Control design for discrete‐time bilinear systems using the scalarized Schur complement

In this paper, controller design for discrete‐time bilinear systems is investigated by using sum of squares programming methods and quadratic Lyapunov functions. The class of rational polynomial controllers is considered, and necessary conditions on the degree of controller polynomials for quadratic stability are derived. Next, a scalarized version of the Schur complement is proposed. For controller design, the Lyapunov difference inequality is converted to a sum of squares problem, and an optimization problem is proposed to design a controller, which maximizes the region of quadratic stability of the bilinear system. Input constraints can also be accounted for. Copyright © 2017 John Wiley & Sons, Ltd.     

基于分层递阶商空间链的图连通性研究

图连通性的判定对于路径规划中任意两点间路径相通性判断以及连通块的划分都具有重要意义。从节点的边连通关系着手分析图的结构层次,通过构建图的分层递阶商空间链,分析不同层次商空间链中各节点分布情况,得出新的图连通性判定方法。与以往各判定方法相比,该方法具有易实现、效率高的优点,不仅能有效地判定图是否连通,还能确定图的连通分支数以及哪些节点位于同一连通分支中。     

基于快速模板匹配的智能视觉传感器设计*

针对传统视觉传感器信号处理能力差、模拟信号输出易受干扰等问题,设计了基于ARM 6410处理器的智能化数字视觉传感器,应用于白车身在线视觉检测系统,完成数据采集、像素级二维定位和通讯控制工作。在Linux平台上,研究了一种快速稳定的像素级模板匹配算法,以去均值归一化灰度互相关法为相似性测度,多分辨率金字塔匹配法为搜索策略,使用“滚动相加补全像素法冶的二维求和新方法来优化计算过程,并进行了全局冗错设计,确保传感器工作稳定性。现场实验表明：采用该匹配算法和冗错机制使得视觉传感器定位功能速度快、精度高、鲁棒性好,能较好完成白车身视觉检测系统前端数据采集和处理任务。     

On partitioning a graph into two connected subgraphs

Suppose a graph G is given with two vertex-disjoint sets of vertices Z₁ and Z₂. Can we partition the remaining vertices of G such that we obtain two connected vertex-disjoint subgraphs of G that contain Z₁ and Z₂, respectively? This problem is known as the 2-Disjoint Connected Subgraphs problem. It is already NP-complete for the class of n-vertex graphs G=(V,E) in which Z₁ and Z₂ each contain a connected set that dominates all vertices in V?(Z₁∪Z₂). We present an O^∗(1.2051ⁿ) time algorithm that solves it for this graph class. As a consequence, we can also solve this problem in O^∗(1.2051ⁿ) time for the classes of n-vertex P₆-free graphs and split graphs. This is an improvement upon a recent O^∗(1.5790ⁿ) time algorithm for these two classes. Our approach translates the problem to a generalized version of hypergraph 2-coloring and combines inclusion/exclusion with measure and conquer.     

求解圆盘图中最小连通支配集的近似算法

针对无线传感器网络常用的拓扑模型单位圆盘图,提出了基于分布式贪心策略的近似算法DDT,在算法执行的每一轮中,根据一跳邻域范围内的权值和邻居的状态信息,选举出节点并和已确定的节点连接,逐步构造出网络图中的一个支配树。用概率方法研究了支配树中的节点度的性质,通过对极大独立集和最小连通支配集之间关系的分析,得到单位圆盘图中最小连通支配集问题一个新的近似比。计算结果表明,和相关的分布式算法相比,DDT产生的连通支配集在规模上更优。     

The Search of Equilibrium Strategies for Controlled Boundary Value Problem

The present paper is focused on the finite‐time differential game of m players with nonzero sum. The principal difference from regular cases consists in the fact that the states of players are subordinated to boundary value system of ordinary differential equations (rather than the initial value system). By the end of the game we understand the equilibrium situation and our purpose is to design a well‐founded suitable method for the equilibrium control search.     

Structural Synthesis of Modular Weakly Connected Neural Networks. I. Methodology of Structural Synthesis of Modular Neural Networks

Structural models of modular neural networks without loops are considered. The notion of a weakly connected network is introduced. A genetic principle of generation of weakly connected neural networks is proposed, and its reproductive power is proved on the basis of the theory of categories. Algorithmic realizations of structural synthesis are considered. Some examples are given.     

An algorithm of file encryption based on sum function sequences

An algorithm of file encryption based on sum function sequences is discussed in this paper. A file is encrypted by applying sum function sequences, bits with exclusive-or operation, and circular cryptographic key. Comparing with traditional algorithms and others, it is harder to decode, and the system cost is lower. New encryption algorithms can be made by transforming source codes with sum function sequences, and it can be used to encrypt different files.     

基于最小连通邻域图的ISOMAP算法

噪音的干扰和邻域大小的不合适会在ISOMAP算法的邻域图中引入“短路”边,使其不能正确表达数据的邻域结构,从而使该算法具有较差的鲁棒性和拓扑稳定性。为此,根据最小连通邻域图能有效避免“短路”边的特点,提出了一种能有效删除“短路”边因而更具鲁棒性和拓扑稳定性的ISOMAP算法——基于最小连通邻域图的ISOMAP（MCNG-ISOMAP）算法。该算法能在一定程度上避免邻域大小难以有效选取的问题,同时还能在不依赖于邻域大小的情况下发现数据真正的固有维数。     

Connected sum of digital closed surfaces

During the past 20 years the research of digital surfaces has proceeded to find their properties in the digital space Zⁿ, such as a topological number, a simple k-point, the 3D-Jordan theorem, a k-separating set, a boundary detecting algorithm and so on. Actually, unlike surfaces in a continuous space, the features of digital surfaces have different characteristics. The aim of this paper is to introduce the notion of a digital closed k-surface in Zⁿ, n ? 3, with the general k-adjacency relations as a generalization of Malgouyres’ and Morgenthaler’s k-surfaces in Z³, to establish some minimal simple closed k-surfaces in Z³ and to find their digital topological properties in relation with the k-fundamental group and k-contractibility. Moreover, a connected sum of two digital closed surfaces is introduced and its digital topological properties are investigated.