A limit set stabilization by means of the Port Hamiltonian system approach

A solution to the stabilization problem of a compact set by means of the Interconnection and Damping Assignment Passivity‐Based Control methodology, for an affine nonlinear system, was introduced. To this end, we expressed the closed‐loop system as a Port Hamiltonian system, having the property of almost all their trajectories asymptotically converge to a convenient limit set, except for a set of measure zero. It was carried out by solving a partial differential equation (PDE) or single matching condition, which allows the desired energy level or limit set E to be shaped explicitly. The control strategy was tested using the magnetic beam balance system and the pendulum actuated by a direct current motor (DC‐motor), having obtained satisfactory results. Copyright © 2014 John Wiley & Sons, Ltd.     

Hamiltonian-connected graphs

For a simple graph G, let . In this paper, we prove that if NCD(G)≥|V(G)|, then either G is Hamiltonian-connected, or G belongs to a well-characterized class of graphs. The former results by Dirac, Ore and Faudree et al. are extended.     

Parallel Lagrange interpolation on <Emphasis Type="Italic">k</Emphasis>-ary <Emphasis Type="Italic">n</Emphasis>-cubes with maximum channel utilization

This paper proposes an efficient parallel algorithm for computing Lagrange interpolation on k-ary n-cube networks. This is done using the fact that a k-ary n-cube can be decomposed into n link-disjoint Hamiltonian cycles. Using these n link-disjoint cycles, we interpolate Lagrange polynomial using full bandwidth of the employed network. Communication in the main phase of the algorithm is based on an all-to-all broadcast algorithm on the n link-disjoint Hamiltonian cycles exploiting all network channels, and thus, resulting in high-efficiency in using network resources. A performance evaluation of the proposed algorithm reveals an optimum speedup for a typical range of system parameters used in current state-of-the-art implementations.

Nonlinear gliding stability and control for vehicles with hydrodynamic forcing

This paper presents Lyapunov functions for proving the stability of steady gliding motions for vehicles with hydrodynamic or aerodynamic forces and moments. Because of lifting forces and moments, system energy cannot be used as a Lyapunov function candidate. A Lyapunov function is constructed using a conservation law discovered by Lanchester in his classical work on phugoid-mode dynamics of an airplane. The phugoid-mode dynamics, which are cast here as Hamiltonian dynamics, correspond to the slow dynamics in a multi-time-scale model of a hydro/aerodynamically-forced vehicle in the longitudinal plane. Singular perturbation theory is used in the proof of stability of gliding motions. As an intermediate step, the simplifying assumptions of Lanchester are made rigorous. It is further shown how to design stabilizing control laws for gliding motions using the derived function as a control Lyapunov function and how to compute the corresponding regions of attraction.     

A new approach to the cheap LQ regulator exploiting the geometric properties of the Hamiltonian system

The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the minimal conditioned invariant of the original system, and the optimal feedback gain is computed as the friend matrix of the resolving subspace. This study yields a new computational framework for the cheap LQ regulator, relying only on the very basic and simple tools of the geometric approach, namely the algorithms for controlled and conditioned invariant subspaces and invariant zeros.     

Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.     

基于域自适应的二屏电能表显示屏质量检测方法

针对人工显示屏检测和机器检测存在精度较低及效率低下的问题,提出了一种基于域自适应的二屏电能表显示屏检测方法。为有效提高检测效率,对奇、偶二屏显示字段的虚显、断显、漏显和多显进行检测,快速实现对电能表显示屏字段、电能表显示屏驱动回路元器件及其生产过程的虚焊、漏焊、连锡等质量问题的检测。利用局部域自适应进行源域和目标域的对齐,提取显示屏中的细粒度信息以获取更高检测精度。实验结果表明,所提方法有效提高了电能表显示屏字段及其驱动回路质量的检测效率和检测精度。     

广义Burgers方程的对称分类及其约化

利用李群方法对广义Burgers方程ut+f(x,t)(ux-uxx)=0的对称分类及其约化作具体讨论,其中f是关于自变量x,u的光滑函数,得到了f(x,t)的八种分类对称及相应的约化方程.该结果对于广义Burgers方程精确解的研究有重要意义.     

Chetaev型非完整系统Nielsen方程Lie对称性导致的一种守恒量

研究Chetaev型非完整系统Nielsen方程Lie对称性导致的一种守恒量,给出无限小群变换下Chetaev型非完整系统Nielsen方程Lie对称性的确定方程,得到Chetaev型非完整系统Nielsen方程Lie对称性直接导致的一种守恒量及其存在条件,并举例说明结果应用.     

The triangular pyramid: Routing and topological properties

In this paper, a new topology for multicomputer interconnection networks, based on triangular mesh, is proposed. The new network, referred to as the triangular pyramid (or tripy for short), has L levels of triangular mesh. We study some basic important properties of the proposed network as well as introduce a routing algorithm for the tripy network based on the routing of triangular meshes. We prove that this form of pyramidal network is Hamiltonian, Hamiltonian-connected, and pancyclic. We also prove that the proposed network is 6-colorable and conduct a brief comparison of the tripy and its traditional pyramid counterpart. Our results show that the proposed network has higher scalability, connectivity, and total network bandwidth while preserving the important properties of the traditional pyramid network.