In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the...In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.展开更多
The problem of mathematical simulation of motion of dynamic systems characteristics and their coincidence with real experimental data which correspond to these characteristics is investigated in this paper. Mathematic...The problem of mathematical simulation of motion of dynamic systems characteristics and their coincidence with real experimental data which correspond to these characteristics is investigated in this paper. Mathematical description of process will be named as adequate mathematical description if the results of mathematical simulation by the help of this description coincide with experiment with inaccuracy of initial data. The synthesis of such description is very important at mathematical modeling and forecast of motion of real physical phenomena. The specified problem is still poorly investigated and hardly adapted to formalization. The requirements to the adequate mathematical description of dynamic system are considered for the case when mathematical description of dynamic systems is represented by linear system of the ordinary differential equations. In this paper the mathematical model of process is given a priori with inexact parameters and then the models of external loads are being determined for which the results of simulation coincide with experiment. The methods of obtaining of the steady models of external loads are suggested. The example of the adequate description construction of the main mechanical line dynamics of rolling mill is given.展开更多
In this paper, a modified sliding-mode adaptive controller is derived to achieve stability and output regulation for a class of dynamical systems represented by a non-homogeneous differential equation with unknown tim...In this paper, a modified sliding-mode adaptive controller is derived to achieve stability and output regulation for a class of dynamical systems represented by a non-homogeneous differential equation with unknown time-varying coefficients and unknown force function. In this scheme, the control law is constructed in terms of estimated values for the bounds of the unknown coefficients, where these values are continuously updated by adaptive laws to ensure asymptotic convergence to zero for the output function. The proposed controller is applied to solve the problem of pitch angle regulation for a floating wind turbine with dynamic uncertainty and external disturbances. Numerical simulations are performed to demonstrate the validity of the designed controller to achieve the desired pitch angle for the floating turbine＇s body.展开更多
The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonl...The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.展开更多
With the development of Global Navigation Satellite System (GNSS),the idea of GNSS interoperability is born and has become the focus of study in the field of satellite navigation.The popularity for GNSS to augment the...With the development of Global Navigation Satellite System (GNSS),the idea of GNSS interoperability is born and has become the focus of study in the field of satellite navigation.The popularity for GNSS to augment the interoperability with the existing ones necessitates the study of the assessment algorithm of this idea.In this paper,an assessment algorithm for interoperability comprehensive benefits based on the differential equation dynamical system is discussed.There are two important aspects in GNSS that interoperability will affect:one is the performance advancement;the other one is the cost of adopting interoperability.While researching the complex relationship between the performance and cost,we found this relationship is similar as what between prey and predator in biomathematics,so the Lotka-Volterra model used to depict the prey-predator relationship is a felicitous tool.After building a differential dynamical model,we analyze the existence and stability of the positive equilibrium in the model.Then a Cost-Effective Function of GNSS is constructed based on the positive equilibrium,which is employed to assess the interoperability,qualitatively and quantitatively.Finally,the paper demonstrates the significance of the model and its application by citing a numerical example.展开更多
A sufficient condition is obtained for a two-agent opinion dynamical system with pro-cessing delay to experience unconditional consensus. To this end, the dynamics proposed is transformed into a general class of delay...A sufficient condition is obtained for a two-agent opinion dynamical system with pro-cessing delay to experience unconditional consensus. To this end, the dynamics proposed is transformed into a general class of delay differential equation and asymptotic stability of the origin is then analyzed. It is also shown that increasing delay can prolong the time needed for the system to realize consensus and even induce a Hopf bifurcation.展开更多
This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string...This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.展开更多
We investigate the stability of steady states of a size- and stage-structured population model, which is a hybrid system of ordinary and partial differential equations with global integral feedbacks. After the formula...We investigate the stability of steady states of a size- and stage-structured population model, which is a hybrid system of ordinary and partial differential equations with global integral feedbacks. After the formulation of a criterion by spectrum method, we derive conditions for global stability of the trivial state and local stability of the positive equilibrium via the basic reproduction rate. Furthermore, some examples and simulations ure .presented to illustrate the obtained results.展开更多
A stochastic celhflar automaton （CA） model for activated sludge system （ASS） is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary diff...A stochastic celhflar automaton （CA） model for activated sludge system （ASS） is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations （ODEs） of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, com- plexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.展开更多
基金Project(2006AA04Z405) supported by the National High Technology Research and Development Program of ChinaProject(3102019) supported by Beijing Municipal Natural Science Foundation,China
文摘In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.
文摘The problem of mathematical simulation of motion of dynamic systems characteristics and their coincidence with real experimental data which correspond to these characteristics is investigated in this paper. Mathematical description of process will be named as adequate mathematical description if the results of mathematical simulation by the help of this description coincide with experiment with inaccuracy of initial data. The synthesis of such description is very important at mathematical modeling and forecast of motion of real physical phenomena. The specified problem is still poorly investigated and hardly adapted to formalization. The requirements to the adequate mathematical description of dynamic system are considered for the case when mathematical description of dynamic systems is represented by linear system of the ordinary differential equations. In this paper the mathematical model of process is given a priori with inexact parameters and then the models of external loads are being determined for which the results of simulation coincide with experiment. The methods of obtaining of the steady models of external loads are suggested. The example of the adequate description construction of the main mechanical line dynamics of rolling mill is given.
文摘In this paper, a modified sliding-mode adaptive controller is derived to achieve stability and output regulation for a class of dynamical systems represented by a non-homogeneous differential equation with unknown time-varying coefficients and unknown force function. In this scheme, the control law is constructed in terms of estimated values for the bounds of the unknown coefficients, where these values are continuously updated by adaptive laws to ensure asymptotic convergence to zero for the output function. The proposed controller is applied to solve the problem of pitch angle regulation for a floating wind turbine with dynamic uncertainty and external disturbances. Numerical simulations are performed to demonstrate the validity of the designed controller to achieve the desired pitch angle for the floating turbine＇s body.
基金supported by National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10925104)the PhD Programs Foundation of Ministry of Education of China(Grant No.20106101110008)the United Funds of NSFC and Henan for Talent Training(Grant No.U1204104)
文摘The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.
基金supported by the National Natural Science Foundation of China (Grant Nos.11073022 and 71072160)the National Basic Research Program of China (Grant No.2007CB815502)the Western Light (Grant No.Y001YR4701)
文摘With the development of Global Navigation Satellite System (GNSS),the idea of GNSS interoperability is born and has become the focus of study in the field of satellite navigation.The popularity for GNSS to augment the interoperability with the existing ones necessitates the study of the assessment algorithm of this idea.In this paper,an assessment algorithm for interoperability comprehensive benefits based on the differential equation dynamical system is discussed.There are two important aspects in GNSS that interoperability will affect:one is the performance advancement;the other one is the cost of adopting interoperability.While researching the complex relationship between the performance and cost,we found this relationship is similar as what between prey and predator in biomathematics,so the Lotka-Volterra model used to depict the prey-predator relationship is a felicitous tool.After building a differential dynamical model,we analyze the existence and stability of the positive equilibrium in the model.Then a Cost-Effective Function of GNSS is constructed based on the positive equilibrium,which is employed to assess the interoperability,qualitatively and quantitatively.Finally,the paper demonstrates the significance of the model and its application by citing a numerical example.
基金This work was jointly supported by National Natural Science Foundation of China （11401577） and Youth Top-notch Talent Support Program of NUDT （2014-2017）.
文摘A sufficient condition is obtained for a two-agent opinion dynamical system with pro-cessing delay to experience unconditional consensus. To this end, the dynamics proposed is transformed into a general class of delay differential equation and asymptotic stability of the origin is then analyzed. It is also shown that increasing delay can prolong the time needed for the system to realize consensus and even induce a Hopf bifurcation.
基金supported by National Natural Science Foundation of China(Grant No.91130005)the US Army Research Office(Grant No.W911NF-11-1-0101)
文摘This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.
文摘We investigate the stability of steady states of a size- and stage-structured population model, which is a hybrid system of ordinary and partial differential equations with global integral feedbacks. After the formulation of a criterion by spectrum method, we derive conditions for global stability of the trivial state and local stability of the positive equilibrium via the basic reproduction rate. Furthermore, some examples and simulations ure .presented to illustrate the obtained results.
基金This research was supported by the National Natural Science Foundation of China （No. 30870397） and the State Key Laboratory of Vegetation and Environmental Change.
文摘A stochastic celhflar automaton （CA） model for activated sludge system （ASS） is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations （ODEs） of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, com- plexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.
