Related papers: Coordination in multiagent systems and Laplacian s…
This paper is concerned with the controllability problem of a connected threshold graph following the Laplacian dynamics. An algorithm is proposed to generate a spanning set of orthogonal Laplacian eigenvectors of the graph from a…
It is well known that if a network topology is a path or line and the states of vertices or nodes evolve according to the consensus policy, then the network is Laplacian controllable by an input connected to its terminal vertex. In this…
In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge weights within certain clusters grow to infinity. As…
We provide a distributed coordinated approach to the stability analysis and control design of large-scale nonlinear dynamical systems by using a vector Lyapunov functions approach. In this formulation the large-scale system is decomposed…
This paper mainly investigates consensus problem with pull-based event-triggered feedback control. For each agent, the diffusion coupling feedbacks are based on the states of its in-neighbors at its latest triggering time and the next…
The power interactions of any component in electric energy systems with the rest of the system happen naturally, as governed by the energy conservation principles. There may, however, occur instances when the rate at which power gets…
The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial…
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…
In recent years, numerous studies have focused on the mathematical modeling of social dynamics, with self-organization, i.e., the autonomous pattern formation, as the main driving concept. Usually, first or second order models are employed…
This paper studies coordination problem for time-varying networks suffering from antagonistic information, quantified by scaling parameters. By such a manner, interacting property of the participating individuals and antagonistic…
This paper considers optimal traffic signal control in smart cities, which has been taken as a complex networked system control problem. Given the interacting dynamics among traffic lights and road networks, attaining controller adaptivity…
The discrete Green's functions are the pseudoinverse (or the inverse) of the Laplacian (or its variations) of a graph. In this paper, we will give combinatorial interpretations of Green's functions in terms of enumerating trees and forests…
The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf…
We give the spectral representation for a class of selfadjoint discrete graph Laplacians $\Delta$, with $\Delta$ depending on a chosen graph $G$ and a conductance function $c$ defined on the edges of $G$. We show that the spectral…
In this paper, the target controllability of multiagent systems under directed weighted topology is studied. A graph partition is constructed, in which part of the nodes are divided into different cells, which are selected as leaders. The…
This paper investigates a distributed formation tracking control law for large-scale networks of mechanical systems. In particular, the formation network is represented by a directed communication graph with leaders and followers, where…
This paper studies cooperative control of noncooperative double-integrator multi-agent systems (MASs) with input delay on connected directed graphs in the context of a differential graphical game (DGG). In the distributed DGG, each agent…
By leveraging information technologies, organizations now have the ability to design their communication networks and crowdsourcing platforms to pursue various performance goals, but existing research on network design does not account for…
In this paper we obtain several tight bounds on different types of alliance numbers of a graph: (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the…
We consider the distributed optimization problem for a multi-agent system. Here, multiple agents cooperatively optimize an objective by sharing information through a communication network and performing computations. In this tutorial, we…