Presents the iterative method of solving Cauchy problem with reproducing kernel for nonlinear hyperbolic equations, and the application of the computational technique of reproducing kernel space to simplify, the itera...Presents the iterative method of solving Cauchy problem with reproducing kernel for nonlinear hyperbolic equations, and the application of the computational technique of reproducing kernel space to simplify, the iterative computation and increase the convergence rate and points out that this method is still effective. Even if the initial condition is discrete.展开更多
Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental pro...Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.展开更多
This note is concerned with a new direct(non-iterative)method for the solution of an elliptic inverse problem.This method is based on the application of the Green's second identity which leads to a moment problem ...This note is concerned with a new direct(non-iterative)method for the solution of an elliptic inverse problem.This method is based on the application of the Green's second identity which leads to a moment problem for the unknown boundary condition.Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition without any need for iterations.Four examples are used to study the applicability of the method with the presence of noise.展开更多
目的:为了保持大规模MIMO系统上行链路信号高检测性能同时降低实现复杂度。方法:在信号检测中,传统最小均方误差(MMSE,minimum mean square error)算法可以获得近似最优检测性能,但需要高维矩阵求逆,复杂度很高。本文通过在最速下降法和...目的:为了保持大规模MIMO系统上行链路信号高检测性能同时降低实现复杂度。方法:在信号检测中,传统最小均方误差(MMSE,minimum mean square error)算法可以获得近似最优检测性能,但需要高维矩阵求逆,复杂度很高。本文通过在最速下降法和Barzilai-Borwein迭代算法结合基础上,采用Richardson算法初始值,在此基础上对步长合理选取,提出一种改进Barzilai-Borwein信号检测方法。结果:该算法相对于MMSE复杂度降低一个数量级,并且算法误码率性能又可以与MMSE算法相当,同时该算法相对于Barzilai-Borwein和CBB(Cauchy Barzilai-Borwein)检测,复杂度提升很少,但性能有较大提升。结论:基于改进修正Barzilai-Borwein迭代大规模MIMO信号检测算法只需4次迭代就可接近MMSE,在保持高检测性能的同时实现了复杂度降低。展开更多
文摘Presents the iterative method of solving Cauchy problem with reproducing kernel for nonlinear hyperbolic equations, and the application of the computational technique of reproducing kernel space to simplify, the iterative computation and increase the convergence rate and points out that this method is still effective. Even if the initial condition is discrete.
基金supported in part by the National Natural Science Foundation of China (62273018)in part by the Science and Technology on Space Intelligent Control Laboratory (HTKJ2022KL502006)。
文摘Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.
文摘This note is concerned with a new direct(non-iterative)method for the solution of an elliptic inverse problem.This method is based on the application of the Green's second identity which leads to a moment problem for the unknown boundary condition.Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition without any need for iterations.Four examples are used to study the applicability of the method with the presence of noise.
文摘目的:为了保持大规模MIMO系统上行链路信号高检测性能同时降低实现复杂度。方法:在信号检测中,传统最小均方误差(MMSE,minimum mean square error)算法可以获得近似最优检测性能,但需要高维矩阵求逆,复杂度很高。本文通过在最速下降法和Barzilai-Borwein迭代算法结合基础上,采用Richardson算法初始值,在此基础上对步长合理选取,提出一种改进Barzilai-Borwein信号检测方法。结果:该算法相对于MMSE复杂度降低一个数量级,并且算法误码率性能又可以与MMSE算法相当,同时该算法相对于Barzilai-Borwein和CBB(Cauchy Barzilai-Borwein)检测,复杂度提升很少,但性能有较大提升。结论:基于改进修正Barzilai-Borwein迭代大规模MIMO信号检测算法只需4次迭代就可接近MMSE,在保持高检测性能的同时实现了复杂度降低。
