Aiming at solving the problems of response lag and lack of precision and stability in constant grinding force control of industrial robot belts,a constant force control strategy combining fuzzy control and proportion ...Aiming at solving the problems of response lag and lack of precision and stability in constant grinding force control of industrial robot belts,a constant force control strategy combining fuzzy control and proportion integration differentiation(PID)was proposed by analyzing the signal transmission process and the dynamic characteristics of the grinding mechanism.The simulation results showed that compared with the classical PID control strategy,the system adjustment time was shortened by 98.7%,the overshoot was reduced by 5.1%,and the control error was 0.2%-0.5%when the system was stabilized.The optimized fuzzy control system had fast adjustment speeds,precise force control and stability.The experimental analysis of the surface morphology of the machined blade was carried out by the industrial robot abrasive grinding mechanism,and the correctness of the theoretical analysis and the effectiveness of the control strategy were verified.展开更多
Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds...Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.展开更多
This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted ...This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the ekistence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.展开更多
The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is...The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant,which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO(IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population diversity.The tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integerorder PID controller, the fractional-order proportion integration differentiation(PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.展开更多
Beer fermentation process is a complex biochemical reaction process.It is the most important to control temperature of the wort in fermentation tank in accordance with the beer fermentation temperature curve so as to ...Beer fermentation process is a complex biochemical reaction process.It is the most important to control temperature of the wort in fermentation tank in accordance with the beer fermentation temperature curve so as to ensure the completion of fermentation.The controlled object is characterized by large inertia,long time delay and mutual coupling of three temperature areas.Based on this,a temperature control method for beer fermentation system is designed.Using digital incremental proportion integration differentiation （PID） control algorithm,the controlled quantity is transmitted to the controlled object after diagonal matrix decoupling.This simulation system can be completed in laboratory using VB and Kingview software,so it has the features of good security and low cost.It is very suitable for experimental teaching.展开更多
Neuron PSD (proportion, sum and differentiation) controller has the ability of on-line change of weights to reach the purpose of regulating parameters of PID using neuron’s self-studying and self-organization and the...Neuron PSD (proportion, sum and differentiation) controller has the ability of on-line change of weights to reach the purpose of regulating parameters of PID using neuron’s self-studying and self-organization and the change of controlled plant, which overcomes the disadvantages of affecting a conventional PID’s accurate regulation because of the change of load, model and non-linearity. LF2407 DSP can reach the purpose of parallel running by using multi-sets of bus. So it can greatly increase operation speed and offer a set of flexible instruction system. The realization of PSD control on DSP can build an ideal electrical machine controller.展开更多
For complex systems with high nonlinearity and strong coupling,the decoupling control technology based on proportion integration differentiation(PID)neural network(PIDNN)is used to eliminate the coupling between loops...For complex systems with high nonlinearity and strong coupling,the decoupling control technology based on proportion integration differentiation(PID)neural network(PIDNN)is used to eliminate the coupling between loops.The connection weights of the PIDNN are easy to fall into local optimum due to the use of the gradient descent learning method.In order to solve this problem,a hybrid particle swarm optimization(PSO)and differential evolution(DE)algorithm(PSO-DE)is proposed for optimizing the connection weights of the PIDNN.The DE algorithm is employed as an acceleration operation to help the swarm to get out of local optima traps in case that the optimal result has not been improved after several iterations.Two multivariable controlled plants with strong coupling between input and output pairs are employed to demonstrate the effectiveness of the proposed method.Simulation results show t hat the proposed met hod has better decoupling capabilities and control quality than the previous approaches.展开更多
Low Earth Orbit(LEO)satellite navigation signal can be used as an opportunity signal in the case of a Global Navigation Satellite System(GNSS)outage,or as an enhancement by means of traditional GNSS positioning algori...Low Earth Orbit(LEO)satellite navigation signal can be used as an opportunity signal in the case of a Global Navigation Satellite System(GNSS)outage,or as an enhancement by means of traditional GNSS positioning algorithms.No matter which service mode is used,signal acquisition is a prerequisite for providing enhanced LEO navigation services.Compared with the medium orbit satellite,the transit time of the LEO satellite is shorter.Thus,it is of great significance to expand the successful acquisition time range of the LEO signal.Previous studies on LEO signal acquisition are based on simulation data.However,signal acquisition research based on real data is crucial.In this work,the signal characteristics of LEO satellites:power space density in free space and the Doppler shift of LEO satellites are individually studied.The unified symbolic definitions of several integration algorithms based on the parallel search signal acquisition algorithm are given.To verify these algorithms for LEO signal acquisition,a Software Defined Receiver(SDR)is developed.The performance of these integration algorithms on expanding the successful acquisition time range is verified by the real data collected from the Luojia-1A satellite.The experimental results show that the integration strategy can expand the successful acquisition time range,and it will not expand indefinitely with the integration duration.The performance of the coherent integration and differential integration algorithms is better than the other two integration algorithms,so the two algorithms are recommended for LEO signal acquisition and a 20 ms integration duration is preferred.The detection threshold of 2.5 is not suitable for all integration algorithms and various integration durations,especially for the Maximum-to-Mean Ratio indicator.展开更多
The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution varia...The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.展开更多
The execution of the gaits generated with the help of a gait planner is a crucial task in biped locomotion. This task is to be achieved with the help of a suitable torque based controller to ensure smooth walk of the ...The execution of the gaits generated with the help of a gait planner is a crucial task in biped locomotion. This task is to be achieved with the help of a suitable torque based controller to ensure smooth walk of the biped robot. It is important to note that the success of the developed proportion integration differentiation （PID） controller depends on the selected gains of the controller. In the present study, an attempt is made to tune the gains of the PID controller for the biped robot ascending and descending the stair case and sloping surface with the help of two non-traditional optimization algorithms, namely modified chaotic invasive weed optimization （MCIWO） and particle swarm optimization （PSO） algorithms. Once the optimal PID controllers are developed, a simulation study has been conducted in computer for obtaining the optimal tuning parameters of the controller of the biped robot. Finally, the optimal gait angles obtained by using the best controller are fed to the real biped robot and found that the biped robot has successfully negotiated the said terrains.展开更多
A PID parameters tuning and optimization method for a turbine engine based on the simplex search method was proposed. Taking time delay of combustion and actuator into account, a simulation model of a PID control syst...A PID parameters tuning and optimization method for a turbine engine based on the simplex search method was proposed. Taking time delay of combustion and actuator into account, a simulation model of a PID control system for a turbine engine was developed. A performance index based on the integral of absolute error （IAE） was given as an objective function of optimization. In order to avoid the sensitivity that resulted from the initial values of the simplex search method, the traditional Ziegler-Nichols method was used to tune PID parameters to obtain the initial values at first, then the simplex search method was applied to optimize PID parameters for the turbine engine. Simulation results indicate that the simplex search method is a reasonable and effective method for PID controller parameters tuning and optimization.展开更多
We present a state-to-state dynamical calculation on the reaction S++ H2→ SH+ +H based on an accurate X2 A″ potential surface. Some reaction properties, such as reaction probability, integral cross sections, product...We present a state-to-state dynamical calculation on the reaction S++ H2→ SH+ +H based on an accurate X2 A″ potential surface. Some reaction properties, such as reaction probability, integral cross sections, product distribution, etc.,are found to be those with characteristics of an indirect reaction. The oscillating structures appearing in reaction probability versus collision energy are considered to be the consequence of the deep potential well in the reaction. The comparison of the present total integral cross sections with the previous quasi-classical trajectory results shows that the quantum effect is more important at low collision energies. In addition, the quantum number inversion in the rotational distribution of the product is regarded as the result of the heavy–light–light mass combination, which is not effective for the vibrational excitation. For the collision energies considered, the product differential cross sections of the title reaction are mainly concentrated in the forward and backward regions, which suggests that there is a long-life intermediate complex in the reaction process.展开更多
In this paper, some classes of differentiation basis are investigated and several positive answers to a conjecture of Zygmund on differentiation of integrals are presented.
The numerical stability of linear neutral Volterra delay integral differential equations is dealt with.Under a sufficient condition such that this system with a lagging argument is asymptotically stable,it is proved t...The numerical stability of linear neutral Volterra delay integral differential equations is dealt with.Under a sufficient condition such that this system with a lagging argument is asymptotically stable,it is proved that every A-stable linear multistep method preserves the delay-independent stabil-ity of its exact solutions.Finally,some numerical experiments are given to demonstrate the main conclu-sion.展开更多
H stability is a new and important concept. In this paper,we discuss the equationx(t)=-a(t)x(t)+∫ t -∞ k(t,s-t,x(s)) d sand we gain a new decision theorem. Using this decision theorem,we obtained a very extensive re...H stability is a new and important concept. In this paper,we discuss the equationx(t)=-a(t)x(t)+∫ t -∞ k(t,s-t,x(s)) d sand we gain a new decision theorem. Using this decision theorem,we obtained a very extensive result of the H uniformly asymptotical stability of this equation. That is,eliminating the restriction that a(t) is bounded.展开更多
The generalized KdV equation is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma￣[2], Ihe isolated wave in transmission line￣[3], and the isolated wave in t...The generalized KdV equation is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma￣[2], Ihe isolated wave in transmission line￣[3], and the isolated wave in the bound-ary surface of the divided layer fluid￣[4]. For the characteristic problem of the gene-ralized KdV equation, this paper, based on the Riemann function, designs a suitablestructure, then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding fixed point, the above integral differential equ-ation has a unique regular solution, so the characteristic problem of the generalizedKdV equation has a. unique solution. The iteration solution derived from the integraldifferential equation sequence is uniformly convegent in.展开更多
The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the ...The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.展开更多
A closed-chain robot has several advantages over an open-chain robot, such as high mechanical rigidity, high payload, high precision. Accurate trajectory control of a robot is essential in practical-use. This paper pr...A closed-chain robot has several advantages over an open-chain robot, such as high mechanical rigidity, high payload, high precision. Accurate trajectory control of a robot is essential in practical-use. This paper presents an adaptive proportional integral differential （PID） control algorithm based on radial basis function （RBF） neural network for trajectory tracking of a two-degree-of-freedom （2-DOF） closed-chain robot. In this scheme, an RBF neural network is used to approximate the unknown nonlinear dynamics of the robot, at the same time, the PID parameters can be adjusted online and the high precision can be obtained. Simulation results show that the control algorithm accurately tracks a 2-DOF closed-chain robot trajectories. The results also indicate that the system robustness and tracking performance are superior to the classic PID method.展开更多
基金Civil Project of China Aerospace Science and Technology CorporationUniversity-Industry Collaborative Education Program of Ministry of Education of China(No.220906517214433)。
文摘Aiming at solving the problems of response lag and lack of precision and stability in constant grinding force control of industrial robot belts,a constant force control strategy combining fuzzy control and proportion integration differentiation(PID)was proposed by analyzing the signal transmission process and the dynamic characteristics of the grinding mechanism.The simulation results showed that compared with the classical PID control strategy,the system adjustment time was shortened by 98.7%,the overshoot was reduced by 5.1%,and the control error was 0.2%-0.5%when the system was stabilized.The optimized fuzzy control system had fast adjustment speeds,precise force control and stability.The experimental analysis of the surface morphology of the machined blade was carried out by the industrial robot abrasive grinding mechanism,and the correctness of the theoretical analysis and the effectiveness of the control strategy were verified.
基金the Bilateral Science and Technology Collaboration Program of Australia 1998 the Natural Science Foundation of China (No. 1
文摘Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.
文摘This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the ekistence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.
基金supported by the National Natural Science Foundation of China(6137415361473138)+2 种基金Natural Science Foundation of Jiangsu Province(BK20151130)Six Talent Peaks Project in Jiangsu Province(2015-DZXX-011)China Scholarship Council Fund(201606845005)
文摘The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant,which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO(IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population diversity.The tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integerorder PID controller, the fractional-order proportion integration differentiation(PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.
基金Shandong Province Department of Education Science and Technology Program(No.J05C11)
文摘Beer fermentation process is a complex biochemical reaction process.It is the most important to control temperature of the wort in fermentation tank in accordance with the beer fermentation temperature curve so as to ensure the completion of fermentation.The controlled object is characterized by large inertia,long time delay and mutual coupling of three temperature areas.Based on this,a temperature control method for beer fermentation system is designed.Using digital incremental proportion integration differentiation （PID） control algorithm,the controlled quantity is transmitted to the controlled object after diagonal matrix decoupling.This simulation system can be completed in laboratory using VB and Kingview software,so it has the features of good security and low cost.It is very suitable for experimental teaching.
文摘Neuron PSD (proportion, sum and differentiation) controller has the ability of on-line change of weights to reach the purpose of regulating parameters of PID using neuron’s self-studying and self-organization and the change of controlled plant, which overcomes the disadvantages of affecting a conventional PID’s accurate regulation because of the change of load, model and non-linearity. LF2407 DSP can reach the purpose of parallel running by using multi-sets of bus. So it can greatly increase operation speed and offer a set of flexible instruction system. The realization of PSD control on DSP can build an ideal electrical machine controller.
基金This work was supported by the Key Project of Chinese Ministry of Education(No.212135)the Guangxi Natural Science Foundation(No.2012GXNSFBA053165)+1 种基金the Projec t of Education Department of Guangxi(No.201203YB131)the Project of Guangxi Key Laboratory(No.14-045-44)。
文摘For complex systems with high nonlinearity and strong coupling,the decoupling control technology based on proportion integration differentiation(PID)neural network(PIDNN)is used to eliminate the coupling between loops.The connection weights of the PIDNN are easy to fall into local optimum due to the use of the gradient descent learning method.In order to solve this problem,a hybrid particle swarm optimization(PSO)and differential evolution(DE)algorithm(PSO-DE)is proposed for optimizing the connection weights of the PIDNN.The DE algorithm is employed as an acceleration operation to help the swarm to get out of local optima traps in case that the optimal result has not been improved after several iterations.Two multivariable controlled plants with strong coupling between input and output pairs are employed to demonstrate the effectiveness of the proposed method.Simulation results show t hat the proposed met hod has better decoupling capabilities and control quality than the previous approaches.
基金the National Key R&D Program of China[grant number 2018YFB0505400]the Natural Science Fund of Hubei Province with Project[grant number 2018CFA007]National Key Research and Development Program of China[2018YFB0505400]。
文摘Low Earth Orbit(LEO)satellite navigation signal can be used as an opportunity signal in the case of a Global Navigation Satellite System(GNSS)outage,or as an enhancement by means of traditional GNSS positioning algorithms.No matter which service mode is used,signal acquisition is a prerequisite for providing enhanced LEO navigation services.Compared with the medium orbit satellite,the transit time of the LEO satellite is shorter.Thus,it is of great significance to expand the successful acquisition time range of the LEO signal.Previous studies on LEO signal acquisition are based on simulation data.However,signal acquisition research based on real data is crucial.In this work,the signal characteristics of LEO satellites:power space density in free space and the Doppler shift of LEO satellites are individually studied.The unified symbolic definitions of several integration algorithms based on the parallel search signal acquisition algorithm are given.To verify these algorithms for LEO signal acquisition,a Software Defined Receiver(SDR)is developed.The performance of these integration algorithms on expanding the successful acquisition time range is verified by the real data collected from the Luojia-1A satellite.The experimental results show that the integration strategy can expand the successful acquisition time range,and it will not expand indefinitely with the integration duration.The performance of the coherent integration and differential integration algorithms is better than the other two integration algorithms,so the two algorithms are recommended for LEO signal acquisition and a 20 ms integration duration is preferred.The detection threshold of 2.5 is not suitable for all integration algorithms and various integration durations,especially for the Maximum-to-Mean Ratio indicator.
文摘The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.
文摘The execution of the gaits generated with the help of a gait planner is a crucial task in biped locomotion. This task is to be achieved with the help of a suitable torque based controller to ensure smooth walk of the biped robot. It is important to note that the success of the developed proportion integration differentiation （PID） controller depends on the selected gains of the controller. In the present study, an attempt is made to tune the gains of the PID controller for the biped robot ascending and descending the stair case and sloping surface with the help of two non-traditional optimization algorithms, namely modified chaotic invasive weed optimization （MCIWO） and particle swarm optimization （PSO） algorithms. Once the optimal PID controllers are developed, a simulation study has been conducted in computer for obtaining the optimal tuning parameters of the controller of the biped robot. Finally, the optimal gait angles obtained by using the best controller are fed to the real biped robot and found that the biped robot has successfully negotiated the said terrains.
文摘A PID parameters tuning and optimization method for a turbine engine based on the simplex search method was proposed. Taking time delay of combustion and actuator into account, a simulation model of a PID control system for a turbine engine was developed. A performance index based on the integral of absolute error （IAE） was given as an objective function of optimization. In order to avoid the sensitivity that resulted from the initial values of the simplex search method, the traditional Ziegler-Nichols method was used to tune PID parameters to obtain the initial values at first, then the simplex search method was applied to optimize PID parameters for the turbine engine. Simulation results indicate that the simplex search method is a reasonable and effective method for PID controller parameters tuning and optimization.
基金National Natural Science Foundation of China(Grant No.11674198)the Taishan Scholar Project of Shandong Province,China(Grant No.ts201511025)the Science Fund from the Shandong Provincial Laboratory of Biophysics.
文摘We present a state-to-state dynamical calculation on the reaction S++ H2→ SH+ +H based on an accurate X2 A″ potential surface. Some reaction properties, such as reaction probability, integral cross sections, product distribution, etc.,are found to be those with characteristics of an indirect reaction. The oscillating structures appearing in reaction probability versus collision energy are considered to be the consequence of the deep potential well in the reaction. The comparison of the present total integral cross sections with the previous quasi-classical trajectory results shows that the quantum effect is more important at low collision energies. In addition, the quantum number inversion in the rotational distribution of the product is regarded as the result of the heavy–light–light mass combination, which is not effective for the vibrational excitation. For the collision energies considered, the product differential cross sections of the title reaction are mainly concentrated in the forward and backward regions, which suggests that there is a long-life intermediate complex in the reaction process.
基金the National Natural Science Foundation of China(10571156)RSDP(20030335019)+1 种基金the Natural Science Foundation of Zhejiang Province(RC97017)supported partially by the National Natural Science Foundation of China(10601046).
文摘In this paper, some classes of differentiation basis are investigated and several positive answers to a conjecture of Zygmund on differentiation of integrals are presented.
基金Supported by the Natural Science Foundation of Heilongjiang Province(A200602)the Project of Science Research Foundation(HITC200710)the Project of Development Program for Outstanding Young Teachers in Harbin Institute of Technology(HITQNJS.2006.053)
文摘The numerical stability of linear neutral Volterra delay integral differential equations is dealt with.Under a sufficient condition such that this system with a lagging argument is asymptotically stable,it is proved that every A-stable linear multistep method preserves the delay-independent stabil-ity of its exact solutions.Finally,some numerical experiments are given to demonstrate the main conclu-sion.
文摘H stability is a new and important concept. In this paper,we discuss the equationx(t)=-a(t)x(t)+∫ t -∞ k(t,s-t,x(s)) d sand we gain a new decision theorem. Using this decision theorem,we obtained a very extensive result of the H uniformly asymptotical stability of this equation. That is,eliminating the restriction that a(t) is bounded.
文摘The generalized KdV equation is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma￣[2], Ihe isolated wave in transmission line￣[3], and the isolated wave in the bound-ary surface of the divided layer fluid￣[4]. For the characteristic problem of the gene-ralized KdV equation, this paper, based on the Riemann function, designs a suitablestructure, then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding fixed point, the above integral differential equ-ation has a unique regular solution, so the characteristic problem of the generalizedKdV equation has a. unique solution. The iteration solution derived from the integraldifferential equation sequence is uniformly convegent in.
基金Supported by the National Natural Science Foundation of China(11171298)the Zhejiang Natural Science Foundation of China(Y6110425)
文摘The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.
基金Project supported bY the National Natural Science Foundation of China （Grant No.50375085）, and the Natural Science Foundation of Shandong Province （Grant No.Y2002F13）
文摘A closed-chain robot has several advantages over an open-chain robot, such as high mechanical rigidity, high payload, high precision. Accurate trajectory control of a robot is essential in practical-use. This paper presents an adaptive proportional integral differential （PID） control algorithm based on radial basis function （RBF） neural network for trajectory tracking of a two-degree-of-freedom （2-DOF） closed-chain robot. In this scheme, an RBF neural network is used to approximate the unknown nonlinear dynamics of the robot, at the same time, the PID parameters can be adjusted online and the high precision can be obtained. Simulation results show that the control algorithm accurately tracks a 2-DOF closed-chain robot trajectories. The results also indicate that the system robustness and tracking performance are superior to the classic PID method.
