In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference me...In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.展开更多
In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an outp...In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.展开更多
When kernel density is in the class of continuous function to possessing sufficient derivative of high order(and needn't in the class of corresponding Holder function),in this paper it is given the continuity and...When kernel density is in the class of continuous function to possessing sufficient derivative of high order(and needn't in the class of corresponding Holder function),in this paper it is given the continuity and the differential formulas for singular integrals of high non--integral order. The above results themselves and in order to prove in future the formulas to changing order of integration for singular integrals of high non-integral order(another paper) will have important significance. The method to prove in this paper is more different from the method in the corresponding cass of singular integrals of high integral order.展开更多
In this paper, we present a new method for solving a class of high-order quasi exactly solvable ordinary differential equations. With this method, the computed solution is expressed as a linear combination of the cano...In this paper, we present a new method for solving a class of high-order quasi exactly solvable ordinary differential equations. With this method, the computed solution is expressed as a linear combination of the canonical polynomials associated with the given differential operator. An iterative algorithm summarizing the procedure is presented and its efficiency is demonstrated through considering two applied problems.展开更多
The method to design sliding-mode observers for systems with unknown inputs and measurement disturbances is presented in the paper. An augmented system is constructed by viewing the measurement disturbances as unknow ...The method to design sliding-mode observers for systems with unknown inputs and measurement disturbances is presented in the paper. An augmented system is constructed by viewing the measurement disturbances as unknow inputs. For such an augmented system, the so-called observer matching condition is not satisfied. Based on the construction of auxiliary outputs, the observer matching condition may be satisfied. High-order sliding-mode differentiators are developed to obtain the estimates of those unmeasurable variables contained in the auxiliary output vector. Employing the estimate of auxiliary output vector, a sliding-mode observer is designed. The simulation results to a real model show that the proposed method is effective.展开更多
By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic d...By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.展开更多
In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos a...In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos and Lorenz chaos and indicated that Qi hyper-chaos based masking can resist attacks of the filtering and power spectrum analysis, while the Lorenz based scheme fails for high amplitude data. To unmask the message at the receiving end, two methods are proposed. In the first method, a model-free synchronizer, i.e. a multivariable higher-order differential feedback controller between the transmitter and receiver is employed to de-convolve the message embedded in the receiving signal. In the second method, no synchronization is required since the message is de-convolved using the information of the estimated derivative.展开更多
基金heprojectissupportedbyNNSFofChina (No .1 9972 0 39) .
文摘In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.
文摘In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.
文摘When kernel density is in the class of continuous function to possessing sufficient derivative of high order(and needn't in the class of corresponding Holder function),in this paper it is given the continuity and the differential formulas for singular integrals of high non--integral order. The above results themselves and in order to prove in future the formulas to changing order of integration for singular integrals of high non-integral order(another paper) will have important significance. The method to prove in this paper is more different from the method in the corresponding cass of singular integrals of high integral order.
文摘In this paper, we present a new method for solving a class of high-order quasi exactly solvable ordinary differential equations. With this method, the computed solution is expressed as a linear combination of the canonical polynomials associated with the given differential operator. An iterative algorithm summarizing the procedure is presented and its efficiency is demonstrated through considering two applied problems.
基金Funded by the National Natural Science Foundation(No.61203299/F030506)
文摘The method to design sliding-mode observers for systems with unknown inputs and measurement disturbances is presented in the paper. An augmented system is constructed by viewing the measurement disturbances as unknow inputs. For such an augmented system, the so-called observer matching condition is not satisfied. Based on the construction of auxiliary outputs, the observer matching condition may be satisfied. High-order sliding-mode differentiators are developed to obtain the estimates of those unmeasurable variables contained in the auxiliary output vector. Employing the estimate of auxiliary output vector, a sliding-mode observer is designed. The simulation results to a real model show that the proposed method is effective.
基金supported by the NSF of China(No.12001539)the NSF of Hunan Province(No.2020JJ5647)China Postdoctoral Science Foundation(No.2019TQ0073).
文摘By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.
基金Project supported by the Incentive Funding National Research Foundation of South Africa(Grant No.70722)the Eskom Tertiary Education Support Programme of South Africa
文摘In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos and Lorenz chaos and indicated that Qi hyper-chaos based masking can resist attacks of the filtering and power spectrum analysis, while the Lorenz based scheme fails for high amplitude data. To unmask the message at the receiving end, two methods are proposed. In the first method, a model-free synchronizer, i.e. a multivariable higher-order differential feedback controller between the transmitter and receiver is employed to de-convolve the message embedded in the receiving signal. In the second method, no synchronization is required since the message is de-convolved using the information of the estimated derivative.
