This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It succes...This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It successfully shows that this method may be valid for solving other nonlinear partial differential equations.展开更多
The lithium-ion batteries have drawn much attention as the major energy storage system.However,the battery state estimation still suffers from inaccuracy under dynamic operational conditions,with the unstable environm...The lithium-ion batteries have drawn much attention as the major energy storage system.However,the battery state estimation still suffers from inaccuracy under dynamic operational conditions,with the unstable environmental noise influencing the robustness of estimation.This paper presents a 5th-order cubature Kalman filter with improvements on adaptivity for real-time state-of-charge estimation.The second-order equivalent circuit model is developed for describing the characteristics of battery,and parameter identification is carried out according to particle swarm optimization.The developed method is validated in stable and dynamic conditions,and simulation results show a satisfactory consistency with the experimental results.The maximum estimation error under static conditions is less than 3%and the maximum error under dynamic conditions is 5%.Numerical analysis indicates that the method has better convergence and robustness than the traditional method under the disturbances of initial error,which demonstrates the potential for EV applications in harsh environments.The proposed method shows application potential for both online estimations and cloud-computing system,indicating its diverse application prospect in electric vehicles.展开更多
This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N),” which generalizes and extends all...This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5<sup>th</sup>-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5<sup>th</sup>-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.展开更多
We study a nonlinear differential equations in the Banach space of real functions and continuous on a bounded and closed interval. With the help of a suitable theorems (fixed point) and some boundary conditions, the 5...We study a nonlinear differential equations in the Banach space of real functions and continuous on a bounded and closed interval. With the help of a suitable theorems (fixed point) and some boundary conditions, the 5th order nonlinear differential equations has at least one positive solution.展开更多
：This paper deals with H∞ control of a 5th-order model of synchronous generators. First,byusing the method of exact linearization, we transform the 5th-order model into a linear one. Then we assignthe pole of the li...：This paper deals with H∞ control of a 5th-order model of synchronous generators. First,byusing the method of exact linearization, we transform the 5th-order model into a linear one. Then we assignthe pole of the linearized model in the open left half plane. Finally, we apply the design method of linear H∞control to get a state feedback controller.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10575082 and 10247008）.
文摘This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It successfully shows that this method may be valid for solving other nonlinear partial differential equations.
基金This work is supported by the National Key Research and Development Program of China(2018YFB0105400).
文摘The lithium-ion batteries have drawn much attention as the major energy storage system.However,the battery state estimation still suffers from inaccuracy under dynamic operational conditions,with the unstable environmental noise influencing the robustness of estimation.This paper presents a 5th-order cubature Kalman filter with improvements on adaptivity for real-time state-of-charge estimation.The second-order equivalent circuit model is developed for describing the characteristics of battery,and parameter identification is carried out according to particle swarm optimization.The developed method is validated in stable and dynamic conditions,and simulation results show a satisfactory consistency with the experimental results.The maximum estimation error under static conditions is less than 3%and the maximum error under dynamic conditions is 5%.Numerical analysis indicates that the method has better convergence and robustness than the traditional method under the disturbances of initial error,which demonstrates the potential for EV applications in harsh environments.The proposed method shows application potential for both online estimations and cloud-computing system,indicating its diverse application prospect in electric vehicles.
文摘This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5<sup>th</sup>-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5<sup>th</sup>-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.
文摘We study a nonlinear differential equations in the Banach space of real functions and continuous on a bounded and closed interval. With the help of a suitable theorems (fixed point) and some boundary conditions, the 5th order nonlinear differential equations has at least one positive solution.
基金Supported by National Natural Science Foundation( G5983 72 70 ,G1 9980 2 0 3 0 8,G1 9980 2 0 3 0 9) and Project 973 of China
文摘：This paper deals with H∞ control of a 5th-order model of synchronous generators. First,byusing the method of exact linearization, we transform the 5th-order model into a linear one. Then we assignthe pole of the linearized model in the open left half plane. Finally, we apply the design method of linear H∞control to get a state feedback controller.
