In this paper,we study an integral system involving m equations■where ui>0 in R^(n),0<α<n,and pi>1(i=1,2,…,m).Based on the optimal integrability intervals,we estimate the decay rates of the positive sol...In this paper,we study an integral system involving m equations■where ui>0 in R^(n),0<α<n,and pi>1(i=1,2,…,m).Based on the optimal integrability intervals,we estimate the decay rates of the positive solutions of the system at infinity.But estimating these rates is difficult because the relation between pi(i=1,2,…,m)is uncertain.To overcome this difficulty,we obtain the asymptotic behavior of all cases by discussing them separately.In addition,we also get the radial symmetry of positive solutions under some integrability condition.展开更多
In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β...In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.展开更多
We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone non...We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n＋α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system：This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate展开更多
In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes...In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes in an integral form which was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions of （0.1） are radially symmetric and decreasing with respect to some point under some general conditions of integrability. The results essentially improve and extend previously known results [4, 8].展开更多
In this paper, Liouville-type theorems of nonnegative solutions for some elliptic integral systems are considered. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of St...In this paper, Liouville-type theorems of nonnegative solutions for some elliptic integral systems are considered. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of Stein-Weiss inequality instead of Maximum Principle.展开更多
Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time nonlinearity.Ho...Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time nonlinearity.However,solving the Hamilton-Jacobi-Bellman(HJB)equations for nonlinear systems requires precise and complicated dynamics.Moreover,the research and application of IRL in continuous-time(CT)systems must be further improved.To develop the IRL of a CT nonlinear system,a data-based adaptive neural dynamic programming(ANDP)method is proposed to investigate the optimal control problem of uncertain CT multi-input systems such that the knowledge of the dynamics in the HJB equation is unnecessary.First,the multi-input model is approximated using a neural network(NN),which can be utilized to design an integral reinforcement signal.Subsequently,two criterion networks and one action network are constructed based on the integral reinforcement signal.A nonzero-sum Nash equilibrium can be reached by learning the optimal strategies of the multi-input model.In this scheme,the NN weights are constantly updated using an adaptive algorithm.The weight convergence and the system stability are analyzed in detail.The optimal control problem of a multi-input nonlinear CT system is effectively solved using the ANDP scheme,and the results are verified by a simulation study.展开更多
This article investigates the anti-disturbance and stabilization problems for the nonlinear uncertain permanent magnet synchronous motor(PMSM)with stator voltage saturation and unknown load.A smooth switching mechanis...This article investigates the anti-disturbance and stabilization problems for the nonlinear uncertain permanent magnet synchronous motor(PMSM)with stator voltage saturation and unknown load.A smooth switching mechanism is presented to structure the adaptive integral terminal sliding mode control(SMC)strategy.The control design consists of compensation control and nominal control,which improves the rapidity and accuracy of trajectory tracking.The smooth saturation model based on the error function is applied to approximate the voltage saturation phenomenon.Additionally,to deal with the adverse effects of various unknown disturbances,including model parameter uncertainties and unknown external load disturbances,an improved disturbance observer(DO)is proposed.This observer effectively suppresses the fluctuations caused by fixed gain during the starting period of the system.Finally,the experimental results under different conditions show that the proposed strategy has good tracking and disturbance suppression performances.展开更多
For any country,the availability of electricity is crucial to the development of the national economy and society.As a result,decision-makers and policy-makers can improve the sustainability and security of the energy...For any country,the availability of electricity is crucial to the development of the national economy and society.As a result,decision-makers and policy-makers can improve the sustainability and security of the energy supply by implementing a variety of actions by using the evaluation of these factors as an early warning system.This research aims to provide a multi-criterion decision-making(MCDM)method for assessing the sustainability and security of the electrical supply.The weights of criteria,which indicate their relative relevance in the assessment of the sustainability and security of the energy supply,the MCDM method allow users to express their opinions.To overcome the impact of uncertainty and vagueness of expert opinion,we explore the notion of picture fuzzy theory,which is a more efficient and dominant mathematical model.Recently,the theory of Aczel-Alsina operations has attained a lot of attraction and has an extensive capability to acquire smooth approximated results during the aggregation process.However,Choquet integral operators are more flexible and are used to express correlation among different attributes.This article diagnoses an innovative theory of picture fuzzy set to derive robust mathematical methodologies of picture fuzzy Choquet Integral Aczel-Alsina aggregation operators.To prove the intensity and validity of invented approaches,some dominant properties and special cases are also discussed.An intelligent decision algorithm for the MCDM problem is designed to resolve complicated real-life applications under multiple conflicting criteria.Additionally,we discussed a numerical example to investigate a suitable electric transformer under consideration of different beneficial key criteria.A comparative study is established to capture the superiority and effectiveness of pioneered mathematical approaches with existing methodologies.展开更多
Since the first design of tactile sensors was proposed by Harmon in 1982,tactile sensors have evolved through four key phases:industrial applications(1980s,basic pressure detection),miniaturization via MEMS(1990s),fle...Since the first design of tactile sensors was proposed by Harmon in 1982,tactile sensors have evolved through four key phases:industrial applications(1980s,basic pressure detection),miniaturization via MEMS(1990s),flexible electronics(2010s,stretchable materials),and intelligent systems(2020s-present,AI-driven multimodal sensing).With the innovation of material,processing techniques,and multimodal fusion of stimuli,the application of tactile sensors has been continuously expanding to a diversity of areas,including but not limited to medical care,aerospace,sports and intelligent robots.Currently,researchers are dedicated to develop tactile sensors with emerging mechanisms and structures,pursuing high-sensitivity,high-resolution,and multimodal characteristics and further constructing tactile systems which imitate and approach the performance of human organs.However,challenges in the combination between the theoretical research and the practical applications are still significant.There is a lack of comprehensive understanding in the state of the art of such knowledge transferring from academic work to technical products.Scaled-up production of laboratory materials faces fatal challenges like high costs,small scale,and inconsistent quality.Ambient factors,such as temperature,humidity,and electromagnetic interference,also impair signal reliability.Moreover,tactile sensors must operate across a wide pressure range(0.1 k Pa to several or even dozens of MPa)to meet diverse application needs.Meanwhile,the existing algorithms,data models and sensing systems commonly reveal insufficient precision as well as undesired robustness in data processing,and there is a realistic gap between the designed and the demanded system response speed.In this review,oriented by the design requirements of intelligent tactile sensing systems,we summarize the common sensing mechanisms,inspired structures,key performance,and optimizing strategies,followed by a brief overview of the recent advances in the perspectives of system integration and algorithm implementation,and the possible roadmap of future development of tactile sensors,providing a forward-looking as well as critical discussions in the future industrial applications of flexible tactile sensors.展开更多
In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^...In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^(1-a_uθ)(x)/|x-y|^(n-a))dx,y∈ ?R_+~n,where n 2, 2-n < a < 1, κ, θ > 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system.展开更多
In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the unique...In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.展开更多
Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. T...Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.展开更多
Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(...Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(x) and K(x) satisfy some suitable conditions.It is shown that every positive regular solution(u(x)1,v(x)) is symmetric about some plane by developing the moving plane method in an integral form.Moreover,regularity of the solution is studied.Finally,the nonexistence of positive solutions to the system in the case 0 < p1q <(n+α)/(n-α) is also discussed.展开更多
By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations ...By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results.展开更多
This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. T...This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.展开更多
Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed ...Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.展开更多
This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a disc...This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.展开更多
This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integ...This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional(LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.展开更多
This paper studies a type of integral and reduction of the generalized Birkhoffian system. An existent condition and the form of the integral are obtained. By using the integral, the dimension of the system can be red...This paper studies a type of integral and reduction of the generalized Birkhoffian system. An existent condition and the form of the integral are obtained. By using the integral, the dimension of the system can be reduced two degrees. An example is given to illustrate the application of the results.展开更多
A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with...A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.展开更多
基金supported by the NSFC(11871278)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX23-1669).
文摘In this paper,we study an integral system involving m equations■where ui>0 in R^(n),0<α<n,and pi>1(i=1,2,…,m).Based on the optimal integrability intervals,we estimate the decay rates of the positive solutions of the system at infinity.But estimating these rates is difficult because the relation between pi(i=1,2,…,m)is uncertain.To overcome this difficulty,we obtain the asymptotic behavior of all cases by discussing them separately.In addition,we also get the radial symmetry of positive solutions under some integrability condition.
基金Chen research is supported by NSF of China (10961015)Yang research is supported by NSF of China (10961016)the GAN PO555 Program of Jiangxi
文摘In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.
基金supported by NSF Grant DMS-0604638Li partially supported by NSF Grant DMS-0401174
文摘We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n＋α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system：This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate
基金Supported by National Natural Science Foundation of China-NSAF (10976026)
文摘In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes in an integral form which was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions of （0.1） are radially symmetric and decreasing with respect to some point under some general conditions of integrability. The results essentially improve and extend previously known results [4, 8].
文摘In this paper, Liouville-type theorems of nonnegative solutions for some elliptic integral systems are considered. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of Stein-Weiss inequality instead of Maximum Principle.
文摘Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time nonlinearity.However,solving the Hamilton-Jacobi-Bellman(HJB)equations for nonlinear systems requires precise and complicated dynamics.Moreover,the research and application of IRL in continuous-time(CT)systems must be further improved.To develop the IRL of a CT nonlinear system,a data-based adaptive neural dynamic programming(ANDP)method is proposed to investigate the optimal control problem of uncertain CT multi-input systems such that the knowledge of the dynamics in the HJB equation is unnecessary.First,the multi-input model is approximated using a neural network(NN),which can be utilized to design an integral reinforcement signal.Subsequently,two criterion networks and one action network are constructed based on the integral reinforcement signal.A nonzero-sum Nash equilibrium can be reached by learning the optimal strategies of the multi-input model.In this scheme,the NN weights are constantly updated using an adaptive algorithm.The weight convergence and the system stability are analyzed in detail.The optimal control problem of a multi-input nonlinear CT system is effectively solved using the ANDP scheme,and the results are verified by a simulation study.
基金supported by the National Natural Science Foundation under Grant 62273189the Shandong Province Natural Science Foundation under Grant ZR2021MF005Systems Science Plus Joint Research Program of Qingdao University under Grant XT2024201 of China supporting this research work.
文摘This article investigates the anti-disturbance and stabilization problems for the nonlinear uncertain permanent magnet synchronous motor(PMSM)with stator voltage saturation and unknown load.A smooth switching mechanism is presented to structure the adaptive integral terminal sliding mode control(SMC)strategy.The control design consists of compensation control and nominal control,which improves the rapidity and accuracy of trajectory tracking.The smooth saturation model based on the error function is applied to approximate the voltage saturation phenomenon.Additionally,to deal with the adverse effects of various unknown disturbances,including model parameter uncertainties and unknown external load disturbances,an improved disturbance observer(DO)is proposed.This observer effectively suppresses the fluctuations caused by fixed gain during the starting period of the system.Finally,the experimental results under different conditions show that the proposed strategy has good tracking and disturbance suppression performances.
文摘For any country,the availability of electricity is crucial to the development of the national economy and society.As a result,decision-makers and policy-makers can improve the sustainability and security of the energy supply by implementing a variety of actions by using the evaluation of these factors as an early warning system.This research aims to provide a multi-criterion decision-making(MCDM)method for assessing the sustainability and security of the electrical supply.The weights of criteria,which indicate their relative relevance in the assessment of the sustainability and security of the energy supply,the MCDM method allow users to express their opinions.To overcome the impact of uncertainty and vagueness of expert opinion,we explore the notion of picture fuzzy theory,which is a more efficient and dominant mathematical model.Recently,the theory of Aczel-Alsina operations has attained a lot of attraction and has an extensive capability to acquire smooth approximated results during the aggregation process.However,Choquet integral operators are more flexible and are used to express correlation among different attributes.This article diagnoses an innovative theory of picture fuzzy set to derive robust mathematical methodologies of picture fuzzy Choquet Integral Aczel-Alsina aggregation operators.To prove the intensity and validity of invented approaches,some dominant properties and special cases are also discussed.An intelligent decision algorithm for the MCDM problem is designed to resolve complicated real-life applications under multiple conflicting criteria.Additionally,we discussed a numerical example to investigate a suitable electric transformer under consideration of different beneficial key criteria.A comparative study is established to capture the superiority and effectiveness of pioneered mathematical approaches with existing methodologies.
基金the financial support of the National Natural Science Foundation of China(NO.52173028)。
文摘Since the first design of tactile sensors was proposed by Harmon in 1982,tactile sensors have evolved through four key phases:industrial applications(1980s,basic pressure detection),miniaturization via MEMS(1990s),flexible electronics(2010s,stretchable materials),and intelligent systems(2020s-present,AI-driven multimodal sensing).With the innovation of material,processing techniques,and multimodal fusion of stimuli,the application of tactile sensors has been continuously expanding to a diversity of areas,including but not limited to medical care,aerospace,sports and intelligent robots.Currently,researchers are dedicated to develop tactile sensors with emerging mechanisms and structures,pursuing high-sensitivity,high-resolution,and multimodal characteristics and further constructing tactile systems which imitate and approach the performance of human organs.However,challenges in the combination between the theoretical research and the practical applications are still significant.There is a lack of comprehensive understanding in the state of the art of such knowledge transferring from academic work to technical products.Scaled-up production of laboratory materials faces fatal challenges like high costs,small scale,and inconsistent quality.Ambient factors,such as temperature,humidity,and electromagnetic interference,also impair signal reliability.Moreover,tactile sensors must operate across a wide pressure range(0.1 k Pa to several or even dozens of MPa)to meet diverse application needs.Meanwhile,the existing algorithms,data models and sensing systems commonly reveal insufficient precision as well as undesired robustness in data processing,and there is a realistic gap between the designed and the demanded system response speed.In this review,oriented by the design requirements of intelligent tactile sensing systems,we summarize the common sensing mechanisms,inspired structures,key performance,and optimizing strategies,followed by a brief overview of the recent advances in the perspectives of system integration and algorithm implementation,and the possible roadmap of future development of tactile sensors,providing a forward-looking as well as critical discussions in the future industrial applications of flexible tactile sensors.
基金supported by National Natural Science Foundation of China (Grant No. 11571268)Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2017JQ1022)the Fundamental Research Funds for the Central Universities (Grant No. GK201802015)
文摘In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^(1-a_uθ)(x)/|x-y|^(n-a))dx,y∈ ?R_+~n,where n 2, 2-n < a < 1, κ, θ > 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system.
文摘In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.
文摘Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.
基金supported by Chinese National Science Fund for Distinguished Young Scholars (Grant No.10925104)National Natural Science Foundation of China (Grant No.11001221)+1 种基金the Foundation of Shaanxi Province Education Department (Grant No. 2010JK549)the Foundation of Xi’an Statistical Research Institute (Grant No.10JD04)
文摘Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(x) and K(x) satisfy some suitable conditions.It is shown that every positive regular solution(u(x)1,v(x)) is symmetric about some plane by developing the moving plane method in an integral form.Moreover,regularity of the solution is studied.Finally,the nonexistence of positive solutions to the system in the case 0 < p1q <(n+α)/(n-α) is also discussed.
基金SuppoSed by the NSF of Anhui Provincial Education Depaxtment(KJ2012A265,KJ2012B187)
文摘By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results.
基金Project supported by State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China （Grant Nos 10672143 and 10471145） and the Natural Science Foundation of Henan Province Government, China （Grant Nos 0311011400 and 0511022200）.
文摘This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.
基金Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No.51521065)
文摘Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.
基金Project partially supported by the National Natural Science Foundation of China （Grant No 10172056） and the Science Research of the Education Bureau of Anhui Province, China （Grant No 2006KJ263B）. Acknowledgement We wish to thank the referees for their careful reading of the manuscript and their useful remarks which helped us to improve the quality of this paper.
文摘This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China(61473070,61433004,61627809)SAPI Fundamental Research Funds(2013ZCX01,2013ZCX14)
文摘This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional(LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10772025, 10932002, and 10972031)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics
文摘This paper studies a type of integral and reduction of the generalized Birkhoffian system. An existent condition and the form of the integral are obtained. By using the integral, the dimension of the system can be reduced two degrees. An example is given to illustrate the application of the results.
基金supported in part by the National Natural Science Foundation of China(6202530361973147)the LiaoNing Revitalization Talents Program(XLYC1907050)。
文摘A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.
