Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the...Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the existing systems.This derivation process consists of three steps:step 1,decomposing the vector field;step 2,solving the Hamilton energy function;and step 3,verifying uniqueness.In order to easily choose an appropriate decomposition method,we propose a classification criterion based on the form of system state variables,i.e.,type-I vector fields that can be directly decomposed and type-II vector fields decomposed via exterior differentiation.Moreover,exterior differentiation is used to represent the curl of low-high dimension vector fields in the process of decomposition.Finally,we exemplify the Hamilton energy function of six classical systems and analyze the relationship between Hamilton energy and dynamic behavior.This solution provides a new approach for deducing the Hamilton energy function,especially in high-dimensional systems.展开更多
由于横向时延滤波和IQ正交滤波在稳定性、收敛速度和误差率等方面的性能差异对于最小均方算法(LMS,Least Mean Squares)在工程上的实际应用具有参考意义,采用数值仿真的方法模拟了两者实现自适应最小均方算法的具体过程,并对比分析了它...由于横向时延滤波和IQ正交滤波在稳定性、收敛速度和误差率等方面的性能差异对于最小均方算法(LMS,Least Mean Squares)在工程上的实际应用具有参考意义,采用数值仿真的方法模拟了两者实现自适应最小均方算法的具体过程,并对比分析了它们的滤波性能。仿真结果显示IQ正交滤波具有更高的稳定性、更快的收敛速度、更小的误差率,其滤波性能优于横向时延滤波。IQ正交滤波器的阶数为2阶,而横向时延滤波器的阶数通常>10,滤波器阶数越多引入的权噪声也会相对增加,对于稳定性、收敛速度和误差率都是不利的,因此实际应用中优先选择阶数较少的IQ正交滤波器。展开更多
基金the National Natural Science Foundation of China(Grant Nos.12305054,12172340,and 12371506)。
文摘Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the existing systems.This derivation process consists of three steps:step 1,decomposing the vector field;step 2,solving the Hamilton energy function;and step 3,verifying uniqueness.In order to easily choose an appropriate decomposition method,we propose a classification criterion based on the form of system state variables,i.e.,type-I vector fields that can be directly decomposed and type-II vector fields decomposed via exterior differentiation.Moreover,exterior differentiation is used to represent the curl of low-high dimension vector fields in the process of decomposition.Finally,we exemplify the Hamilton energy function of six classical systems and analyze the relationship between Hamilton energy and dynamic behavior.This solution provides a new approach for deducing the Hamilton energy function,especially in high-dimensional systems.
文摘由于横向时延滤波和IQ正交滤波在稳定性、收敛速度和误差率等方面的性能差异对于最小均方算法(LMS,Least Mean Squares)在工程上的实际应用具有参考意义,采用数值仿真的方法模拟了两者实现自适应最小均方算法的具体过程,并对比分析了它们的滤波性能。仿真结果显示IQ正交滤波具有更高的稳定性、更快的收敛速度、更小的误差率,其滤波性能优于横向时延滤波。IQ正交滤波器的阶数为2阶,而横向时延滤波器的阶数通常>10,滤波器阶数越多引入的权噪声也会相对增加,对于稳定性、收敛速度和误差率都是不利的,因此实际应用中优先选择阶数较少的IQ正交滤波器。
