Controllability and observability of multi-agent systems with heterogeneous and switching topologies

ABSTRACT

This paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.     

A Lattice Approach to Image Segmentation

After a formal definition of segmentation as the largest partition of the space according to a criterion σ and a function f, the notion of a morphological connection is reminded. It is used as an input to a central theorem of the paper (Theorem 8), that identifies segmentation with the connections that are based on connective criteria. Just as connections, the segmentations can then be regrouped by suprema and infima. The generality of the theorem makes it valid for functions from any space to any other one. Two propositions make precise the AND and OR combinations of connective criteria. The soundness of the approach is demonstrated by listing a series of segmentation techniques. One considers first the cases when the segmentation under study does not involve initial seeds. Various modes of regularity are discussed, which all derive from Lipschitz functions. A second category of examples involves the presence of seeds around which the partition of the space is organized. An overall proposition shows that these examples are a matter for the central theorem. Watershed and jump connection based segmentations illustrate this type of situation. The third and last category of examples deals with cases when the segmentation occurs in an indirect space, such as an histogram, and is then projected back on the actual space under study. The relationships between filtering and segmentation are then investigated. A theoretical chapter introduces and studies the two notions of a pulse opening and of a connected operator. The conditions under which a family of pulse openings can yield a connected filter are clarified. The ability of segmentations to generate pyramids, or hierarchies, is analyzed. A distinction is made between weak hierarchies where the partitions increase when going up in the pyramid, and the strong hierarchies where the various levels are structured as semi-groups, and particularly as granulometric semi-groups. The last section is based on one example, and goes back over the controversy about “lattice” versus “functional” optimization. The problem is now tackled via a case of colour segmentation, where the saturation serves as a cursor between luminance and hue. The emphasis is put on the difficulty of grouping the various necessary optimizations into a single one.     

Efficient Parallel Algorithms for Some Graph Theory Problems

In this paper,a sequential algorithm computing the aww vertex pair distance matrix D and the path matrix Pis given.On a PRAM EREW model with p,1≤p≤n^2,processors,a parallel version of the sequential algorithm is shown.This method can also be used to get a parallel algorithm to compute transitive closure array A^* of an undirected graph.The time complexity of the parallel algorithm is O(n^3/p).If D,P and A^* are known,it is shown that the problems to find all connected components,to compute the diameter of an undirected graph,to determine the center of a directed graph and to search for a directed cycle with the minimum(maximum)length in a directed graph can all be solved in O(n^2/p logp)time.     

A new distributed approximation algorithm for constructing minimum connected dominating set in wireless ad hoc networks

In recent years, constructing a virtual backbone by nodes in a connected dominating set (CDS) has been proposed to improve the performance of ad hoc wireless networks. In general, a dominating set satisfies that every vertex in the graph is either in the set or adjacent to a vertex in the set. A CDS is a dominating set that also induces a connected sub‐graph. However, finding the minimum connected dominating set (MCDS) is a well‐known NP‐hard problem in graph theory. Approximation algorithms for MCDS have been proposed in the literature. Most of these algorithms suffer from a poor approximation ratio, and from high time complexity and message complexity. In this paper, we present a new distributed approximation algorithm that constructs a MCDS for wireless ad hoc networks based on a maximal independent set (MIS). Our algorithm, which is fully localized, has a constant approximation ratio, and O(n) time and O(n) message complexity. In this algorithm, each node only requires the knowledge of its one‐hop neighbours and there is only one shortest path connecting two dominators that are at most three hops away. We not only give theoretical performance analysis for our algorithm, but also conduct extensive simulation to compare our algorithm with other algorithms in the literature. Simulation results and theoretical analysis show that our algorithm has better efficiency and performance than others. Copyright © 2005 John Wiley & Sons, Ltd.     

虚拟专用网的体系结构及实现

提出VPN接入设备的体系结构 ,包括系统的应用模型、层次划分和内部详细结构 ,阐述实现VPN的关键技术。     

An ideal topology type convergent theorem on scale effect algebras

The famous Antosik-Mikusinski convergent theorem on the Abel topological groups has very extensive applications in measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on a class of effect algebras equipped with the ideal topology. This paper shows also that the ideal topology of effect algebras is a useful topology in studying the quantum logic the- ory.     

The Role of Network Topologies in the Optical Core of IP-over-WDM Networks with Static Wavelength Routing

In this paper, we present a performance analysis of network topologies for the optical core of IP-over-WDM networks with static wavelength routing. The performance analysis is focused on regular degree four topologies, and, for comparison purposes, degree three topologies are also considered. It is shown that the increase of the nodal degree from three (degree three topology with smallest diameter) to four (degree four topology with smallest diameter) improves the network performance if a larger number of wavelengths per link is available. However, the influence of wavelength interchange on the nodal degree gain is small. The performance of regular degree four topologies with smallest diameter is also compared with the performance of mesh–torus topologies (which are also degree four topologies), and it is shown that the blocking probability of degree four topologies with smallest diameter is about two orders of magnitude lower than the blocking probability of mesh–torus topologies. It is also presented a performance comparison of WDM-based networks with nodal degrees ranging from two to five and it is shown that the increase of the nodal degree from two to three leads to high nodal degree gains, while de increase of the nodal degree from four to five leads to low nodal degree gains. These results show that degree three and degree four topologies are very attractive for use in the optical core of IP-over-WDM networks.     

无源微波遥感用于地震预报的实验研究

对无源微波遥感用于地震预报在理论研究的基础上对不同岩性不同结构的岩石试件进行了加载实验，测量了岩石试件的微波辐射随载荷的变化．实验得出：岩石试件的微波辐射能量随岩石应力状态变化而显著变化；而且，不同的波段变化的幅度不同；同一波段不同极化方式的波随应力变化的变化量也不同；微波辐射能量的变化能够被卫星微波遥感探测器探测到．实验还发现，岩石试件临破裂前出现明显的微波辐射异常．     

Means of enhancing and promoting the use of solar energy

The development of renewable technologies in the last decade has been exceptional. In photovoltaic (PV) for example, efforts were not only limited to merely improving their efficiency but also to the reduction of the cost of cells and modules via volume production for commercial markets. There are many national schemes promoting the use of PV technology and regional targets for a share of renewable energy production. This paper attempts to relay to the reader a journey, based on experience, approaches for enhancing the prospect of utilising solar energy within the society we live in. The issue of expansion or enhancing the utilisation of solar energy can be undertaken by individuals, groups, institutions and governments. The aim of this paper is to provide some examples, which could serve as a framework in which action could be taken to promote solar technology.     

A novel method of suppressing the inrush current of transformers by using a series‐connected voltage‐source PWM converter

This paper proposes a novel method of suppressing the inrush current of transformers. A small‐rated voltage‐source PWM converter is connected in series to the transformers through a matching transformer. As the connected PWM converter serves as a resistor for the source current, no inrush phenomena occurs. The required rating of the PWM converter, which serves as the damping resistor for the inrush phenomena, is 1/400 that of the main transformers in single‐phase circuits. In three‐phase circuits, it is 1/900. The basic principle of the proposed method is discussed. Digital computer simulation is implemented to confirm the validity and excellent practicability of the proposed method using the PSCAD/EMTDC. A prototype experimental model is constructed and tested. The experimental results demonstrate that the proposed method can perfectly suppress the inrush phenomena. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 157(4): 56–65, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20174