in part by the National Natural Science Foundation of China(Grant No.12432001)Natural Science Foundation of Hunan Province(Grant Nos.2023JJ60527,2023JJ30152,and 2023JJ30259)the Natural Science Foundation of Changsha(KQ2202133).
文摘This study investigates the nonlinear resonance responses of suspended cables subjected to multi-frequency excitations and time-delayed feedback.Two specific combinations and simultaneous resonances are selected for detailed examination.Initially,utilizing Hamilton’s variational principle,a nonlinear vibration control model of suspended cables under multi-frequency excitations and longitudinal time-delayed velocity feedback is developed,and the Galerkin method is employed to obtain the discrete model.Subsequently,focusing solely on single-mode discretization,analytical solutions for the two simultaneous resonances are derived using the method of multiple scales.The frequency response equations are derived,and the stability analysis is presented for two simultaneous resonance cases.The results demonstrate that suspended cables exhibit complex nonlinearity under multi-frequency excitations.Multiple solutions under multi-frequency excitation can be distinguished through the frequency–response and the detuning-phase curves.By adjusting the control gain and time delay,the resonance range,response amplitude,and phase of suspended cables can be modified.
基金supported by the Zhejiang Provincial Natural Science Foundation(LY24F030011,LY23F030005)the National Natural Science Foundation of China(62373131).
文摘In this paper,a pair of dynamic high-gain observer and output feedback controller is proposed for nonlinear systems with multiple unknown time delays.By constructing Lyapunov-Krasovskii functionals,it shows that global state asymptotic regulation can be ensured by introducing a single dynamic gain;furthermore,global asymptotic stabilization can be achieved by choosing a sufficiently large static scaling gain when the upper bounds of all system parameters are known.Especially,the output coefficient is allowed to be non-differentiable with unknown upper bound.This paper proposes a generalized Lyapunov matrix inequality based dynamic-gain scaling method,which significantly simplifies the design computational complexity by comparing with the classic backstepping method.
基金supported by the Autonomous Innovation Team Foundation for“20 Items of the New University”of Jinan City(202228087)the National Natural Science Foundation of China(62073190).
文摘This paper studies global stabilization via predictor-based sampled-data output feedback for a class of feedforward nonlinear time-delay systems.Note that the traditional sampled-data observer via zero-order holder may result in the performance degradation of the observer.In this paper,an improved predictor-based observer is designed to compensate for the influence of the unmeasurable states,sampling errors and output delay.In addition,a sampled-data output-feedback controller is also constructed using the gain scaling technique.By the Lyapunov-Krasovskii functional method,the global exponential stability of the resulting closed-loop system can be guaranteed under some sufficient conditions.The simulation results are provided to demonstrate the main results.
基金supported by the National Natural Science Foundation of China(62103175)Taishan Scholar Project of Shandong Province of China。
文摘Dear Editor,to This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities.By constructing reduced-order observer,based on homogeneous domination theory together with the adding a power integrator method,an output feedback controller is developed guarantee the equilibrium of the closed system globally uniformly asymptotically stable.
文摘A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dynamic absorbers with different structural and control parameters as examples, the effects of third-order nonlinear coefficients, time-delay control parameters, and negative stiffness coefficients on reducing the replication of the main system were discussed. The nonlinear dynamic absorber has a very good vibration reduction effect at the resonance point of the main system and a nearby area, and when 1 increases to a certain level, the stable region of the system continues to increase. The amplitude curve of the main system of a nonlinear dynamic absorber will generate Hop bifurcation and saddle node bifurcation in the region far from the resonance point, resulting in almost periodic motion and jumping phenomena in the system. For nonlinear dynamic absorbers with determined structural parameters, time-delay feedback control can be adopted to control the amplitude of the main system. For different negative stiffness coefficients, there exists a minimum damping point for the amplitude of the main system under the determined system structural parameters and time-delay feedback control parameters.
基金supported by the fund of Beijing Municipal Commission of Education(Nos.22019821001 and KM202210017001)the Natural Science Foundation of Henan Province(No.222300420253).
文摘This paper discusses the problem of global state regulation via output feedback for a class of feedforward nonlinear time-delay systems with unknown measurement sensitivity. Different from previous works, the nonlinear terms are dominated by upper triangular linear unmeasured (delayed) states multiplied by unknown growth rate. The unknown growth rate is composed of an unknown constant, a power function of output, and an input function. Furthermore, due to the measurement uncertainty of the system output, it is more difficult to solve this problem. It is proved that the presented output feedback controller can globally regulate all states of the nonlinear systems using the dynamic gain scaling technique and choosing the appropriate Lyapunov–Krasovskii functionals.
基金co-supported by the National Key R&D Program of China(No.2023YFB4704400)the Zhejiang Provincial Natural Science Foundation of China(No.LQ24F030012)the National Natural Science Foundation of China General Project(No.62373033)。
文摘A composite anti-disturbance predictive control strategy employing a Multi-dimensional Taylor Network(MTN)is presented for unmanned systems subject to time-delay and multi-source disturbances.First,the multi-source disturbances are addressed according to their specific characteristics as follows:(A)an MTN data-driven model,which is used for uncertainty description,is designed accompanied with the mechanism model to represent the unmanned systems;(B)an adaptive MTN filter is used to remove the influence of the internal disturbance;(C)an MTN disturbance observer is constructed to estimate and compensate for the influence of the external disturbance;(D)the Extended Kalman Filter(EKF)algorithm is utilized as the learning mechanism for MTNs.Second,to address the time-delay effect,a recursiveτstep-ahead MTN predictive model is designed utilizing recursive technology,aiming to mitigate the impact of time-delay,and the EKF algorithm is employed as its learning mechanism.Then,the MTN predictive control law is designed based on the quadratic performance index.By implementing the proposed composite controller to unmanned systems,simultaneous feedforward compensation and feedback suppression to the multi-source disturbances are conducted.Finally,the convergence of the MTN and the stability of the closed-loop system are established utilizing the Lyapunov theorem.Two exemplary applications of unmanned systems involving unmanned vehicle and rigid spacecraft are presented to validate the effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China(Grant Nos.42150204 and 2288101)supported by the China National Postdoctoral Program for Innovative Talents(BX20230045)the China Postdoctoral Science Foundation(2023M730279)。
文摘A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.
基金supported by the National Key Research and Development Program of China(No.2022YFB3203600)the National Natural Science Foundation of China(Nos.12202355,12132013,and 12172323)the Zhejiang Provincial Natural Science Foundation of China(No.LZ22A020003)。
文摘Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
文摘In the modal analysis and control of nonlinear dynamical systems,participation factors(PFs)of state variables with respect to a critical or selected mode serve as a pivotal tool for simplifying stability studies by focusing on a subset of highly influential state variables.For linear systems,PFs are uniquely determined by the mode’s composition and shape,which are defined by the system’s left and right eigenvectors,respectively.However,the uniqueness of other types of PFs has not been thoroughly addressed in literatures.This paper establishes sufficient conditions for the uniqueness of nonlinear PFs and five other PF variants,taking into account uncertain scaling factors in a mode’s shape and composition.These scaling factors arise from variations in the choice of physical units,which depend on the value ranges of real-world state variables.Understanding these sufficient conditions is essential for the correct application of PFs in practical stability analysis and control design.
基金funded by the National Key R&D Program of China(Grant No.2022YFC2903904)the National Natural Science Foundation of China(Grant Nos.51904057 and U1906208).
文摘Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.
基金supported by the National Key Research and Development Program of China (2019YFB1803905)the National Natural Science Foundation of China (No.62171022)+2 种基金Beijing Natural Science Foundation (4222009)Guangdong Basic and Applied Basic Research Foundation (2021B1515120057)the Scientific and Technological Innovation Foundation of Shunde Graduate School,USTB (No.BK19AF005)。
文摘In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigation but also monitor the optical power and dispersion profile over multi-span links.The link status information can be extracted by the characteristics of the learned optical fiber parameters without any other measuring instruments.The efficiency and feasibility of this method have been investigated in different fiber link conditions,including various launch power,transmission distance,and the location and the amount of the abnormal losses.A good monitoring performance can be obtained while the launch optical power is 2 dBm which does not affect the normal operation of the optical communication system and the step size of DBP is 20 km which can provide a better distance resolution.This scheme successfully detects the location of single or multiple optical attenuators in long-distance multi-span fiber links,including different abnormal losses of 2 dB,4 dB,and 6 dB in 360 km and serval combinations of abnormal losses of(1 dB,5 dB),(3 dB,3 dB),(5 dB,1 dB)in 360 km and 760 km.Meanwhile,the transfer relationship of the estimated coefficient values with different step sizes is further investigated to reduce the complexity of the fiber nonlinear damage compensation.These results provide an attractive approach for precisely sensing the optical fiber link status information and making correct strategies timely to ensure optical communication system operations.
文摘Herein,we report the synthesis and third-order nonlinear optical(NLO)properties of a novel cage-based 2D metal-organic framework constructed from Ti_(4)L_(6)(L4-=embonate)cage combined with Mg^(2+)and tris[4-(1H-imidazol-1-yl)phenyl]amine(tipa)ligand,whose molecular formula is(Me_(2)CH_(2))_(2)[Mg_(3)(Ti_(4)L_(6))(tipa)(H_(2)O)_(12)](PTC‑378).The Ti_(4)L_(6)tetrahedral cages serve as robust building units,while the Mg^(2+)ions and tipa ligands provide structural stability and tunable optical properties.The resulting PTC‑378 film exhibited intriguing third-order NLO property,which was systematically investigated using Z-scan techniques.Our results demonstrate that the synergistic interaction between Ti_(4)L_(6)cages andπ-conjugated ligands significantly enhances the NLO performance of the materials.CCDC:2453909.
文摘Resonant linear and nonlinear properties in terahertz range of 2D materials graphene and silicene placed into a bias magnetic field are investigated theoretically on the base of the quasi-classical kinetic theory. When the electromagnetic frequency is close to the cyclotron one, the linear conductivity increases two orders. Under the resonant frequencies nonlinearity becomes essential at low magnitudes of terahertz electric fields. In absence of a bias magnetic field the nonlinear dependences of the surface electric currents on terahertz electric field are practically the same simulated from kinetics and electron hydrodynamics with nonzero “kinetic” electron effective mass. Graphene possesses higher values of nonlinearity of the resonant conductivity, whereas in absence of a bias magnetic field, the electron nonlinearity is higher in silicene.
基金Supported by the National Natural Science Foundation of China(12201368,62376252)Key Project of Natural Science Foundation of Zhejiang Province(LZ22F030003)Zhejiang Province Leading Geese Plan(2024C02G1123882,2024C01SA100795).
文摘With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.
