The global robust output regulation problem of the singular nonlinear system is investigated. Motivated by the input-output linearization of the normal affine nonlinear system, a global diffeomorphism map is designed ...The global robust output regulation problem of the singular nonlinear system is investigated. Motivated by the input-output linearization of the normal affine nonlinear system, a global diffeomorphism map is designed under the assumption that the singular nonlinear system has a strong relative degree. The global diffeomorphism map transfers the singular nonlinear system into a new singular nonlinear system with a special structure. Attaching an internal model to the new singular nonlinear system yields an augmented singular nonlinear system and the global robust stabilization solution of the augmented system implies the global robust output regulation solution of the original singular nonlinear system. Then the global stabilization problem is solved by some appropriate assumptions and the solvability conditions of the global robust output regulation problem are established. Finally, a simulation example is given to illustrate the design approach.展开更多
A new fault detection and diagnosis approach is developed in this paper for a class of singular nonlinear systems via the use of adaptive updating rules. Both detection and diagnostic observers are established, where ...A new fault detection and diagnosis approach is developed in this paper for a class of singular nonlinear systems via the use of adaptive updating rules. Both detection and diagnostic observers are established, where Lyapunov stability theory is used to obtain the required adaptive tuning rules for the estimation of the process faults. This has led to stable observation error systems for both fault detection and diagnosis. A simulated numerical example is included to demonstrate the use of the proposed approach and encouraging results have been obtained.展开更多
The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently ...The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently transformed into a differential-algebraic system.Next,it is proved that the state feedback can be used as an adaptive H_(∞) finite-time boundedness controller of NSHS.Finally,the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.展开更多
We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） ...We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） quenches at the originx = 0 at the same time ＇1＇ （see Theorem 4.3）. We also tind various other conditions tor the solution to quench in a finite time and obtain the corresponding decay rate of the solution near the quenching time.展开更多
This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feed...This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.展开更多
In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Un...In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Under suitable assumptions, by using the method of many-parameter expansion and the technique of diagonalization, the existence oj the solution of perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.展开更多
The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapuno...The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapunov function and Lyapunov stability theory. Based on which, a sufficient condition is presented such that the system is zero solution asymptotically stable and has H∞ norm constraint γ. Then, the static output feedback H∞ controller is designed to guarantee the resulting closed-loop system has the same performance. Finally, an example proves the effectiveness of the conclusion.展开更多
This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- an...This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- and upper-solution pair, a concept defined in this paper, and employ the Nagumo conditions and algebraic boundary layer functions to ensure the existence of solutions of the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems have nonlinear dependence on all order derivatives of the unknown.展开更多
A control synthesis method for output regulation based on singular perturbation theory combined with inverting design is considered for a class of nonaffine nonlinear systems. The resulting control signal is defined a...A control synthesis method for output regulation based on singular perturbation theory combined with inverting design is considered for a class of nonaffine nonlinear systems. The resulting control signal is defined as a solution to ＂fast＂ dynamics which inverts a series error model, whose state is exponentially stable. It is shown that, under sufficient conditions being consistent with the assumptions of singular perturbation theory, this problem is solvable with （ε） tracking error if and only if a set of first-order nonlinear partial differential equations are solvable. The control law can be easily constructed and the simulations show the feasibility and effectiveness of the controller.展开更多
In this paper, the singular perturbation of nonlinear differential equation system with nonlinear boundary conditions is discussed. Under suitable assumptions, with the asymptotic method of Lyusternik-Vishik([1]) and ...In this paper, the singular perturbation of nonlinear differential equation system with nonlinear boundary conditions is discussed. Under suitable assumptions, with the asymptotic method of Lyusternik-Vishik([1]) and fixed point theory, the existence of the solution of the perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.展开更多
Based on the T-S model, the output regulation of nonlinear singularly perturbed systems via state feedback is discussed. It is shown that, under standard assumptions, this problean is solvable if and only if certain l...Based on the T-S model, the output regulation of nonlinear singularly perturbed systems via state feedback is discussed. It is shown that, under standard assumptions, this problean is solvable if and only if certain linear matrix equations are solvable. Once these equations are solvable, the state feedback regulator can easily be constructed.展开更多
In this paper, by the technique and the method of diagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with: epsilon y '=f(t, y, y', epsilon), ...In this paper, by the technique and the method of diagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with: epsilon y '=f(t, y, y', epsilon), y(0, epsilon)=a(epsilon), y(1,epsilon)=b(epsilon) The existance of the solution and its asymptotic properties are discussed when the eigenvalues of Jacobi matrix f(y') has K negative real parts and N-K positve real parts.展开更多
A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asy...A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.展开更多
Methods for the approximation of solution of nonlinear system of equations often fail when the Jacobians of the systems are singular at iteration points. In this paper, multi-step families of quadrature based iterativ...Methods for the approximation of solution of nonlinear system of equations often fail when the Jacobians of the systems are singular at iteration points. In this paper, multi-step families of quadrature based iterative methods for approximating the solution of nonlinear system of equations with singular Jacobian are developed using decomposition technique. The methods proposed in this study are of convergence order , and require only the evaluation of first-order Frechet derivative per iteration. The approximate solutions generated by the proposed iterative methods in this paper compared with some existing contemporary methods in literature, show that methods developed herein are efficient and adequate in approximating the solution of nonlinear system of equations whose Jacobians are singular and non-singular at iteration points.展开更多
Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an ...Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an output feedback CNF controllaw are constructed respectively for the output regulation problemof singular linear systems with input saturation. It is shown thatthe output regulation problem by CNF control is solvable underthe same solvability conditions of the output regulation problemby linear control. However, with the virtue of the CNF control, thetransient performance of the closed-loop system can be improvedby carefully designing the linear part and the nonlinear part of theCNF control law. The design procedure and the improvement ofthe transient performance of the closed-loop system are illustratedwith a numerical simulation.展开更多
In this paper the existence and multiplicities of positive solutions for a class of quasiliear differential systems with singular nonlinearities via Leray Schauder degree theory are established.
A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of ...A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied.展开更多
We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a ...We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a positive constant.By using a variational method and the critical point theory for a nonsmooth functional,we obtain the existence of two positive solutions.This result generalizes and improves upon recent results in the literature.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 method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and t...In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.展开更多
基金supported by the National Natural Science Foundation of China(61374035)the Fundamental Research Funds for the Central Universities(20720150177)
文摘The global robust output regulation problem of the singular nonlinear system is investigated. Motivated by the input-output linearization of the normal affine nonlinear system, a global diffeomorphism map is designed under the assumption that the singular nonlinear system has a strong relative degree. The global diffeomorphism map transfers the singular nonlinear system into a new singular nonlinear system with a special structure. Attaching an internal model to the new singular nonlinear system yields an augmented singular nonlinear system and the global robust stabilization solution of the augmented system implies the global robust output regulation solution of the original singular nonlinear system. Then the global stabilization problem is solved by some appropriate assumptions and the solvability conditions of the global robust output regulation problem are established. Finally, a simulation example is given to illustrate the design approach.
基金the Outstanding Oversea Award of the Chinese Academy of Sciences (No. 2004-1-4)the Natural Science Foundationof China (No. 60534010)
文摘A new fault detection and diagnosis approach is developed in this paper for a class of singular nonlinear systems via the use of adaptive updating rules. Both detection and diagnostic observers are established, where Lyapunov stability theory is used to obtain the required adaptive tuning rules for the estimation of the process faults. This has led to stable observation error systems for both fault detection and diagnosis. A simulated numerical example is included to demonstrate the use of the proposed approach and encouraging results have been obtained.
基金supported by the National Nature Science Foundation of China (61877028, 61773015).
文摘The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently transformed into a differential-algebraic system.Next,it is proved that the state feedback can be used as an adaptive H_(∞) finite-time boundedness controller of NSHS.Finally,the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.
基金supported by NSFC(11201380)the Fundamental Research Funds for the Central Universities(XDJK2012B007)+1 种基金Doctor Fund of Southwest University(SWU111021)Educational Fund of Southwest University(2010JY053)
文摘We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） quenches at the originx = 0 at the same time ＇1＇ （see Theorem 4.3）. We also tind various other conditions tor the solution to quench in a finite time and obtain the corresponding decay rate of the solution near the quenching time.
基金supported by Russian Foundation for Basic Research(No.15-08-06859a)and by the Ministry of Education and Science of the Russian Federation in the framework of the basic part of the state order(No.2.8629.2017).
文摘This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.
文摘In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Under suitable assumptions, by using the method of many-parameter expansion and the technique of diagonalization, the existence oj the solution of perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.
基金supported by the National Natural Science Foundation of China (60574011)
文摘The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapunov function and Lyapunov stability theory. Based on which, a sufficient condition is presented such that the system is zero solution asymptotically stable and has H∞ norm constraint γ. Then, the static output feedback H∞ controller is designed to guarantee the resulting closed-loop system has the same performance. Finally, an example proves the effectiveness of the conclusion.
基金supported by the National Natural Science Foundation of China (Grant No.10771212)the Natural Science Foundation of Jiangsu Province (Grant No.BK2008119)the Natural Science Foundation of the Education Division of Jiangsu Province (Grant No.08KJB110011)
文摘This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- and upper-solution pair, a concept defined in this paper, and employ the Nagumo conditions and algebraic boundary layer functions to ensure the existence of solutions of the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems have nonlinear dependence on all order derivatives of the unknown.
基金supported by the National Natural Science Foundation of China (No.60274009)Specialized Research Fund for the Doctoral Program of Higher Education (No.20020145007)
文摘A control synthesis method for output regulation based on singular perturbation theory combined with inverting design is considered for a class of nonaffine nonlinear systems. The resulting control signal is defined as a solution to ＂fast＂ dynamics which inverts a series error model, whose state is exponentially stable. It is shown that, under sufficient conditions being consistent with the assumptions of singular perturbation theory, this problem is solvable with （ε） tracking error if and only if a set of first-order nonlinear partial differential equations are solvable. The control law can be easily constructed and the simulations show the feasibility and effectiveness of the controller.
文摘In this paper, the singular perturbation of nonlinear differential equation system with nonlinear boundary conditions is discussed. Under suitable assumptions, with the asymptotic method of Lyusternik-Vishik([1]) and fixed point theory, the existence of the solution of the perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.
文摘Based on the T-S model, the output regulation of nonlinear singularly perturbed systems via state feedback is discussed. It is shown that, under standard assumptions, this problean is solvable if and only if certain linear matrix equations are solvable. Once these equations are solvable, the state feedback regulator can easily be constructed.
文摘In this paper, by the technique and the method of diagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with: epsilon y '=f(t, y, y', epsilon), y(0, epsilon)=a(epsilon), y(1,epsilon)=b(epsilon) The existance of the solution and its asymptotic properties are discussed when the eigenvalues of Jacobi matrix f(y') has K negative real parts and N-K positve real parts.
文摘A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.
文摘Methods for the approximation of solution of nonlinear system of equations often fail when the Jacobians of the systems are singular at iteration points. In this paper, multi-step families of quadrature based iterative methods for approximating the solution of nonlinear system of equations with singular Jacobian are developed using decomposition technique. The methods proposed in this study are of convergence order , and require only the evaluation of first-order Frechet derivative per iteration. The approximate solutions generated by the proposed iterative methods in this paper compared with some existing contemporary methods in literature, show that methods developed herein are efficient and adequate in approximating the solution of nonlinear system of equations whose Jacobians are singular and non-singular at iteration points.
基金supported by the National Natural Science Foundation of China(61374035)
文摘Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an output feedback CNF controllaw are constructed respectively for the output regulation problemof singular linear systems with input saturation. It is shown thatthe output regulation problem by CNF control is solvable underthe same solvability conditions of the output regulation problemby linear control. However, with the virtue of the CNF control, thetransient performance of the closed-loop system can be improvedby carefully designing the linear part and the nonlinear part of theCNF control law. The design procedure and the improvement ofthe transient performance of the closed-loop system are illustratedwith a numerical simulation.
文摘In this paper the existence and multiplicities of positive solutions for a class of quasiliear differential systems with singular nonlinearities via Leray Schauder degree theory are established.
基金The Project Supported by National Natural Science Foundation of China(10071045)
文摘A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied.
基金supported by Natural Science Foundation of Guizhou Minzu University(20185773-YB03)supported by Fundamental Research Funds of China West Normal University(18B015)+2 种基金Innovative Research Team of China West Normal University(CXTD2018-8)supported by National Natural Science Foundation of China(11861021)supported by National Natural Science Foundation of China(11661021)。
文摘We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a positive constant.By using a variational method and the critical point theory for a nonsmooth functional,we obtain the existence of two positive solutions.This result generalizes and improves upon recent results in the literature.
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.
基金Project Supported by the Science Fund of the Chinese Academy of Sciences
文摘In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.
