Related papers: Generalizing Laplacian Controllability of Paths
This paper characterizes the graphical properties of an optimal topology with minimal Laplacian energy under the constraint of fixed numbers of vertices and edges, and devises an algorithm to construct such connected optimal graphs. These…
This paper considers the controllability problem for multi-agent systems. In particular, the structural controllability of multi-agent systems under switching topologies is investigated. The structural controllability of multi-agent systems…
The number of walks from one vertex to another in a finite graph can be counted by the adjacency matrix. In this paper, we prove two theorems that connect the graph Laplacian with two types of walks in a graph. By defining two types of…
Many real-world systems are composed of many individual components that interact with one another in a complex pattern to produce diverse behaviors. Understanding how to intervene in these systems to guide behaviors is critically important…
We study the asymptotic behavior of the number of paths of length $N$ on several classes of infinite graphs with a single special vertex. This vertex can work as an entropic trap for the path, i.e. under certain conditions the dominant part…
A network of coupled dynamical systems is represented by a graph whose vertices represent individual cells and whose edges represent couplings between cells. Motivated by the impact of synchronization results of the Kuramoto networks, we…
We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that when a quantum network is described by such a graph, the network is efficiently controllable, in…
Multiagent systems consist of agents that locally exchange information through a physical network subject to a graph topology. Current control methods for networked multiagent systems assume the knowledge of graph topologies in order to…
In this paper, we study the well-posedness and approximate controllability of a class of network systems having delays and controls at the boundary conditions. The particularity of this work is that the network system is defined on infinite…
In a coupled network cells can interact in several ways. There is a vast literature from the last twenty years that investigates this interacting dynamics under a graph theory formalism, namely as a graph endowed with an input-equivalence…
Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
A consistent path system in a graph $G$ is an intersection-closed collection of paths, with exactly one path between any two vertices in $G$. We call $G$ metrizable if every consistent path system in it is the system of geodesic paths…
A common goal in the control of a large network is to minimize the number of driver nodes or control inputs. Yet, the physical determination of control signals and the properties of the resulting control trajectories remain widely…
It is known that if a nonlinear control affine system without drift is bracket generating, then its associated sub-Laplacian is invertible under some conditions on the domain. In this note, we investigate the converse. We show how…
Control theory concerns with the question if and how it is possible to drive the behavior of a complex dynamical system. A system is said to be controllable if we can drive it from any initial state to any desired final state in finite…
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…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
The purpose of this short paper is to provide a theoretical analysis for the consensus problem under nonlinear protocols. A main contribution of this work is to generalize the previous consensus problems under nonlinear protocols for…
This paper studies the controllability of networked multi-input-multi-output (MIMO) systems, in which the network topology is weighted and directed, and the nodes are heterogeneous higher-dimensional linear time-invariant (LTI) dynamical…