A deky-dependent H-infinity control for descriptor systems with a state-delayis investigated. The purpose of the problem is to design a linear memoryless state-feedbackcontroller such that the resulting closed-loop sy...A deky-dependent H-infinity control for descriptor systems with a state-delayis investigated. The purpose of the problem is to design a linear memoryless state-feedbackcontroller such that the resulting closed-loop system is regular, impulse free and stable with anH-infinity norm bound. Firstly, a deky-dependent bounded real lemma(BRL) of the time-deky descriptorsystems is presented in terms of linear matrix inequalities(LMIs) by using a descriptor modeltransformation of the system and by taking a new Lyapunov-Krasovsii functional. The introducedfunctional does not require bounding for cross terms, so it has less conservation. Secondly, withthe help of the obtained bounded real lemma, a sufficient condition for the existence of a newdeky-dependent H-infinity state-feedback controller is shown in terms of nonlinear matrixinequalities and the solvability of the problem can be obtained by using an iterative algorithminvolving convex optimization. Finally, numerical examples are given to demonstrate theeffectiveness of the new method presented.展开更多
The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then...The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.展开更多
A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under considera...A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control desin methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples.展开更多
In this note we show that for a given controllable pair (A, B) and any λ > 0, a gain matrix K can be chosen so that the transition matrix e {(A+BK)t} of the system x = (A + BK) x decays at the exponential rate e ?...In this note we show that for a given controllable pair (A, B) and any λ > 0, a gain matrix K can be chosen so that the transition matrix e {(A+BK)t} of the system x = (A + BK) x decays at the exponential rate e ?λt and the overshoot of the transition matrix can be bounded by Mλ L for some constants M and L that are independent of λ. As a consequence, for any h > 0, a gain matrix K can be chosen so that the magnitude of the transition matrix e (A+BK)t can be reduced by 1/2 (or by any given portion) over [0, h]. An interesting application of the result is in the stabilization of switched linear systems with any given switching rate.展开更多
A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics sys...A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. A time-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the time evolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate the local dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is tested for the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this prediction technique can improve the prediction of chaotic time series.展开更多
In order to investigate the problem of quadratic stability of switched linear systems via cascading, all the real invariant subspaces of a given linear system were investigated, and the result was used to provide comp...In order to investigate the problem of quadratic stability of switched linear systems via cascading, all the real invariant subspaces of a given linear system were investigated, and the result was used to provide comparable cascading form of switching models. Using the common cascading form, a common quadratic Lyapunov function (CQLF) can be found by the set of CQLF of diagonal blocks.展开更多
In this paper, a systematic and powerful scheme is proposed to address a generalized-type synchronization of a class of continuous-time systems, which includes generalized lag synchronization, generalized anticipated ...In this paper, a systematic and powerful scheme is proposed to address a generalized-type synchronization of a class of continuous-time systems, which includes generalized lag synchronization, generalized anticipated synchronization, and generalized synchronization. The presented scheme is used to investigate the generalized-type synchronization of the 4D hyperchaotic oscillator and the hyperchaotic oscillator with gyrators. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme is more powerful than the scalar signal scheme due to Grassi and Mascolo.展开更多
Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into ano...Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+ 1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function.Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.展开更多
The science of complexity studies the behavior and properties of complex systems in nature and human society. Particular interest has been put on their certain simple common properties. Symmetry is one of such propert...The science of complexity studies the behavior and properties of complex systems in nature and human society. Particular interest has been put on their certain simple common properties. Symmetry is one of such properties. Symmetric phenomena can be found in many complex systems. The purpose of this paper is to reveal the internal reason of the symmetry. Using some physical systems and geometric objects, the paper shows that many symmetries are caused by optimization under certain criteria. It has also been revealed that an evolutional process may lead to symmetry.展开更多
The existence ofpositive radialsolutions ofthe equation - div(｜Du｜p- 2Du)= f(u) is studied in annular dom ains in Rn,n≥2. Itisproved thatiff(0)≥0, f is somewhere negativein (0,∞), lim u→0+ f′(u)= 0and lim u→...The existence ofpositive radialsolutions ofthe equation - div(｜Du｜p- 2Du)= f(u) is studied in annular dom ains in Rn,n≥2. Itisproved thatiff(0)≥0, f is somewhere negativein (0,∞), lim u→0+ f′(u)= 0and lim u→∞(f(u)/up- 1)= ∞, then thereisa largepositiveradialsolution on allannuli.Iff(0)< 0 and satisfiescertain condi- tions, then the equation has no radialsolution ifthe annuliare too wide.展开更多
In this note, the author proves that the inverse problem of submodular function on digraphs with l∞ objective function can be solved by strongly polynomial algorithm. The result shows that most inverse network optimi...In this note, the author proves that the inverse problem of submodular function on digraphs with l∞ objective function can be solved by strongly polynomial algorithm. The result shows that most inverse network optimization problems with l∞ objective function can be solved in the polynomial time.展开更多
The difficulty in crude oil price forecasting, due to inherent complexity, has attracted much attention of academic researchers and business practitioners. Various methods have been tried to solve the problem of forec...The difficulty in crude oil price forecasting, due to inherent complexity, has attracted much attention of academic researchers and business practitioners. Various methods have been tried to solve the problem of forecasting crude oil prices. However, all of the existing models of prediction can not meet practical needs. Very recently, Wang and Yu proposed a new methodology for handling complex systems-TEI@I methodology by means of a systematic integration of text mining, econometrics and intelligent techniques.Within the framework of TEI@I methodology, econometrical models are used to model the linear components of crude oil price time series (i.e., main trends) while nonlinear components of crude oil price time series (i.e., error terms) are modelled by using artificial neural network (ANN) models. In addition, the impact of irregular and infrequent future events on crude oil price is explored using web-based text mining (WTM) and rule-based expert systems (RES) techniques. Thus, a fully novel nonlinear integrated forecasting approach with error correction and judgmental adjustment is formulated to improve prediction performance within the framework of the TEI@I methodology. The proposed methodology and the novel forecasting approach are illustrated via an example.展开更多
Input selection is probably one of the most critical decision issues in neural network designing, because it has a great impact on forecasting performance. Among the many applications of artificial neural networks to ...Input selection is probably one of the most critical decision issues in neural network designing, because it has a great impact on forecasting performance. Among the many applications of artificial neural networks to finance, time series forecasting is perhaps one of the most challenging issues. Considering the features of neural networks, we propose a general approach called Autocorrelation Criterion (AC) to determine the inputs variables for a neural network. The purpose is to seek optimal lag periods, which are more predictive and less correlated. AC is a data-driven approach in that there is no prior assumptiona bout the models for time series under study. So it has extensive applications and avoids a lengthy experimentation and tinkering in input selection. We apply the approach to the determination of input variables for foreign exchange rate forecasting and conductcomparisons between AC and information-based in-sample model selection criterion. The experiment results show that AC outperforms information-based in-sample model selection criterion.展开更多
The greedy algorithm is a strong local searching algorithm. The genetic algorithm is generally applied to the global optimization problems. In this paper, we combine the greedy idea and the genetic algorithm to propos...The greedy algorithm is a strong local searching algorithm. The genetic algorithm is generally applied to the global optimization problems. In this paper, we combine the greedy idea and the genetic algorithm to propose the greedy genetic algorithm which incorporates the global exploring ability of the genetic algorithm and the local convergent ability of the greedy algorithm. Experimental results show that greedy genetic algorithm gives much better results than the classical genetic algorithm.展开更多
Various mathematical models have been commonly used in time series analysis and forecasting. In these processes, academic researchers and business practitioners often come up against two important problems. One is whe...Various mathematical models have been commonly used in time series analysis and forecasting. In these processes, academic researchers and business practitioners often come up against two important problems. One is whether to select an appropriate modeling approach for prediction purposes or to combine these different individual approaches into a single forecast for the different/dissimilar modeling approaches. Another is whether to select the best candidate model for forecasting or to mix the various candidate models with different parameters into a new forecast for the same/similar modeling approaches. In this study, we propose a set of computational procedures to solve the above two issues via two judgmental criteria. Meanwhile, in view of the problems presented in the literature, a novel modeling technique is also proposed to overcome the drawbacks of existing combined forecasting methods. To verify the efficiency and reliability of the proposed procedure and modeling technique, the simulations and real data examples are conducted in this study.The results obtained reveal that the proposed procedure and modeling technique can be used as a feasible solution for time series forecasting with multiple candidate models.展开更多
This work develops hybrid models for large-scale singular differential system and analyzes their asymptotic properties. To take into consideration the discrete shifts in regime across which the behavior of the corresp...This work develops hybrid models for large-scale singular differential system and analyzes their asymptotic properties. To take into consideration the discrete shifts in regime across which the behavior of the corresponding dynamic systems is markedly different, our goals are to develop hybrid systems in which continuous dynamics are intertwined with discrete events under random-jump disturbances and to reduce complexity of large-scale singular systems via singularly perturbed Markov chains. To reduce the complexity of large-scale hybrid singular systems, two-time scale is used in the formulation. Under general assumptions, limit behavior of the underlying system is examined. Using weak convergence methods, it is shown that the systems can be approximated by limit systems in which the coefficients are averaged out with respect to the quasi-stationary distributions. Since the limit systems have fewer states, the complexity is much reduced.展开更多
Superconvergence of the mixed finite element methods for 2-d Maxwell equations is studied in this paper. Two order of superconvergent factor can be obtained for the k-th Nedelec elements on the rectangular meshes.
文摘A deky-dependent H-infinity control for descriptor systems with a state-delayis investigated. The purpose of the problem is to design a linear memoryless state-feedbackcontroller such that the resulting closed-loop system is regular, impulse free and stable with anH-infinity norm bound. Firstly, a deky-dependent bounded real lemma(BRL) of the time-deky descriptorsystems is presented in terms of linear matrix inequalities(LMIs) by using a descriptor modeltransformation of the system and by taking a new Lyapunov-Krasovsii functional. The introducedfunctional does not require bounding for cross terms, so it has less conservation. Secondly, withthe help of the obtained bounded real lemma, a sufficient condition for the existence of a newdeky-dependent H-infinity state-feedback controller is shown in terms of nonlinear matrixinequalities and the solvability of the problem can be obtained by using an iterative algorithminvolving convex optimization. Finally, numerical examples are given to demonstrate theeffectiveness of the new method presented.
文摘The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.
基金This work was supported in part by NNSF and Project 973 of China(No.60221301 and No.60334040)
文摘A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control desin methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples.
基金This work was supported partly by the Chinese National Natural Science Foundation. The work of Wang was also supported partly by the US National Science Foundation (No. DMS - 0072620).
文摘In this note we show that for a given controllable pair (A, B) and any λ > 0, a gain matrix K can be chosen so that the transition matrix e {(A+BK)t} of the system x = (A + BK) x decays at the exponential rate e ?λt and the overshoot of the transition matrix can be bounded by Mλ L for some constants M and L that are independent of λ. As a consequence, for any h > 0, a gain matrix K can be chosen so that the magnitude of the transition matrix e (A+BK)t can be reduced by 1/2 (or by any given portion) over [0, h]. An interesting application of the result is in the stabilization of switched linear systems with any given switching rate.
文摘A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. A time-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the time evolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate the local dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is tested for the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this prediction technique can improve the prediction of chaotic time series.
文摘In order to investigate the problem of quadratic stability of switched linear systems via cascading, all the real invariant subspaces of a given linear system were investigated, and the result was used to provide comparable cascading form of switching models. Using the common cascading form, a common quadratic Lyapunov function (CQLF) can be found by the set of CQLF of diagonal blocks.
文摘In this paper, a systematic and powerful scheme is proposed to address a generalized-type synchronization of a class of continuous-time systems, which includes generalized lag synchronization, generalized anticipated synchronization, and generalized synchronization. The presented scheme is used to investigate the generalized-type synchronization of the 4D hyperchaotic oscillator and the hyperchaotic oscillator with gyrators. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme is more powerful than the scalar signal scheme due to Grassi and Mascolo.
基金National Key Basic Research Project of China under，国家自然科学基金，教育部留学回国人员科研启动基金
文摘Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+ 1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function.Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.
基金The work done by the second and third authors are partly supported by the National Natural Saence Foundation of China (No. 60343001,60274010).
文摘The science of complexity studies the behavior and properties of complex systems in nature and human society. Particular interest has been put on their certain simple common properties. Symmetry is one of such properties. Symmetric phenomena can be found in many complex systems. The purpose of this paper is to reveal the internal reason of the symmetry. Using some physical systems and geometric objects, the paper shows that many symmetries are caused by optimization under certain criteria. It has also been revealed that an evolutional process may lead to symmetry.
文摘The existence ofpositive radialsolutions ofthe equation - div(｜Du｜p- 2Du)= f(u) is studied in annular dom ains in Rn,n≥2. Itisproved thatiff(0)≥0, f is somewhere negativein (0,∞), lim u→0+ f′(u)= 0and lim u→∞(f(u)/up- 1)= ∞, then thereisa largepositiveradialsolution on allannuli.Iff(0)< 0 and satisfiescertain condi- tions, then the equation has no radialsolution ifthe annuliare too wide.
文摘In this note, the author proves that the inverse problem of submodular function on digraphs with l∞ objective function can be solved by strongly polynomial algorithm. The result shows that most inverse network optimization problems with l∞ objective function can be solved in the polynomial time.
基金This research is partially supported by NSFC, CAS, RGC of Hong Kong and Ministry of Education and Technology of Japan
文摘The difficulty in crude oil price forecasting, due to inherent complexity, has attracted much attention of academic researchers and business practitioners. Various methods have been tried to solve the problem of forecasting crude oil prices. However, all of the existing models of prediction can not meet practical needs. Very recently, Wang and Yu proposed a new methodology for handling complex systems-TEI@I methodology by means of a systematic integration of text mining, econometrics and intelligent techniques.Within the framework of TEI@I methodology, econometrical models are used to model the linear components of crude oil price time series (i.e., main trends) while nonlinear components of crude oil price time series (i.e., error terms) are modelled by using artificial neural network (ANN) models. In addition, the impact of irregular and infrequent future events on crude oil price is explored using web-based text mining (WTM) and rule-based expert systems (RES) techniques. Thus, a fully novel nonlinear integrated forecasting approach with error correction and judgmental adjustment is formulated to improve prediction performance within the framework of the TEI@I methodology. The proposed methodology and the novel forecasting approach are illustrated via an example.
基金This research is partially supported by Chinese Academy of SciencesNational Science Foundation of ChinaJapan Society for the Promotion of Science.
文摘Input selection is probably one of the most critical decision issues in neural network designing, because it has a great impact on forecasting performance. Among the many applications of artificial neural networks to finance, time series forecasting is perhaps one of the most challenging issues. Considering the features of neural networks, we propose a general approach called Autocorrelation Criterion (AC) to determine the inputs variables for a neural network. The purpose is to seek optimal lag periods, which are more predictive and less correlated. AC is a data-driven approach in that there is no prior assumptiona bout the models for time series under study. So it has extensive applications and avoids a lengthy experimentation and tinkering in input selection. We apply the approach to the determination of input variables for foreign exchange rate forecasting and conductcomparisons between AC and information-based in-sample model selection criterion. The experiment results show that AC outperforms information-based in-sample model selection criterion.
文摘The greedy algorithm is a strong local searching algorithm. The genetic algorithm is generally applied to the global optimization problems. In this paper, we combine the greedy idea and the genetic algorithm to propose the greedy genetic algorithm which incorporates the global exploring ability of the genetic algorithm and the local convergent ability of the greedy algorithm. Experimental results show that greedy genetic algorithm gives much better results than the classical genetic algorithm.
基金This paper was partially supported by NSFC,CAS,RGC of Hong Kong and Ministry of Education and Technology of Japan.
文摘Various mathematical models have been commonly used in time series analysis and forecasting. In these processes, academic researchers and business practitioners often come up against two important problems. One is whether to select an appropriate modeling approach for prediction purposes or to combine these different individual approaches into a single forecast for the different/dissimilar modeling approaches. Another is whether to select the best candidate model for forecasting or to mix the various candidate models with different parameters into a new forecast for the same/similar modeling approaches. In this study, we propose a set of computational procedures to solve the above two issues via two judgmental criteria. Meanwhile, in view of the problems presented in the literature, a novel modeling technique is also proposed to overcome the drawbacks of existing combined forecasting methods. To verify the efficiency and reliability of the proposed procedure and modeling technique, the simulations and real data examples are conducted in this study.The results obtained reveal that the proposed procedure and modeling technique can be used as a feasible solution for time series forecasting with multiple candidate models.
基金Yin Gang was supported by the National Science Foundation of US (Grant No.DMS-9877090) and Zhang Jifeng was supported by the National Natural Science Foundation of China (Grant No. 69725006).
文摘This work develops hybrid models for large-scale singular differential system and analyzes their asymptotic properties. To take into consideration the discrete shifts in regime across which the behavior of the corresponding dynamic systems is markedly different, our goals are to develop hybrid systems in which continuous dynamics are intertwined with discrete events under random-jump disturbances and to reduce complexity of large-scale singular systems via singularly perturbed Markov chains. To reduce the complexity of large-scale hybrid singular systems, two-time scale is used in the formulation. Under general assumptions, limit behavior of the underlying system is examined. Using weak convergence methods, it is shown that the systems can be approximated by limit systems in which the coefficients are averaged out with respect to the quasi-stationary distributions. Since the limit systems have fewer states, the complexity is much reduced.
基金This work is subsidized by the special funds for major state basic research projects (No. 1999032800).
文摘Superconvergence of the mixed finite element methods for 2-d Maxwell equations is studied in this paper. Two order of superconvergent factor can be obtained for the k-th Nedelec elements on the rectangular meshes.
