Related papers: Fast Consensus Topology Design via Minimizing Lapl…
This paper studies an open consensus network design problem: identifying the optimal simple directed graphs, given a fixed number of vertices and arcs, that maximize the second smallest real part of all Laplacian eigenvalues, referred to as…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…
We consider network structures that optimize the $\mathcal{H}_2$ norm of weighted, time scaled consensus networks, under a minimal representation of such consensus networks described by the edge Laplacian. We show that a greedy algorithm…
Let $N$ local decision makers in a sensor network communicate with their neighbors to reach a decision \emph{consensus}. Communication is local, among neighboring sensors only, through noiseless or noisy links. We study the design of the…
We study an optimal control problem aimed at achieving a desired tradeoff between the network coherence and communication requirements in the distributed controller. Our objective is to add a certain number of edges to an undirected…
Despite the vast literature on network dynamics, we still lack basic insights into dynamics on higher-order structures (e.g., edges, triangles, and more generally, $k$-dimensional "simplices") and how they are influenced through…
We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…
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…
Reaching consensus among states of a multi-agent system is a key requirement for many distributed control/optimization problems. Such a consensus is often achieved using the standard Laplacian matrix (for continuous system) or Perron matrix…
Algebraic connectivity is one way to quantify graph connectivity, which in turn gauges robustness as a network. In this paper, we consider the problem of maximising algebraic connectivity both local and globally over all simple, undirected,…
We propose an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected graphs with cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian.…
We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly…
In this paper, we design an optimal energy cost controller for linear systems asymptotic consensus given the topology of the graph. The controller depends only on relative information of the agents. Since finding the control gain for such…
Consensus over networked agents is typically studied using undirected or directed communication graphs. Undirected graphs enforce symmetry in information exchange, leading to convergence to the average of initial states, while directed…
The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
This paper provides a construction method of the nearest graph Laplacian to a matrix identified from measurement data of graph Laplacian dynamics that include biochemical systems, synchronization systems, and multi-agent systems. We…
We propose that clusters interconnected with network topologies having minimal mean path length will increase their overall performance for a variety of applications. We approach our heuristic by constructing clusters of up to 36 nodes…
We consider the problem on finding the edge weights that maximize the algebraic connectivity of a graph (smallest positive eigenvalue of the Laplacian), subject to the condition that the total effective resistance is kept constant. We…