In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (posit...In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R0 >1. The global stability of diseases-free equilibrium is also established when R0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R0.展开更多
The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this cond...The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.展开更多
In this paper, we present an extended Exp-function method to differential-difference equation（s）. With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a se...In this paper, we present an extended Exp-function method to differential-difference equation（s）. With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.展开更多
This study investigates the nonlinear dynamic properties of rotating functionally graded sandwich rectangular plates in a thermal environment.The nonlinear vibration equations for a rotating metal-ceramic functionally...This study investigates the nonlinear dynamic properties of rotating functionally graded sandwich rectangular plates in a thermal environment.The nonlinear vibration equations for a rotating metal-ceramic functionally graded sandwich rectangular plate in a thermal environment are derived using classical thin plate theory and Hamilton’s principle,considering geometric nonlinearity,temperature-dependent material properties,and power law distribution of components through the thickness.With cantilever boundary conditions,the flexural nonlinear differential equations of the rectangular sandwich plate are obtained via the Galerkin method.Since the natural vibration differential equations exhibit nonlinear characteristics,the multiscale method is employed to derive the expression for nonlinear natural frequency.An example analysis reveals how the natural frequency of a functionally graded sandwich rectangular plate varies with rotational speed and temperature.Results show that the nonlinear/linear frequency ratio increases with rotational angular velocity Ω and thickness-to-length ratio h/a,follows a cosine-like periodic pattern with the setting angle,and shows a sharp decrease followed by a rapid increase with increasing width-to-length ratio b/a.The derived analytical solutions for nonlinear frequency provide valuable insights for assessing the dynamic characteristics of functionally graded structures.展开更多
In this paper,we propose a symmetric difference data enhancement physics-informed neural network(SDE-PINN)to study soliton solutions for discrete nonlinear lattice equations(NLEs).By considering known and unknown symm...In this paper,we propose a symmetric difference data enhancement physics-informed neural network(SDE-PINN)to study soliton solutions for discrete nonlinear lattice equations(NLEs).By considering known and unknown symmetric points,numerical simulations are conducted to one-soliton and two-soliton solutions of a discrete KdV equation,as well as a one-soliton solution of a discrete Toda lattice equation.Compared with the existing discrete deep learning approach,the numerical results reveal that within the specified spatiotemporal domain,the prediction accuracy by SDE-PINN is excellent regardless of the interior or extrapolation prediction,with a significant reduction in training time.The proposed data enhancement technique and symmetric structure development provides a new perspective for the deep learning approach to solve discrete NLEs.The newly proposed SDE-PINN can also be applied to solve continuous nonlinear equations and other discrete NLEs numerically.展开更多
By using the extended hyperbolic function method, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soli...By using the extended hyperbolic function method, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution, bright and dark soliton solution, alternating phase bright soliton solution, alternating phase dark soliton solution, and alternating phase bright and dark soliton solution, if a special relation is bound on the coefficients of the equation.展开更多
The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonl...The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonlinearity is incorporated into the model,and the constitutive equations are derived.The physical parameters of functionally graded materials(FGMs),which exhibit continuous variation across the thickness gradient,are of particular interest.The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton's principle.The nonlinear partial differential equations are discretized with the Galerkin method,and the analytical expression of traveling wave frequencies is derived with an approximate method.The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions.Finally,the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies.The results show that the factors including the power-law index,temperature,magnetic field intensity,and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.展开更多
In this paper we propose a new discrete bidirectional associative memory (DBAM) which is derived from our previous continuous linear bidirectional associative memory (LBAM). The DBAM performs bidirectionally the opti...In this paper we propose a new discrete bidirectional associative memory (DBAM) which is derived from our previous continuous linear bidirectional associative memory (LBAM). The DBAM performs bidirectionally the optimal associative mapping proposed by Kohonen. Like LBAM and NBAM proposed by one of the present authors,the present BAM ensures the guaranteed recall of all stored patterns,and possesses far higher capacity compared with other existing BAMs,and like NBAM, has the strong ability to suppress the noise occurring in the output patterns and therefore reduce largely the spurious patterns. The derivation of DBAM is given and the stability of DBAM is proved. We also derive a learning algorithm for DBAM,which has iterative form and make the network learn new patterns easily. Compared with NBAM the present BAM can be easily implemented by software.展开更多
This work deals with robust inverse neural control strategy for a class of single-input single-output(SISO) discrete-time nonlinear system affected by parametric uncertainties. According to the control scheme, in the ...This work deals with robust inverse neural control strategy for a class of single-input single-output(SISO) discrete-time nonlinear system affected by parametric uncertainties. According to the control scheme, in the first step, a direct neural model(DNM)is used to learn the behavior of the system, then, an inverse neural model(INM) is synthesized using a specialized learning technique and cascaded to the uncertain system as a controller. In previous works, the neural models are trained classically by backpropagation(BP) algorithm. In this work, the sliding mode-backpropagation(SM-BP) algorithm, presenting some important properties such as robustness and speedy learning, is investigated. Moreover, four combinations using classical BP and SM-BP are tested to determine the best configuration for the robust control of uncertain nonlinear systems. Two simulation examples are treated to illustrate the effectiveness of the proposed control strategy.展开更多
A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is cou...A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is coupled with the modified Bouc-Wen model of hysteresis.The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET)to concentrate the energy locally on the nonlinear oscillator,and then dissipates it through damping in the NES with NiTi-ST.The generalized vibration transmissibility,obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs.Finally,the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption.The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system,without changing its natural frequency.Moreover,the NES with NiTi-ST can be directly used in practical engineering applications.展开更多
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference...Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.展开更多
The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is signifi...The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.展开更多
The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state dela...The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state delay. Firstly, a new sliding function including a present value and a past value of the state, called dynamic surface, is designed by means of linear matrix inequalities （LMIs）. Then, using this dynamic function and the rolling optimization method in the predictive control strategy, a discrete predictive sliding mode controller is synthesized. This new strategy is proposed to eliminate the undesirable effect of the delay term in the closed loop system. Also, the designed control strategy is more robust, and has a chattering reduction property and a faster convergence of the system s state. Finally, a numerical example is given to illustrate the effectiveness of the proposed control.展开更多
The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematica...The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.展开更多
A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identifica...A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.展开更多
Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also der...Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.展开更多
The algorithm proposed by T. F. Colemen and A. R. Conn is improved in this paper, and the improved algorithm can solve nonlinear programming problem with quality constraints. It is shown that the improved algorithm po...The algorithm proposed by T. F. Colemen and A. R. Conn is improved in this paper, and the improved algorithm can solve nonlinear programming problem with quality constraints. It is shown that the improved algorithm possesses global convergence, and under some conditions, it possesses locally supperlinear convergence.展开更多
Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the ...Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to展开更多
The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation...The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system.展开更多
This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of...This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.展开更多
文摘In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R0 >1. The global stability of diseases-free equilibrium is also established when R0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R0.
基金the Natural Science Foundation of China (60774011)the Natural ScienceFoundation of Zhejiang Province in China (Y105141)
文摘The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.
基金National Natural Science Foundation of China under Grant No.10671121
文摘In this paper, we present an extended Exp-function method to differential-difference equation（s）. With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.
基金supported by the National Natural Science Foundation of China(No.11772090).
文摘This study investigates the nonlinear dynamic properties of rotating functionally graded sandwich rectangular plates in a thermal environment.The nonlinear vibration equations for a rotating metal-ceramic functionally graded sandwich rectangular plate in a thermal environment are derived using classical thin plate theory and Hamilton’s principle,considering geometric nonlinearity,temperature-dependent material properties,and power law distribution of components through the thickness.With cantilever boundary conditions,the flexural nonlinear differential equations of the rectangular sandwich plate are obtained via the Galerkin method.Since the natural vibration differential equations exhibit nonlinear characteristics,the multiscale method is employed to derive the expression for nonlinear natural frequency.An example analysis reveals how the natural frequency of a functionally graded sandwich rectangular plate varies with rotational speed and temperature.Results show that the nonlinear/linear frequency ratio increases with rotational angular velocity Ω and thickness-to-length ratio h/a,follows a cosine-like periodic pattern with the setting angle,and shows a sharp decrease followed by a rapid increase with increasing width-to-length ratio b/a.The derived analytical solutions for nonlinear frequency provide valuable insights for assessing the dynamic characteristics of functionally graded structures.
基金supported by the National Natural Science Foundation of China(Grant No.12071042)the Beijing Natural Science Foundation(Grant No.1202004)Promoting the Development of University Classification-Student Innovation and Entrepreneurship Training Programme(Grant No.5112410857)。
文摘In this paper,we propose a symmetric difference data enhancement physics-informed neural network(SDE-PINN)to study soliton solutions for discrete nonlinear lattice equations(NLEs).By considering known and unknown symmetric points,numerical simulations are conducted to one-soliton and two-soliton solutions of a discrete KdV equation,as well as a one-soliton solution of a discrete Toda lattice equation.Compared with the existing discrete deep learning approach,the numerical results reveal that within the specified spatiotemporal domain,the prediction accuracy by SDE-PINN is excellent regardless of the interior or extrapolation prediction,with a significant reduction in training time.The proposed data enhancement technique and symmetric structure development provides a new perspective for the deep learning approach to solve discrete NLEs.The newly proposed SDE-PINN can also be applied to solve continuous nonlinear equations and other discrete NLEs numerically.
基金The project supported by National Natural Science Foundation of China, the Natural Science Foundation of Shandong Province of China, and the Natural Scienoe Foundation of Liaocheng University
文摘By using the extended hyperbolic function method, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution, bright and dark soliton solution, alternating phase bright soliton solution, alternating phase dark soliton solution, and alternating phase bright and dark soliton solution, if a special relation is bound on the coefficients of the equation.
基金supported by the National Natural Science Foundation of China(No.12172321)。
文摘The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonlinearity is incorporated into the model,and the constitutive equations are derived.The physical parameters of functionally graded materials(FGMs),which exhibit continuous variation across the thickness gradient,are of particular interest.The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton's principle.The nonlinear partial differential equations are discretized with the Galerkin method,and the analytical expression of traveling wave frequencies is derived with an approximate method.The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions.Finally,the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies.The results show that the factors including the power-law index,temperature,magnetic field intensity,and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.
文摘In this paper we propose a new discrete bidirectional associative memory (DBAM) which is derived from our previous continuous linear bidirectional associative memory (LBAM). The DBAM performs bidirectionally the optimal associative mapping proposed by Kohonen. Like LBAM and NBAM proposed by one of the present authors,the present BAM ensures the guaranteed recall of all stored patterns,and possesses far higher capacity compared with other existing BAMs,and like NBAM, has the strong ability to suppress the noise occurring in the output patterns and therefore reduce largely the spurious patterns. The derivation of DBAM is given and the stability of DBAM is proved. We also derive a learning algorithm for DBAM,which has iterative form and make the network learn new patterns easily. Compared with NBAM the present BAM can be easily implemented by software.
文摘This work deals with robust inverse neural control strategy for a class of single-input single-output(SISO) discrete-time nonlinear system affected by parametric uncertainties. According to the control scheme, in the first step, a direct neural model(DNM)is used to learn the behavior of the system, then, an inverse neural model(INM) is synthesized using a specialized learning technique and cascaded to the uncertain system as a controller. In previous works, the neural models are trained classically by backpropagation(BP) algorithm. In this work, the sliding mode-backpropagation(SM-BP) algorithm, presenting some important properties such as robustness and speedy learning, is investigated. Moreover, four combinations using classical BP and SM-BP are tested to determine the best configuration for the robust control of uncertain nonlinear systems. Two simulation examples are treated to illustrate the effectiveness of the proposed control strategy.
基金Project supported by the National Natural Science Foundation of China(No.11772205)the Scientific Research Fund of Liaoning Provincial Education Department(No.L201703)+1 种基金the Liaoning Revitalization Talent Program(No.XLYC1807172)the Training Project of Liaoning Higher Education Institutions in Domestic and Overseas(No.2018LNGXGJWPY-YB008)
文摘A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is coupled with the modified Bouc-Wen model of hysteresis.The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET)to concentrate the energy locally on the nonlinear oscillator,and then dissipates it through damping in the NES with NiTi-ST.The generalized vibration transmissibility,obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs.Finally,the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption.The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system,without changing its natural frequency.Moreover,the NES with NiTi-ST can be directly used in practical engineering applications.
基金Project supported by the National Natural Science Foundation of China （Grant No 10461006）, the Natural Science Foundation （Grant No 200408020103）, the High Education Science Research Program （Grant No NJ02035） of Inner Mongolia, China and the Youth Foundation （Grant No QN004024） of Inner Mongolia Normal University, China.
文摘Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.
基金supported by the National Science Foundation of China (70771080)Social Science Foundation of Ministry of Education (10YJC630233)
文摘The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.
基金supported by Ministry of the Higher Education and Scientific Research in Tunisa
文摘The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state delay. Firstly, a new sliding function including a present value and a past value of the state, called dynamic surface, is designed by means of linear matrix inequalities （LMIs）. Then, using this dynamic function and the rolling optimization method in the predictive control strategy, a discrete predictive sliding mode controller is synthesized. This new strategy is proposed to eliminate the undesirable effect of the delay term in the closed loop system. Also, the designed control strategy is more robust, and has a chattering reduction property and a faster convergence of the system s state. Finally, a numerical example is given to illustrate the effectiveness of the proposed control.
基金Supported by Natural Science Foundation of Zhejiang Province P. R. China (Y105141)Natural Science Foundation of Fujian Province P.R.China (A0510025)Technological Project of Zhejiang Education Department,P. R. China(20050291)
文摘The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.
基金Support by China 973 Project (No. 2002CB312200).
文摘A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.
基金Supported by the Natural Science Foundation of Guangdong Pronvince( 0 1 1 471 ) and Education Bu-reau( 0 1 76)
文摘Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.
基金the National+4 种基金 Natural Science Foundation of China
文摘The algorithm proposed by T. F. Colemen and A. R. Conn is improved in this paper, and the improved algorithm can solve nonlinear programming problem with quality constraints. It is shown that the improved algorithm possesses global convergence, and under some conditions, it possesses locally supperlinear convergence.
文摘Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to
基金The project partially supported by the Research Grants Council under Grant Nos, HKU 7123/05E and HKU 7184/04E
文摘The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system.
文摘This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.
