Compensation for time-delayed feedback bang-bang control of quasi-integrable Hamiltonian systems

The stochastic averaging method for quasi-integrable Hamiltonian systems with time-delayed feedback bang-bang control is first introduced. Then, two time delay compensation methods, namely the method of changing control force amplitude (CFA) and the method of changing control delay time (CDT), are proposed. The conditions applicable to each compensation method are discussed. Finally, an example is worked out in detail to illustrate the application and effectiveness of the proposed methods and the two compensation methods in combination.

Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems

The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.

On traceable iterated line graph and hamiltonian path index

Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.

Universal Machine Learning Kohn–Sham Hamiltonian for Materials

While density functional theory(DFT)serves as a prevalent computational approach in electronic structure calculations,its computational demands and scalability limitations persist.Recently,leveraging neural networks to parameterize the Kohn-Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations.Despite advancements,challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate machine learning models for multi-elemental materials still exist.Addressing these hurdles,this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project.We demonstrate its generality in predicting electronic structures across the whole periodic table,including complex multi-elemental systems,solid-state electrolytes,Moir´e twisted bilayer heterostructure,and metal-organic frameworks.Moreover,we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GNoME datasets,identifying 3940 crystals with direct band gaps and 5109 crystals with flat bands.By offering a reliable efficient framework for computing electronic properties,this universal Hamiltonian model lays the groundwork for advancements in diverse fields,such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

An Eight Component Integrable Hamiltonian Hierarchy from a Reduced Seventh-Order Matrix Spectral Problem

We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.

基于Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪

在计算机视觉领域,由镜头切换、目标动力学突变、低帧率视频等引起的突变运动存在极大的不确定性,使得突变运动跟踪成为该领域的挑战性课题.以贝叶斯滤波框架为基础,提出一种基于有序超松弛Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪算法.该算法将Hamiltonian动力学融入MCMC(Markov chain Monte Carlo)算法,目标状态被扩张为原始目标状态变量与一个动量项的组合.在提议阶段,为抑制由Gibbs采样带来的随机游动行为,提出采用有序超松弛迭代方法来抽取目标动量项.同时,提出自适应步长的Hamiltonian动力学实现方法,在跟踪过程中自适应地调整步长,以减少模拟误差.提出的跟踪算法可以避免传统的基于随机游动的MCMC跟踪算法所存在的局部最优问题,提高了跟踪的准确性而不需要额外的计算时间.实验结果表明,该算法在处理多种类型的突变运动时表现出出色的处理能力.

Hamiltonian[k,k+1]-因子(英文)

本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性。Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\e)<n/2(对任意的e∈E(G)),则称G为n/2-临界图。设k为大于等于2的整数,G为n/2-临界图(其中n≥4k-6且n≥7),我们证明了对于G的任何Hamiltonian圈C,G中必存在包含C的[k,k+1]-因子。该结果改进了现有的一些有关Hamiltonian[k,k+1]-因子存在性的结果。

基于I&I与Hamiltonian理论的机器人速度观测器设计

近期,Astolfi和Stamnes等对一类机械系统设计了速度观测器.采用了分步设计Lyapunov函数的方法,这导致观测误差系统结构复杂、证明繁琐.而且设计的偏微分方程(Partial differential equation,PDE)不合理,导致计算量大、不易求解.本文在Astolfi和Stamnes等的基础上,对一类机械(机器人)系统设计了速度观测器.通过对观测误差系统的Hamiltonian实现,克服了Astolfi和Stamnes等方法中的上述缺点.并设计了一类偏微分方程,避免了繁琐计算.最后,将所设计的速度观测器应用到一类关节机器人中,仿真结果验证了设计方法的有效性.

一类具有幂零中心四次Hamiltonian的Abelian积分的零点个数

该文证明了Hamiltonian H(x,y)=-x^2+ax^2y^2+bx^4+cy^4的Abelian积分在区间(c/(a^2-4bc),0)上零点的个数不超过3n+3[(n-1)/4]+14(计重数),其中a>0,b<-2,c<0,a^2>4bc.

基于Hamiltonian三角剖分的三角网格多分辨率表示

三角网格模型的多分辨率表示是几何模型绘制与传输的基础,本文通过三角形之间的拓扑相邻关系将三角网格划分为广义三角形带的集合,然后利用Hamiltonian三角剖分的性质构造三角网格的多分辨率表示。该方法统一了单分辨率网格和多分辨率网格的表示方法,当模型有c个不同分辨率表示时,其编码效率为(logc+5)bit/vertex。

一类对称二阶Hamiltonian系统的偶同宿轨(英文)

利用临界点理论中的山路引理,采用零边值问题解逼近的方法,证明了一类对称超二次二阶Hamiltonian系统非平凡偶同宿轨的存在性.

两类树图的Hamiltonian色数

一个n阶连通图G的Hamiltonian染色是从G的顶点集V(G)到正整数集N(称为颜色集)的一个映射c,使得对于G的任意2个不同的顶点u和v满足|c(u)-c(v)|+D(u,v)≥n-1,其中D(u,v)表示G中u到v的最长路径的长度。对一个Hamiltonian染色c,将max{c(u):u∈V(G)}称为c的值,记作hc(c)。将min{hc(c):c是G的任意Hamiltonian染色}称为G的Hamiltonian色数,记作hc(G)。本次研究得到了满足max{D(u,v)|u,v∈V(G),u≠v}≤n/2的d-重似星树和广义双星这两类树图的Hamiltonian色数的确切值。

Kirchhoff型分数阶Hamiltonian系统基态解的存在性和集中性

研究一类Kirchhoff型分数阶Hamiltonian系统基态解的存在性和渐近行为.通过构造合适的分数阶空间,在对称矩阵L(t)满足半正定的条件下,给出新的嵌入定理及几个重要的不等式,利用临界点理论,得到上述系统基态解的存在性和集中性结果.

一类Hamiltonian系统的Abelian积分的零点

该文得到了一类Hamiltonian系统的Abelian积分的零点的个数的上界.该Abelian积分有k+2个生成元,并且这些生成元满足两个不同的Picard-Fuchs方程.最后,用两个例子说明理论结果的应用.

基于Hamiltonian理论的受控电力系统暂态稳定分析方法

从电力系统暂态能量函数出发,应用哈密顿系统理论首次提出新的李亚普诺夫函数。用该函数分析了具有切机切负荷稳定控制的简单电力系统的暂态稳定性。对单机无穷大系统的测试仿真结果表明:按该稳定性条件的切机控制能有效改善故障后系统的功角稳定性。最后指出了该研究的应用前景。

二阶非自治离散Hamiltonian系统的多重周期解

研究了二阶非自治离散Hamiltonian系统周期解的存在性.在非线性项是线性增长时,将这类Hamiltonian系统的周期解转化为定义在一个适当空间上泛函的临界点,然后利用临界点理论建立此类系统周期解的存在性结果.

测试Hamiltonian矩阵结构问题的辛算法

对于有着广泛应用背景的Hamiltonian矩阵,研究了在Hamiltonian矩阵的辛约化过程中,构建用于各阶段的测试Hamiltonian矩阵结构问题的辛算法,其Hamilton结构得到充分保证,通过检验,文中方法简易可行,提供的算法具有较强的有效性和稳定性。

混合状态Hamiltonian元的半解析解和叠层板的计算

本文给出混合状态方程的一种强有力的半离散半解析解法,并给出了矩形域和叠层板的算例,讨论了可能的发展和应用。

势函数V(r)=Z^2r^(-4)-d_1d_2r^(-3)的离子的Hamiltonian本征方程的精确解

采用连分法,得到离子之间相互作用势为V(r)=Z2r-4-d1d2r-3的离子的Hamiltonian算符的精确能量本征值和能量本征函数.