The invariance of the ordinary differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities for the singular Lagrange system. The determining equations, ...The invariance of the ordinary differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities for the singular Lagrange system. The determining equations, the restriction equations of the Lie symmetries and the form of conserved quantities of the system are obtained.展开更多
The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First...The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First, by using the switched Lyapunov function approach, some new sufficient conditions ensuring the nominal discrete-time SLS system to be regular, casual and asymptotically stable for arbitrary switching laws are derived in terms of linear matrix inequalities. Then, the robust admissibility condition for the uncertain discrete-time SLS systems is presented. The obtained results can be viewed as an extension of previous works on the switched Lyapunov function approach from the regular switched linear systems to the switched linear singular cases. Numerical examples show the reduced conservatism and effectiveness of the proposed conditions.展开更多
Chemical processes are usually nonlinear singular systems.In this study,a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes,whic...Chemical processes are usually nonlinear singular systems.In this study,a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes,which are augmented as state variables.Based on the observability of the singular system,this paper presents a simplified observability criterion under certain conditions for unknown inputs and uncertain model parameters.When the observability is satisfied,the unknown inputs and the uncertain model parameters are estimated online by the soft sensor using augmented nonlinear singular state observer.The riser reactor of fluid catalytic cracking unit is used as an example for analysis and simulation.With the catalyst circulation rate as the only unknown input without model error,one temperature sensor at the riser reactor outlet will ensure the correct estimation for the catalyst circulation rate.However,when uncertain model parameters also exist,additional temperature sensors must be used to ensure correct estimation for unknown inputs and uncertain model parameters of chemical processes.展开更多
In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invarianc...In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.展开更多
We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the e...We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the existence and the uniqueness theoremsof the generalized global solution of the mentioned problem.展开更多
In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of cl...In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.展开更多
Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom ...Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom been studied and we only find few results. Thus it is necessary for us to investigate the related singular systems deeply. In this paper, a quasilinear elliptic system is investigated, which involves multiple Hardy-type terms and concave-convex nonlinearities. To the best of our knowledge, such a problem has not been discussed. By using a variational method involving the Nehari manifold and some analytical techniques, we prove that there exist at least two positive solutions to the system.展开更多
This paper shows how the so called von Karman model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear κ tends to infinity, provided a regularizing ter...This paper shows how the so called von Karman model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear κ tends to infinity, provided a regularizing term through a fourth order dispersive operator is added. Introducing damping mechanisms, the authors also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter k. As κ→∞, the authors obtain the damped von Karman model with associated energy exponentially decaying to zero as well.展开更多
This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diff...This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion coefficient.This control problem is difficult to solve with the classical method of spike variation.The authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control problem.Sufficient optimality conditions are also investigated.展开更多
Synthesis and design of output variable structure controller for time-invariant linear timedelay singular system are studied. In the case that the system is regular and the system index is one, switching function with...Synthesis and design of output variable structure controller for time-invariant linear timedelay singular system are studied. In the case that the system is regular and the system index is one, switching function with integral compensator and variable structure controller are designed, which guarantee that the sliding mode is asymptotically stable and the solution trajectory of the system arrives at the switching manifold in limited time. The design method is applicable to the systems which can be regularized. Finally, a numerical example is given to demonstrate effectiveness and simplicity of the design method.展开更多
The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.
We present in this paper a structural decomposition for linear multivariable singular systems. Such a decomposition has a distinct feature of capturing and displaying all the structural properties, such as the finite ...We present in this paper a structural decomposition for linear multivariable singular systems. Such a decomposition has a distinct feature of capturing and displaying all the structural properties, such as the finite and infinite zero structures, invertibility structures, and redundant dynamics of the given system. As its counterpart for non-singular systems, we believe that the technique is a powerful tool in solving control problems for singular systems.展开更多
This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance pri...This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.展开更多
This paper is a continuation of the authors' previous paper [1]. In this paper the authors prove, assuming additional conditions on the initial data, some results about the existence and uniqueness of the entropy ...This paper is a continuation of the authors' previous paper [1]. In this paper the authors prove, assuming additional conditions on the initial data, some results about the existence and uniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolic system展开更多
In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficie...In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficiently smooth.In this case,the proposed method leads to a fully discrete linear system.We show that the fully discrete integral operator is stable in both infinite and weighted square norms.Furthermore,we establish that the approximate solution arrives at an optimal convergence order under the two norms.Finally,we give some numerical examples,which confirm the theoretical prediction of the exponential rate of convergence.展开更多
文摘The invariance of the ordinary differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities for the singular Lagrange system. The determining equations, the restriction equations of the Lie symmetries and the form of conserved quantities of the system are obtained.
基金The National Natural Science Foundation of China(No.60835001)the Key Project of Ministry of Education of China (No.108060)
文摘The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First, by using the switched Lyapunov function approach, some new sufficient conditions ensuring the nominal discrete-time SLS system to be regular, casual and asymptotically stable for arbitrary switching laws are derived in terms of linear matrix inequalities. Then, the robust admissibility condition for the uncertain discrete-time SLS systems is presented. The obtained results can be viewed as an extension of previous works on the switched Lyapunov function approach from the regular switched linear systems to the switched linear singular cases. Numerical examples show the reduced conservatism and effectiveness of the proposed conditions.
基金Supported by the National Natural Science Foundation of China （21006127）, the National Basic Research Program of China （2012CB720500） and the Science Foundation of China University of Petroleum, Beijing （KYJJ2012-05-28）.
文摘Chemical processes are usually nonlinear singular systems.In this study,a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes,which are augmented as state variables.Based on the observability of the singular system,this paper presents a simplified observability criterion under certain conditions for unknown inputs and uncertain model parameters.When the observability is satisfied,the unknown inputs and the uncertain model parameters are estimated online by the soft sensor using augmented nonlinear singular state observer.The riser reactor of fluid catalytic cracking unit is used as an example for analysis and simulation.With the catalyst circulation rate as the only unknown input without model error,one temperature sensor at the riser reactor outlet will ensure the correct estimation for the catalyst circulation rate.However,when uncertain model parameters also exist,additional temperature sensors must be used to ensure correct estimation for unknown inputs and uncertain model parameters of chemical processes.
文摘In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.
文摘We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the existence and the uniqueness theoremsof the generalized global solution of the mentioned problem.
文摘In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.
文摘Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom been studied and we only find few results. Thus it is necessary for us to investigate the related singular systems deeply. In this paper, a quasilinear elliptic system is investigated, which involves multiple Hardy-type terms and concave-convex nonlinearities. To the best of our knowledge, such a problem has not been discussed. By using a variational method involving the Nehari manifold and some analytical techniques, we prove that there exist at least two positive solutions to the system.
基金supported by INCTMat, FAPESQ-PB, CNPq (Brazil) under Grant Nos. 308150/2008-2 and 620108/2008-8the MICINN (Spain) under Grant No. MTM2008-03541+1 种基金the Advanced Grant FP7-246775 NUMERIWAVES of the ERCthe Project PI2010-04 of the Basque Government
文摘This paper shows how the so called von Karman model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear κ tends to infinity, provided a regularizing term through a fourth order dispersive operator is added. Introducing damping mechanisms, the authors also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter k. As κ→∞, the authors obtain the damped von Karman model with associated energy exponentially decaying to zero as well.
基金supported by the National Natural Science Foundation of China under Grant Nos.11201268and 61105077the Natural Science Foundation of Shandong Province under Grant Nos.ZR2011AQ018 andZR2012AQ013
文摘This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion coefficient.This control problem is difficult to solve with the classical method of spike variation.The authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control problem.Sufficient optimality conditions are also investigated.
基金The project is supported by National Nature Science Foundation of China under Grant No.60574005.
文摘Synthesis and design of output variable structure controller for time-invariant linear timedelay singular system are studied. In the case that the system is regular and the system index is one, switching function with integral compensator and variable structure controller are designed, which guarantee that the sliding mode is asymptotically stable and the solution trajectory of the system arrives at the switching manifold in limited time. The design method is applicable to the systems which can be regularized. Finally, a numerical example is given to demonstrate effectiveness and simplicity of the design method.
文摘The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.
文摘We present in this paper a structural decomposition for linear multivariable singular systems. Such a decomposition has a distinct feature of capturing and displaying all the structural properties, such as the finite and infinite zero structures, invertibility structures, and redundant dynamics of the given system. As its counterpart for non-singular systems, we believe that the technique is a powerful tool in solving control problems for singular systems.
基金supported by the National Natural Science Fundation of China under Grant No.60874006
文摘This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.
文摘This paper is a continuation of the authors' previous paper [1]. In this paper the authors prove, assuming additional conditions on the initial data, some results about the existence and uniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolic system
基金supported by National Natural Science Foundation of China(Grant No.10901093)National Science Foundation of Shandong Province(Grant No.ZR2013AM006)
文摘In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficiently smooth.In this case,the proposed method leads to a fully discrete linear system.We show that the fully discrete integral operator is stable in both infinite and weighted square norms.Furthermore,we establish that the approximate solution arrives at an optimal convergence order under the two norms.Finally,we give some numerical examples,which confirm the theoretical prediction of the exponential rate of convergence.
