Leader-follower consensus control of Lipschitz nonlinear systems by output feedback

This paper deals with the leader-follower consensus problem of Lipschitz nonlinear systems under fixed directed communication networks. Both state and output feedback control are proposed based on state and output measurements of neighbouring agents, respectively. Laplacian matrix features are explored for the stability analysis, and the sufficient conditions are derived to solve the consensus problem. Finally, simulation results are included to demonstrate the effectiveness of the output-based consensus controller.     

A consensus model for hesitant fuzzy preference relations and its application in water allocation management

This paper investigates a consensus model for hesitant fuzzy preference relations (HFPRs). First, we present a revised definition of HFPRs, in which the values are not ordered for the hesitant fuzzy element. Second, we propose an additive consistency based estimation measure to normalize the HFPRs, based on which, a consensus model is developed. Here, two feedback mechanisms are proposed, namely, interactive mechanism and automatic mechanism, to obtain a solution with desired consistency and consensus levels. In the interactive mechanism, the experts are suggested to give their new preference values in a specific range. If the experts are unwilling to offer their updated preferences, the automatic mechanism could be adopted to carry out the consensus process. Induced ordered weighted averaging (IOWA) operator is used to aggregate the individual HFPRs into a collective one. A score HFPR is proposed for collective HFPR, and then the quantifier-guided dominance degrees of alternatives by using an OWA operator are obtained to rank the alternatives. Finally, both a case of study for water allocation management in Jiangxi Province of China and a comparison with the existing approaches are carried out to show the advantages of the proposed method.     

Set-valued Lyapunov functions for difference inclusions

The paper relates set-valued Lyapunov functions to pointwise asymptotic stability in systems described by a difference inclusion. Pointwise asymptotic stability of a set is a property which requires that each point of the set be Lyapunov stable and that every solution to the inclusion, from a neighborhood of the set, be convergent and have the limit in the set. Weak set-valued Lyapunov functions are shown, via an argument resembling an invariance principle, to imply this property. Strict set-valued Lyapunov functions are shown, in the spirit of converse Lyapunov results, to always exist for closed sets that are pointwise asymptotically stable.     

An internal model principle is necessary and sufficient for linear output synchronization

Output synchronization of a network of heterogeneous linear state–space models under time-varying and directed interconnection structures is investigated. It is shown that, assuming stabilizability and detectability of the individual systems and imposing very mild connectedness assumptions on the interconnection structure, an internal model requirement is necessary and sufficient for synchronizability of the network to polynomially bounded trajectories. The resulting dynamic feedback couplings can be interpreted as a generalization of existing methods for identical linear systems.     

Finite-time weighted average consensus with respect to a monotonic function and its application

The consensus state is an important and fundamental quantity for consensus problems of multi-agent systems, which indicates where all the dynamical agents reach. In this paper, weighted average consensus with respect to a monotonic function, which means that the trajectories of the monotonic function along the state of each agent reach the weighted average of their initial values, is studied for a group of kinematic agents with time-varying topology. By constructing a continuous nonlinear distributed protocol, such a consensus problem can be solved in finite time even though the time-varying topology involves unconnected graphs. Then the distributed protocol is employed to compute the maximum-likelihood estimation of unknown parameters over sensor networks. Compared with the existing results, the estimate scheme proposed here may reduce the costs of data communication, storage memory, book-keeping and computational overheads.     

Consensus models: Computational complexity aspects in modern approaches to the list coloring problem

In the paper we study new approaches to the problem of list coloring of graphs. In the problem we are given a simple graph G=(V,E) and, for every v∈V, a nonempty set of integers S(v); we ask if there is a coloring c of G such that c(v)∈S(v) for every v∈V. Modern approaches, connected with applications, change the question—we now ask if S can be changed, using only some elementary transformations, to ensure that there is such a coloring and, if the answer is yes, what is the minimal number of changes. In the paper for studying the adding, the trading and the exchange models of list coloring, we use the following transformations:

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adding of colors (the adding model): select two vertices u, v and a color c∈S(u); add c to S(v), i.e. set S(v):=S(v)∪{c};

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trading of colors (the trading model): select two vertices u, v and a color c∈S(u); move c from S(u) to S(v), i.e. set S(u):=S(u)?{c} and S(v):=S(v)∪{c};

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exchange of colors (the exchange model): select two vertices u, v and two colors c∈S(u), d∈S(v); exchange c with d, i.e. set S(u):=(S(u)?{c})∪{d} and S(v):=(S(v)?{d})∪{c}.

Our study focuses on computational complexity of the above models and their edge versions. We consider these problems on complete graphs, graphs with bounded cyclicity and partial k-trees, receiving in all cases polynomial algorithms or proofs of NP-hardness.     

Comparing and aggregating partially resolved trees

Partially-resolved-that is, non-binary-trees arise frequently in the analysis of species evolution. Non-binary nodes, also called multifurcations, must be treated carefully, since they can be interpreted as reflecting either lack of information or actual evolutionary history. While several distance measures exist for comparing trees, none of them deal explicitly with this dichotomy. Here we introduce two kinds of distance measures between rooted and unrooted partially-resolved phylogenetic trees over the same set of species; the measures address multifurcations directly. For rooted trees, the measures are based on the topologies the input trees induce on triplets; that is, on three-element subsets of the set of species. For unrooted trees, the measures are based on quartets (four-element subsets). The first class of measures are parametric distances, where there is a parameter that weighs the difference between an unresolved triplet/quartet topology and a resolved one. The second class of measures are based on the Hausdorff distance, where each tree is viewed as a set of all possible ways in which the tree can be refined to eliminate unresolved nodes. We give efficient algorithms for computing parametric distances and give conditions under which Hausdorff distances can be calculated approximately in polynomial time. Additionally, we (i) derive the expected value of the parametric distance between two random trees, (ii) characterize the conditions under which parametric distances are near-metrics or metrics, (iii) study the computational and algorithmic properties of consensus tree methods based on the measures, and (iv) analyze the interrelationships among Hausdorff and parametric distances.     

一种调和序列生成及其在故障定位中的应用

为了提高软件的可靠性,在软件运行发生故障时,快速、准确地定位故障点成为非常有意义的研究课题。与以往方法不同,在将故障运行序列和最部近运行序列进行差异对比前,为了避免选取第一条最近成功路径时引起的“盲区”使得后期搜索空间加大,引入了生物学基因序列比对原理,对最部近运行序列不是通过编辑距离比较进行选取,而是通过一条调和序列进行处理。实验表明,方法的故障定位效果较好。     

Failure detection and consensus in the crash-recovery model

Summary. We study the problems of failure detection and consensus in asynchronous systems in which processes may crash and recover, and links may lose messages. We first propose new failure detectors that are particularly suitable to the crash-recovery model. We next determine under what conditions stable storage is necessary to solve consensus in this model. Using the new failure detectors, we give two consensus algorithms that match these conditions: one requires stable storage and the other does not. Both algorithms tolerate link failures and are particularly efficient in the runs that are most likely in practice – those with no failures or failure detector mistakes. In such runs, consensus is achieved within time and with 4 n messages, where is the maximum message delay and n is the number of processes in the system. Received: May 1998 / Accepted: November 1999