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This study proposes a secondary voltage and frequency control scheme based on the distributed cooperative control of multi-agent systems. The proposed secondary control is implemented through a communication network with one-way communication links. The required communication network is modelled by a directed graph (digraph). The proposed secondary control is fully distributed such that each distributed generator only requires its own information and the information of its neighbours on the communication digraph. Thus, the requirements for a central controller and complex communication network are obviated, and the system reliability is improved. The simulation results verify the effectiveness of the proposed secondary control for a microgrid test system.

A directed graph, consisting of vertices linked by directed edges or arcs, is a crucial structure utilized in analyzing various scenarios such as electrical circuits, optimal routes, and social connections. Graph theory introduces graph products, a binary operation applied to graphs. Similarly, directed graphs can undergo product operations analogous to those of standard graphs. Several authors have explored specific product operations in directed graphs, including the Cartesian, lexicographic, and strong products. In this study, we broaden the scope by extending definitions of product operations from standard graphs, such as categorical, modular, disjunctive, homomorphic, rooted, and corona products, to directed graphs. Furthermore, we delve into their properties.

This study introduces a robust strategy for regulating output voltage in the presence of false data injection (FDI) attacks. Employing a hierarchical approach, we disentangle the distributed secondary control problem into two distinct facets: an observer-based resilient tracking control problem and a decentralized control problem tailored for real systems. Notably, our strategy eliminates the reliance on global information and effectively mitigates the impact of FDI attacks on directed communication networks. Ultimately, simulation results corroborate the efficacy of our approach, demonstrating successful voltage regulation within the system and proficient management of FDI attacks.

In this paper we introduce the linear clique-width, linear NLC-width, neighbourhood-width, and linear rank-width for directed graphs. We compare these parameters with each other as well as with the previously defined parameters directed path-width and directed cut-width. It turns out that the parameters directed linear clique-width, directed linear NLC-width, directed neighbourhood-width, and directed linear rank-width are equivalent in that sense, that all of these parameters can be upper bounded by each of the others. For the restriction to digraphs of bounded vertex degree directed path-width and directed cut-width are equivalent. Further for the restriction to semicomplete digraphs of bounded vertex degree all six mentioned width parameters are equivalent. We also show close relations of the measures to their undirected versions of the underlying undirected graphs, which allow us to show the hardness of computing the considered linear width parameters for directed graphs. Further we give first characterizations for directed graphs defined by parameters of small width.

We prove a conjecture on the second minimal odd periodic orbits with respect to Sharkovski ordering for the continuous endomorphisms on the real line. A (2k+1)-periodic orbit β1<β2<⋯<β2k+1, (k≥3) is called second minimal for the map f, if 2k−1 is a minimal period of f|[β1,β2k+1] in the Sharkovski ordering. Full classification of second minimal orbits is presented in terms of cyclic permutations and directed graphs of transitions. It is proved that second minimal odd orbits either have a Stefan-type structure like minimal odd orbits or one of the 4k−3 types, each characterized with unique cyclic permutations and directed graphs of transitions with an accuracy up to the inverses. The new concept of second minimal orbits and its classification have an important application towards an understanding of the universal structure of the distribution of the periodic windows in the bifurcation diagram generated by the chaotic dynamics of nonlinear maps on the interval.

This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA

Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or high-dimensional consistency. In contrast to the plain faithfulness assumption, the set of distributions that is not strong-faithful has nonzero Lebesgue measure and in fact, can be surprisingly large as we show in this paper. We study the strong-faithfulness condition from a geometric and combinatorial point of view and give upper and lower bounds on the Lebesgue measure of strong-faithful distributions for various classes of directed acyclic graphs. Our results imply fundamental limitations for the PC-algorithm and potentially also for other algorithms based on partial correlation testing in the Gaussian case.

High-efficiency video coding (HEVC) is the next generation standard of video coding. The deblocking filter (DF) constitutes a significant part of the HEVC decoder complexity. A three-step parallel framework (TPF) is proposed for the H.264/AVC DF, which is also suitable for HEVC except the third step. The third step of the TPF is replaced with a directed acyclic graph-based order. Experiments show that the proposed method dramatically accelerates more than the state-of-the-art parallel method.

This study presents a consensus region approach to designing distributed consensus protocols for multi-agent systems with general continuous-time linear node dynamics. The consensus region approach has a favourable decoupling feature, which decouples the design of the feedback gain matrices of the consensus protocols from the communication graph. Multi-step algorithms are presented to construct the fixed-gain consensus protocols, which requires the smallest non-zero eigenvalue of the Laplacian matrix. To remove this limitation, distributed adaptive protocols with time-varying coupling weights are designed for the cases with undirected and directed graphs, which can be implemented in a fully distributed fashion. The robustness issue of the adaptive protocols in the presence of external disturbances is also discussed. For the case where there exists a leader of bounded unknown control input, distributed discontinuous and continuous controllers are designed to solve the distributed tracking problem.

Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of conditional independences that is imposed on the variables' joint distribution. Focusing on Gaussian models, we review classical graphical models. For these models the defining conditional independences are equivalent to vanishing of certain (partial) correlation coefficients associated with individual edges that are absent from the graph. Hence, Gaussian graphical model selection can be performed by multiple testing of hypotheses about vanishing (partial) correlation coefficients. We show and exemplify how this approach allows one to perform model selection while controlling error rates for incorrect edge inclusion.