Related papers: Generalizing Laplacian Controllability of Paths
The problem of leaders location plays an important role in the controllability of undirected graphs.The concept of minimal perfect critical vertex set is introduced by drawing support from the eigenvector of Laplace matrix. Using the notion…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
A metrized graph is a compact singular 1-manifold endowed with a metric. A given metrized graph can be modelled by a family of weighted combinatorial graphs. If one chooses a sequence of models from this family such that the vertices become…
We present a framework based on spectral graph theory that captures the interplay among network topology, system inertia, and generator and load damping in determining the overall grid behavior and performance. Specifically, we show that…
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…
A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network…
This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…
In this article, various aspects of Laplacian spectra of power graphs of finite cyclic, dicyclic and finite $p$-groups are studied. Algebraic connectivity of power graphs of the above groups are considered and determined completely for that…
A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act…
For arrays of identical linear systems coupled through relative actuation four problems are studied: controllability, positive controllability, pairwise controllability, and positive pairwise controllability. To this end, related to the…
We consider problems in which a simple path of fixed length, in an undirected graph, is to be shifted from a start position to a goal position by moves that add an edge to either end of the path and remove an edge from the other end. We…
To achieve control objectives for extremely large-scale complex networks using standard methods is essentially intractable. In this work a theory of the approximate control of complex network systems is proposed and developed by the use of…
This work examines the problem of topology inference over discrete-time nonlinear stochastic networked dynamical systems. The goal is to recover the underlying digraph linking the network agents, from observations of their state-evolution.…
This paper studies the problem of selecting input nodes (leaders) to make networks strong structurally controllable despite misbehaving nodes and edges. We utilize a graph-based characterization of network strong structural controllability…
Let $G$ be a simple, undirected graph on the vertex set $V=\{1,2,\ldots ,n\}$ and let $A$ be the adjacency matrix of $G.$ A non-empty subset $ \{i_{1},i_{2},\ldots ,i_{k}\}$ of $V$ is called a driver set for $G$ if the system…
In this paper, we investigate optimal control of network-coupled subsystems where the dynamics and the cost couplings depend on an underlying undirected weighted graph. The graph coupling matrix in the dynamics may be the adjacency matrix,…
Network controllability is a powerful tool to study causal relationships in complex systems and identify the driver nodes for steering the network dynamics into desired states. However, due to ill-posed conditions, results become unreliable…
The recent paper by W.-X. Wang, Y.-C. Lai, J. Ren, B. Li & C. Grebogi [arXiv:1107.2177v1] proposed a method for the control of complex networks with nonlinear dynamics based on linearizing the system around a finite number of local desired…
Observability of an array of identical LTI systems with incommensurable output matrices is studied, where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems. It is…
Understanding conformational change is crucial for programming and controlling the function of many mechanical systems such as allosteric enzymes and tunable metamaterials. Of particular interest is the relationship between the network…