Related papers: The Graph Geometric Control Condition
It is well known that both the heat equation with Dirichlet or Neumann boundary conditions are null controlable as soon as the control acts in a non trivial domain (i.e. a set of positive measure, see [10, 11, 12, 1, 6]. In this article, we…
This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift…
The $\chi$-stability index ${\rm es}_{\chi}(G)$ of a graph $G$ is the minimum number of its edges whose removal results in a graph with the chromatic number smaller than that of $G$. In this paper three open problems from [European J.\…
A well-studied coloring problem is to assign colors to the edges of a graph $G$ so that, for every pair of vertices, all edges of at least one shortest path between them receive different colors. The minimum number of colors necessary in…
In this article we study a controllability problem for a parabolic and a hyperbolic partial differential equations in which the control is the shape of the domain where the equation holds. The quantity to be controlled is the trace of the…
We prove boundary controllability results for wave equations (with lower-order terms) on Lorentzian manifolds with time-dependent geometry satisfying suitable curvature bounds. The main ingredient is a novel global Carleman estimate on…
Primary Frequency Control (PFC) is a fast acting mechanism used to ensure high-quality power for the grid that is becoming an increasingly attractive option for load participation. Due to speed requirement and other considerations, it is…
In this article, we consider the operations of insertion and deletion working in a graph-controlled manner. We show that like in the case of context-free productions, the computational power is strictly increased when using a control graph:…
Let $D$ be an oriented graph with skew adjacency matrix $S(D)$. Two oriented graphs $D$ and $C$ are said to share the same generalized skew spectrum if $S(D)$ and $S(C)$ have the same eigenvalues, and $J-S(D)$ and $J-S(C)$ also have the…
Graph-controlled insertion-deletion (GCID) systems are regulated extensions of insertion-deletion systems. Such a system has several components and each component contains some insertion-deletion rules. The components are the vertices of a…
We introduce the controllable graph generation problem, formulated as controlling graph attributes during the generative process to produce desired graphs with understandable structures. Using a transparent and straightforward Markov model…
The chromatic edge-stability number ${\rm es}_{\chi}(G)$ of a graph $G$ is the minimum number of edges whose removal results in a spanning subgraph $G'$ with $\chi(G')=\chi(G)-1$. Edge-stability critical graphs are introduced as the graphs…
The linear-quadratic controller is one of the fundamental problems in control theory. The optimal solution is a linear controller that requires access to the state of the entire system at any given time. When considering a network system,…
A proper coloring of a graph is \emph{conflict-free} if, for every non-isolated vertex, some color is used exactly once on its neighborhood. Caro, Petru\v{s}evski, and \v{S}krekovski proved that every graph $G$ has a proper conflict-free…
The dominating graph of a graph G is a graph whose vertices correspond to the dominating sets of G and two vertices are adjacent whenever their corresponding dominating sets differ in exactly one vertex. Studying properties of dominating…
We prove controllability of the Schr\"odinger equation in $\mathbb{R}^d$ in any time $T > 0$ with internal control supported on nonempty, periodic, open sets. This demonstrates in particular that controllability of the Schr\"odinger…
The purpose of this paper is to close the remaining gaps in the understanding of the role that the constrained generalized continuous algebraic Riccati equation plays in singular linear-quadratic (LQ) optimal control. Indeed, in spite of…
An edge colouring $c$ of a graph $G$ is called conflic-free if every non-isolated edge of $G$ has a uniquely coloured neighbour in its open edge neighbourhood. The least number of colours admitting such a colouring is denoted by $\chi'_{\rm…
In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched…
Deep learning-based graph generation approaches have remarkable capacities for graph data modeling, allowing them to solve a wide range of real-world problems. Making these methods able to consider different conditions during the generation…