This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output(MIMO)nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and no...This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output(MIMO)nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and non-vanishing uncertainties make the prescribed-time control problem become much more nontrivial. The solution to address the challenges mentioned above involves incorporating a prescribed-time filter, as opposed to a finite-time filter, and formulating a prescribed-time Lyapunov stability lemma(Lemma 5). The prescribed-time Lyapunov stability lemma is based on time axis shifting time-varying yet bounded gain, which establishes a novel link between the fixed-time and prescribed-time control method. This allows the restriction condition that the time-varying gain function must satisfy as imposed in most exist prescribed-time control works to be removed. Under the proposed control method, the desire trajectory is ensured to closely track the output of the system in prescribed time. The effectiveness of the theoretical results are verified through numerical simulation.展开更多
This paper presents a novel fixed-time stabilization control(FSC)method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics.The key feature of the proposed method is the design of two...This paper presents a novel fixed-time stabilization control(FSC)method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics.The key feature of the proposed method is the design of two dynamic parameters.Specifically,a set of auxiliary variables is first introduced through state transformation.These variables combine the original system states and the two introduced dynamic parameters,facilitating the closed-loop system stability analyses.Then,the two dynamic parameters are delicately designed by utilizing the Lyapunov method,ensuring that all the closed-loop system states are globally fixed-time stable.Compared with existing results,the“explosion of complexity”problem of backstepping control is avoided.Moreover,the two designed dynamic parameters are dependent on system states rather than a time-varying function,thus the proposed controller is still valid beyond the given fixedtime convergence instant.The effectiveness of the proposed method is demonstrated through two practical systems.展开更多
In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation p...In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.展开更多
A neural-network-based adaptive gain scheduling backstepping sliding mode control（NNAGS-BSMC） approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain st...A neural-network-based adaptive gain scheduling backstepping sliding mode control（NNAGS-BSMC） approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain strict-feedback nonlinear systems is formulated. Second, the detailed design of NNAGSBSMC is described. The sliding mode control（SMC） law is designed to track a referenced output via backstepping technique.To decrease chattering result from SMC, a radial basis function neural network（RBFNN） is employed to construct the NNAGSBSMC to facilitate adaptive gain scheduling, in which the gains are scheduled adaptively via neural network（NN）, with sliding surface and its differential as NN inputs and the gains as NN outputs. Finally, the verification example is given to show the effectiveness and robustness of the proposed approach. Contrasting simulation results indicate that the NNAGS-BSMC decreases the chattering effectively and has better control performance against the BSMC.展开更多
In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlin...In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.展开更多
In this paper,we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients,which mainly includes the following steps.Firstly,by intr...In this paper,we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients,which mainly includes the following steps.Firstly,by introducing several key transformation functions and selecting the initial value of the time-varying scaling function,the symmetric prescribed performance with global and semi-global properties can be handled uniformly,without the need for control re-design.Secondly,to handle the problem of unknown time-varying control coefficient with an unknown sign,we propose an enhanced Nussbaum function(ENF)bearing some unique properties and characteristics,with which the complex stability analysis based on specific Nussbaum functions as commonly used is no longer required.Thirdly,by utilizing the core-function information technique,the nonparametric uncertainties in the system are gracefully handled so that no approximator is required.Furthermore,simulation results verify the effectiveness and benefits of the approach.展开更多
In this paper,an adaptive dynamic event-triggered asymptotic control scheme is designed for strict-feedback systems with time-varying parameters.The congelation of variables technique is employed to address the time-v...In this paper,an adaptive dynamic event-triggered asymptotic control scheme is designed for strict-feedback systems with time-varying parameters.The congelation of variables technique is employed to address the time-varying parameters in the system.During the controller design,two parameter estimation adaptive laws are constructed.The tuning function is introduced in the design process to avoid over-parameterization.To further conserve communication resources,a dynamic eventtriggered approach is proposed,in which a non-negative variable is introduced to update the threshold parameter dynamically.The global uniform asymptotic stability of the closed-loop system is proven through the Lyapunov stability analysis.The feasibility of the scheme is demonstrated by simulation.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A...This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.展开更多
The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.展开更多
We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝa...We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.展开更多
This study develops an event-triggered control strategy utilizing the fully actuated system approach for nonlinear interconnected large-scale systems containing actuator failures.First,to reduce the complexity of the ...This study develops an event-triggered control strategy utilizing the fully actuated system approach for nonlinear interconnected large-scale systems containing actuator failures.First,to reduce the complexity of the design process,we transform the studied system into the form of a fully actuated system through a state transformation.Then,to address the unknown nonlinear functions and actuator fault parameters,we employ neural networks and adaptive estimation techniques,respectively.Moreover,to reduce the control cost and improve the control efficiency,we introduce event-triggered inputs into the control strategy.It is proved by the Lyapunov stability analysis that all signals of the closed-loop system are bounded and the output of system eventually converge to a bounded region.The efficacy of the control approach is ultimately demonstrated via the simulation of an actual machine feeding system.展开更多
Magnetorheological(MR)bearings,with their field-controllable rheological properties,offer new possibilities for control of rotor instabilities.However,their nonlinear dynamic behaviors and the underlying physical mech...Magnetorheological(MR)bearings,with their field-controllable rheological properties,offer new possibilities for control of rotor instabilities.However,their nonlinear dynamic behaviors and the underlying physical mechanisms governing these instabilities remain insufficiently understood.This work develops a coupled MR bearingrotor system model,where the oil film force is derived from a novel bilinear constitutive equation to capture the field-sensitive shear behaviors of MR fluids.Complex nonlinear dynamic behaviors including period doubling,quasi-period,and chaos are revealed,which emerge from the interaction between oil film vortex dynamics and magnetic excitation.The critical instability mechanism is identified from the evolution of intrinsic dynamic characteristics of MR bearings.When the whirl speed within the oil film reaches approximately half of the rotor speed,the damping force balances the destabilizing force,thereby defining a critical threshold beyond which the system transitions to instability.This threshold can be effectively tuned by adjusting the excitation current,which modifies the yield stress of MR fluids and consequently regulates the damping force.As a result,the nonlinear vibrations of oil whirl and whip can be suppressed,and the system stability can be significantly enhanced.These findings provide both theoretical insight and practical guidance for the design and control of MR bearing supported rotor systems.展开更多
In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is de...In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.展开更多
Achieving non-centrosymmetric(NCS) configurations in ABX3-type hybrid halides remains a critical challenge for nonlinear optical(NLO) materials due to the conflicting requirements of high second-harmonic generation(SH...Achieving non-centrosymmetric(NCS) configurations in ABX3-type hybrid halides remains a critical challenge for nonlinear optical(NLO) materials due to the conflicting requirements of high second-harmonic generation(SHG) response,wide bandgap,and phase-matching capabilities.Herein,we propose a triplesite modulation strategy by synergistically tailoring the A-site cations(2-methylimidazole cation/1-ethyl-3-methylimidazole cation),B-site metals(Sn^(2+)/Pb^(2+)),and X-site halogens(Cl/Br),which effectively disrupts lattice symmetry and enables NCS crystallization.Our results demonstrate a strong SHG response,an expanded optical bandgap and increased birefringence.The optimized compound C_(6)H_(11)N_(2)PbCl_(3) exhibits a moderately strong SHG efficiency of 3.8 × KDP,a wide bandgap(3.87 eV),and enhanced birefringence(0.139@1064 nm),surpassing majority hybrid NLO materials.The innovative anionic framework introduced here broadens the scope of hybrid NLO crystals,facilitating the integration of various aromatic heterocyclic cations.This research provides a robust strategic framework for the development of advanced NLO materials.展开更多
The equilibrium dynamics and nonlinear rheology of unentangled polymer blends remain inadequately understood,especially regarding the influence of short-chain matrix length N_(S) on the structure and rheological behav...The equilibrium dynamics and nonlinear rheology of unentangled polymer blends remain inadequately understood,especially regarding the influence of short-chain matrix length N_(S) on the structure and rheological behavior of dispersed long chains.Using molecular dynamics simulations based on the Kremer-Grest model,we systematically explore the N_(S)-dependence of static conformations,equilibrium dynamics,and nonlinear shear responses in unentangled long-chain/short-chain polymer blends.Our results demonstrate a decoupling between the static and dynamic sensitivity to N_(S):while the static chain size,R_g,follows Flory theory with slight swelling at small N_(S) due to incomplete excluded volume screening,the diffusion coefficient,D,and the relaxation time,τ_(0),exhibit a strong,non-monotonic N_(S)-dependence,transitioning from monomeric friction dominance at small N_(S) to collective segmental rearrangement at large N_(S).Additionally,we observe partial decoupling between the viscous and normal stress responses:while the zero-shear viscosity,η,is strongly N_(S)-dependent,the first and second normal stress coefficients,Ψ_(1) and Ψ_(2),collapse onto universal curves when scaled by the dimensionless shear rate,γτ_(0),suggesting a common mechanism of orientation and stretching.Under shear,long chains compress in the vorticity direction λ_(z)~Wi^(-0.2),which reduces collision frequency and contributes to shear thinning,while the scaling of weaker orientation resistance m_(G)~Wi^(0.35)reflects hydrodynamic screening by the short-chain matrix.These findings highlight the limitations of single-chain models and emphasize the necessity of considering N_(S)-dependent matrix dynamics and flow-induced structural changes in understanding the rheology of unentangled polymer blends.展开更多
Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are o...Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are often effective for stabilization but may not directly optimize long-term performance.To address this limitation,this study develops an integrated framework that combines optimal control principles with reinforcement learning for a single-link robotic manipulator.The proposed scheme adopts an actor–critic structure,where the critic network approximates the value function associated with the Hamilton–Jacobi–Bellman equation,and the actor network generates near-optimal control signals in real time.This dual adaptation enables the controller to refine its policy online without explicit system knowledge.Stability of the closed-loop system is analyzed through Lyapunov theory,ensuring boundedness of the tracking error.Numerical simulations on the single-link manipulator demonstrate that themethod achieves accurate trajectory followingwhile maintaining lowcontrol effort.The results further showthat the actor–critic learning mechanism accelerates convergence of the control policy compared with conventional optimization-based strategies.This work highlights the potential of reinforcement learning integrated with optimal control for robotic manipulators and provides a foundation for future extensions to more complex multi-degree-of-freedom systems.The proposed controller is further validated in a physics-based virtual Gazebo environment,demonstrating stable adaptation and real-time feasibility.展开更多
The flow of a tetra-hybrid Casson nanofluid(Al_(2)O_(3)-CuO-TiO_(2)-Ag/H_(2)O)over a nonlinear stretching sheet is investigated.The Buongiorno model is used to account for thermophoresis and Brownian motion,while ther...The flow of a tetra-hybrid Casson nanofluid(Al_(2)O_(3)-CuO-TiO_(2)-Ag/H_(2)O)over a nonlinear stretching sheet is investigated.The Buongiorno model is used to account for thermophoresis and Brownian motion,while thermal radiation is incorporated to examine its influence on the thermal boundary layer.The governing partial differential equations(PDEs)are reduced to a system of nonlinear ordinary differential equations(ODEs)with fully non-dimensional similarity transformations involving all independent variables.To solve the obtained highly nonlinear system of differential equations,a novel Clique polynomial collocation method is applied.The analysis focuses on the effects of the Casson parameter,power index,radiation parameter,thermophoresis parameter,Brownian motion parameter,and Lewis number.The key findings show that thermal radiation intensifies the thermal boundary layer,the Casson parameter reduces the velocity,and the Lewis number suppresses the concentration with direct relevance to polymer processing,coating flows,electronic cooling,and biomedical applications.展开更多
Transforming urban spatial structures to promote green and low-carbon development is an effective strategy.Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic devel...Transforming urban spatial structures to promote green and low-carbon development is an effective strategy.Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic development,research on its role in the synergistic relationship between these factors regarding carbon emission efficiency is limited.Furthermore,existing literature often overlooks nonlinear effects and interactions with other urban variables.This paper analyzed data from 295 Chinese cities in 2020,calculating urban population polycentricity,population dispersion indices,and carbon emission efficiency.Utilizing local spatial autocorrelation tools,we reveal interactions among urban population polycentricity,dispersion,carbon emissions,and carbon emission efficiency.We then employ a gradient boosting decision tree model(GBDT)to explore nonlinear and synergistic effects of polycentric urbanization.Key findings include:1)polycentric urbanization in Chinese cities exhibits significant spatial differentiation characteristics.The Polycentricity index is relatively high in economically developed eastern coastal regions with an overall low level,carbon emissions are concentrated in industrialized north-central cities and some Yangtze River Delta hubs,and carbon emission efficiency is the highest in the Yangtze River Delta while relatively low in Northeast China;there are significant spatially heterogeneous interaction characteristics among population polycentricity,population dispersion,carbon emissions,and carbon emission efficiency.2)Urban population polycentricity contributes 9.42%to total carbon emissions and 6.24%to carbon emission efficiency.3)The polycentricity index has a nonlinear impact on carbon emissions and carbon emission efficiency:no significant effect when below 0.50 or above 0.55,increased carbon emissions in 0.50-0.53,and reduced carbon emissions with improved efficiency in 0.53-0.55.4)The polycentricity index has an interaction effect with other variables;specifically,when the polycentricity index is between 0.53 and 0.55,its interaction with urban gross domestic product(GDP),urban population,urban built-up area,green coverage rate in built-up areas,urban technological expenditure,and the proportion of the output value of the secondary industry will reduce carbon emissions and improve carbon emission efficiency.These findings enhance the understanding of urban spatial structures and carbon emissions,providing valuable insights for policymakers in developing green and low-carbon strategies.展开更多
Traditional dynamic analysis of mechanical structures,often limited to individual beams or plates,fails to fully capture their dynamic behaviors.In systems where space and mass are constrained,such as the battery supp...Traditional dynamic analysis of mechanical structures,often limited to individual beams or plates,fails to fully capture their dynamic behaviors.In systems where space and mass are constrained,such as the battery support structures in electric aircraft,conventional absorbers and isolators are insufficient for effective vibration control.This study simplifies the battery support structure of electric aircraft as an integrated composite beam consisting of three interconnected beams,and investigated its structural dynamics properties and nonlinear vibration control under thermal conditions caused by battery heat.The nonlinear vibration control is performed using the Nitinol steel wire ropes(Ni Ti-ST),with nonlinear damping properties.The natural frequencies of system are determined using the Rayleigh-Ritz technique.Theoretical results are validated through both Finite Element Method(FEM)and hammer tests.Moreover,the dynamic equations are derived using the Lagrange method and discretized via the Galerkin Truncation Method(GTM).The Harmonic Balance Method(HBM)is used to evaluate the vibration responses of the integrated model,with further verification through the Runge-Kutta Method(RKM).The experiments are conducted to corroborate the theoretical analysis.The results show that the system frequency changes in stages with the increase of the stiffness of the integrated composite beam connection.Especially in the case of varying environments,as the temperature increases,the frequency of system will first increase to a certain maximum value and then gradually decrease.Furthermore,the NiTi-ST effectively reduces vibration in the integrated composite beam,particularly under varying temperatures and external excitations.展开更多
基金supported in part by the National Key Research and Development Program of China(2023YFA1011803)the National Natural Science Foundation of China(62273064,61991400/61991403,61933012,62250710167,62203078)+2 种基金Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0588)the Central University Project(2023CDJKYJH047)the Innovation Support Program for International Students Returning to China(cx2022016)
文摘This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output(MIMO)nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and non-vanishing uncertainties make the prescribed-time control problem become much more nontrivial. The solution to address the challenges mentioned above involves incorporating a prescribed-time filter, as opposed to a finite-time filter, and formulating a prescribed-time Lyapunov stability lemma(Lemma 5). The prescribed-time Lyapunov stability lemma is based on time axis shifting time-varying yet bounded gain, which establishes a novel link between the fixed-time and prescribed-time control method. This allows the restriction condition that the time-varying gain function must satisfy as imposed in most exist prescribed-time control works to be removed. Under the proposed control method, the desire trajectory is ensured to closely track the output of the system in prescribed time. The effectiveness of the theoretical results are verified through numerical simulation.
基金supported by the National Natural Science Foundation of China(61821004,U1964207,20221017-10)。
文摘This paper presents a novel fixed-time stabilization control(FSC)method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics.The key feature of the proposed method is the design of two dynamic parameters.Specifically,a set of auxiliary variables is first introduced through state transformation.These variables combine the original system states and the two introduced dynamic parameters,facilitating the closed-loop system stability analyses.Then,the two dynamic parameters are delicately designed by utilizing the Lyapunov method,ensuring that all the closed-loop system states are globally fixed-time stable.Compared with existing results,the“explosion of complexity”problem of backstepping control is avoided.Moreover,the two designed dynamic parameters are dependent on system states rather than a time-varying function,thus the proposed controller is still valid beyond the given fixedtime convergence instant.The effectiveness of the proposed method is demonstrated through two practical systems.
文摘In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.
基金supported by the National Natural Science Foundation of China(11502288)the Natural Science Foundation of Hunan Province(2016JJ3019)+1 种基金the Aeronautical Science Foundation of China(2017ZA88001)the Scientific Research Project of National University of Defense Technology(ZK17-03-32)
文摘A neural-network-based adaptive gain scheduling backstepping sliding mode control（NNAGS-BSMC） approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain strict-feedback nonlinear systems is formulated. Second, the detailed design of NNAGSBSMC is described. The sliding mode control（SMC） law is designed to track a referenced output via backstepping technique.To decrease chattering result from SMC, a radial basis function neural network（RBFNN） is employed to construct the NNAGSBSMC to facilitate adaptive gain scheduling, in which the gains are scheduled adaptively via neural network（NN）, with sliding surface and its differential as NN inputs and the gains as NN outputs. Finally, the verification example is given to show the effectiveness and robustness of the proposed approach. Contrasting simulation results indicate that the NNAGS-BSMC decreases the chattering effectively and has better control performance against the BSMC.
基金This work was supported by the National Natural Science Foundation of China (No.60674055)the Taishan Scholar programme and the NaturalScience Foundation of Shandong Province (No.Y2006G04)
文摘In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.
基金supported in part by the National Key Research and Development Program of China(2021ZD0201300)in part by the National Natural Science Foundation of China(61860206008,61933012)。
文摘In this paper,we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients,which mainly includes the following steps.Firstly,by introducing several key transformation functions and selecting the initial value of the time-varying scaling function,the symmetric prescribed performance with global and semi-global properties can be handled uniformly,without the need for control re-design.Secondly,to handle the problem of unknown time-varying control coefficient with an unknown sign,we propose an enhanced Nussbaum function(ENF)bearing some unique properties and characteristics,with which the complex stability analysis based on specific Nussbaum functions as commonly used is no longer required.Thirdly,by utilizing the core-function information technique,the nonparametric uncertainties in the system are gracefully handled so that no approximator is required.Furthermore,simulation results verify the effectiveness and benefits of the approach.
基金supported by the Shandong Provincial Natural Science Foundation(Nos.ZR2023QF039 and ZR2024MF068)the Qingdao Natural Science Foundation(No.23-2-1-123-zyyd-jch)+2 种基金the Taishan Scholars Project of Shandong Province of China(No.tstp20230624)the Science and Technology Plan for Youth Innovation of Universities in Shandong Province(No.2022KJ301)the National Natural Science Foundation of China(No.62373205).
文摘In this paper,an adaptive dynamic event-triggered asymptotic control scheme is designed for strict-feedback systems with time-varying parameters.The congelation of variables technique is employed to address the time-varying parameters in the system.During the controller design,two parameter estimation adaptive laws are constructed.The tuning function is introduced in the design process to avoid over-parameterization.To further conserve communication resources,a dynamic eventtriggered approach is proposed,in which a non-negative variable is introduced to update the threshold parameter dynamically.The global uniform asymptotic stability of the closed-loop system is proven through the Lyapunov stability analysis.The feasibility of the scheme is demonstrated by simulation.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
文摘This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(2022A1515012138)the NSFC(12271436,12371119)supported by the Natural Science Basic Research Program of Shaanxi(2022JC-04).
文摘We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.
基金supported by the Science Center Program of National Natural Science Foundation of China under Grant 62188101the National Natural Science Foundation of China under Grant 62573265.
文摘This study develops an event-triggered control strategy utilizing the fully actuated system approach for nonlinear interconnected large-scale systems containing actuator failures.First,to reduce the complexity of the design process,we transform the studied system into the form of a fully actuated system through a state transformation.Then,to address the unknown nonlinear functions and actuator fault parameters,we employ neural networks and adaptive estimation techniques,respectively.Moreover,to reduce the control cost and improve the control efficiency,we introduce event-triggered inputs into the control strategy.It is proved by the Lyapunov stability analysis that all signals of the closed-loop system are bounded and the output of system eventually converge to a bounded region.The efficacy of the control approach is ultimately demonstrated via the simulation of an actual machine feeding system.
基金Project supported by the National Natural Science Foundation of China(Nos.52575093 and 12202229)the China Postdoctoral Science Foundation(No.2025M771368)the Fundamental Research Funds for the Central Universities of China(Nos.buctrc202405 and JD2522)。
文摘Magnetorheological(MR)bearings,with their field-controllable rheological properties,offer new possibilities for control of rotor instabilities.However,their nonlinear dynamic behaviors and the underlying physical mechanisms governing these instabilities remain insufficiently understood.This work develops a coupled MR bearingrotor system model,where the oil film force is derived from a novel bilinear constitutive equation to capture the field-sensitive shear behaviors of MR fluids.Complex nonlinear dynamic behaviors including period doubling,quasi-period,and chaos are revealed,which emerge from the interaction between oil film vortex dynamics and magnetic excitation.The critical instability mechanism is identified from the evolution of intrinsic dynamic characteristics of MR bearings.When the whirl speed within the oil film reaches approximately half of the rotor speed,the damping force balances the destabilizing force,thereby defining a critical threshold beyond which the system transitions to instability.This threshold can be effectively tuned by adjusting the excitation current,which modifies the yield stress of MR fluids and consequently regulates the damping force.As a result,the nonlinear vibrations of oil whirl and whip can be suppressed,and the system stability can be significantly enhanced.These findings provide both theoretical insight and practical guidance for the design and control of MR bearing supported rotor systems.
基金The Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“RBF-Hermite difference scheme for the time-fractional kdv-Burgers equation”(2024D01C43)。
文摘In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.
基金supported by the National Natural Science Foundation of China (No.22275052)Department of Science and Technology of Hubei Province (Nos.2025AFA111 and 2024CSA076)。
文摘Achieving non-centrosymmetric(NCS) configurations in ABX3-type hybrid halides remains a critical challenge for nonlinear optical(NLO) materials due to the conflicting requirements of high second-harmonic generation(SHG) response,wide bandgap,and phase-matching capabilities.Herein,we propose a triplesite modulation strategy by synergistically tailoring the A-site cations(2-methylimidazole cation/1-ethyl-3-methylimidazole cation),B-site metals(Sn^(2+)/Pb^(2+)),and X-site halogens(Cl/Br),which effectively disrupts lattice symmetry and enables NCS crystallization.Our results demonstrate a strong SHG response,an expanded optical bandgap and increased birefringence.The optimized compound C_(6)H_(11)N_(2)PbCl_(3) exhibits a moderately strong SHG efficiency of 3.8 × KDP,a wide bandgap(3.87 eV),and enhanced birefringence(0.139@1064 nm),surpassing majority hybrid NLO materials.The innovative anionic framework introduced here broadens the scope of hybrid NLO crystals,facilitating the integration of various aromatic heterocyclic cations.This research provides a robust strategic framework for the development of advanced NLO materials.
基金financially supported by the National Natural Science Foundation of China(Nos.22341304,22303100 and 12205270)the National Key R&D Program of China(Nos.2023YFA1008800 and 2020YFA0713601)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDC0180303)。
文摘The equilibrium dynamics and nonlinear rheology of unentangled polymer blends remain inadequately understood,especially regarding the influence of short-chain matrix length N_(S) on the structure and rheological behavior of dispersed long chains.Using molecular dynamics simulations based on the Kremer-Grest model,we systematically explore the N_(S)-dependence of static conformations,equilibrium dynamics,and nonlinear shear responses in unentangled long-chain/short-chain polymer blends.Our results demonstrate a decoupling between the static and dynamic sensitivity to N_(S):while the static chain size,R_g,follows Flory theory with slight swelling at small N_(S) due to incomplete excluded volume screening,the diffusion coefficient,D,and the relaxation time,τ_(0),exhibit a strong,non-monotonic N_(S)-dependence,transitioning from monomeric friction dominance at small N_(S) to collective segmental rearrangement at large N_(S).Additionally,we observe partial decoupling between the viscous and normal stress responses:while the zero-shear viscosity,η,is strongly N_(S)-dependent,the first and second normal stress coefficients,Ψ_(1) and Ψ_(2),collapse onto universal curves when scaled by the dimensionless shear rate,γτ_(0),suggesting a common mechanism of orientation and stretching.Under shear,long chains compress in the vorticity direction λ_(z)~Wi^(-0.2),which reduces collision frequency and contributes to shear thinning,while the scaling of weaker orientation resistance m_(G)~Wi^(0.35)reflects hydrodynamic screening by the short-chain matrix.These findings highlight the limitations of single-chain models and emphasize the necessity of considering N_(S)-dependent matrix dynamics and flow-induced structural changes in understanding the rheology of unentangled polymer blends.
基金supported in part by the National Science and Technology Council under Grant NSTC 114-2221-E-027-104.
文摘Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are often effective for stabilization but may not directly optimize long-term performance.To address this limitation,this study develops an integrated framework that combines optimal control principles with reinforcement learning for a single-link robotic manipulator.The proposed scheme adopts an actor–critic structure,where the critic network approximates the value function associated with the Hamilton–Jacobi–Bellman equation,and the actor network generates near-optimal control signals in real time.This dual adaptation enables the controller to refine its policy online without explicit system knowledge.Stability of the closed-loop system is analyzed through Lyapunov theory,ensuring boundedness of the tracking error.Numerical simulations on the single-link manipulator demonstrate that themethod achieves accurate trajectory followingwhile maintaining lowcontrol effort.The results further showthat the actor–critic learning mechanism accelerates convergence of the control policy compared with conventional optimization-based strategies.This work highlights the potential of reinforcement learning integrated with optimal control for robotic manipulators and provides a foundation for future extensions to more complex multi-degree-of-freedom systems.The proposed controller is further validated in a physics-based virtual Gazebo environment,demonstrating stable adaptation and real-time feasibility.
基金the UGC,New Delhi,India for financial assistance via the UGC-Junior Research Fellowship(CSIR-UGC NET JULY 2024)(Student ID:241610090610)。
文摘The flow of a tetra-hybrid Casson nanofluid(Al_(2)O_(3)-CuO-TiO_(2)-Ag/H_(2)O)over a nonlinear stretching sheet is investigated.The Buongiorno model is used to account for thermophoresis and Brownian motion,while thermal radiation is incorporated to examine its influence on the thermal boundary layer.The governing partial differential equations(PDEs)are reduced to a system of nonlinear ordinary differential equations(ODEs)with fully non-dimensional similarity transformations involving all independent variables.To solve the obtained highly nonlinear system of differential equations,a novel Clique polynomial collocation method is applied.The analysis focuses on the effects of the Casson parameter,power index,radiation parameter,thermophoresis parameter,Brownian motion parameter,and Lewis number.The key findings show that thermal radiation intensifies the thermal boundary layer,the Casson parameter reduces the velocity,and the Lewis number suppresses the concentration with direct relevance to polymer processing,coating flows,electronic cooling,and biomedical applications.
基金Under the auspices of National Natural Science Foundation of China(No.42571300)。
文摘Transforming urban spatial structures to promote green and low-carbon development is an effective strategy.Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic development,research on its role in the synergistic relationship between these factors regarding carbon emission efficiency is limited.Furthermore,existing literature often overlooks nonlinear effects and interactions with other urban variables.This paper analyzed data from 295 Chinese cities in 2020,calculating urban population polycentricity,population dispersion indices,and carbon emission efficiency.Utilizing local spatial autocorrelation tools,we reveal interactions among urban population polycentricity,dispersion,carbon emissions,and carbon emission efficiency.We then employ a gradient boosting decision tree model(GBDT)to explore nonlinear and synergistic effects of polycentric urbanization.Key findings include:1)polycentric urbanization in Chinese cities exhibits significant spatial differentiation characteristics.The Polycentricity index is relatively high in economically developed eastern coastal regions with an overall low level,carbon emissions are concentrated in industrialized north-central cities and some Yangtze River Delta hubs,and carbon emission efficiency is the highest in the Yangtze River Delta while relatively low in Northeast China;there are significant spatially heterogeneous interaction characteristics among population polycentricity,population dispersion,carbon emissions,and carbon emission efficiency.2)Urban population polycentricity contributes 9.42%to total carbon emissions and 6.24%to carbon emission efficiency.3)The polycentricity index has a nonlinear impact on carbon emissions and carbon emission efficiency:no significant effect when below 0.50 or above 0.55,increased carbon emissions in 0.50-0.53,and reduced carbon emissions with improved efficiency in 0.53-0.55.4)The polycentricity index has an interaction effect with other variables;specifically,when the polycentricity index is between 0.53 and 0.55,its interaction with urban gross domestic product(GDP),urban population,urban built-up area,green coverage rate in built-up areas,urban technological expenditure,and the proportion of the output value of the secondary industry will reduce carbon emissions and improve carbon emission efficiency.These findings enhance the understanding of urban spatial structures and carbon emissions,providing valuable insights for policymakers in developing green and low-carbon strategies.
基金supported by the National Natural Science Foundation of China(No.12272240)the Liaoning Revitalization Talents Program,China(No.XLYC2203197)。
文摘Traditional dynamic analysis of mechanical structures,often limited to individual beams or plates,fails to fully capture their dynamic behaviors.In systems where space and mass are constrained,such as the battery support structures in electric aircraft,conventional absorbers and isolators are insufficient for effective vibration control.This study simplifies the battery support structure of electric aircraft as an integrated composite beam consisting of three interconnected beams,and investigated its structural dynamics properties and nonlinear vibration control under thermal conditions caused by battery heat.The nonlinear vibration control is performed using the Nitinol steel wire ropes(Ni Ti-ST),with nonlinear damping properties.The natural frequencies of system are determined using the Rayleigh-Ritz technique.Theoretical results are validated through both Finite Element Method(FEM)and hammer tests.Moreover,the dynamic equations are derived using the Lagrange method and discretized via the Galerkin Truncation Method(GTM).The Harmonic Balance Method(HBM)is used to evaluate the vibration responses of the integrated model,with further verification through the Runge-Kutta Method(RKM).The experiments are conducted to corroborate the theoretical analysis.The results show that the system frequency changes in stages with the increase of the stiffness of the integrated composite beam connection.Especially in the case of varying environments,as the temperature increases,the frequency of system will first increase to a certain maximum value and then gradually decrease.Furthermore,the NiTi-ST effectively reduces vibration in the integrated composite beam,particularly under varying temperatures and external excitations.
