Related papers: Structural Controllability on Graphs for Drifted B…
In this paper, we present conditions for the existence and uniqueness of chain control sets of discrete-time linear systems on the affine two-dimensional Lie group. More specifically, we prove that these chain control sets are given by the…
The lack of studying the complex organization of directed network usually limits to the understanding of underlying relationship between network structures and functions. Structural controllability and structural predictability, two…
In this paper, we examine the controllability of Laplacian dynamic networks on cographs. Cographs appear in modeling a wide range of networks and include as special instances, the threshold graphs. In this work, we present necessary and…
Various controllability conditions have been obtained by researchers for heterogeneous networked systems with linear dynamics. However, the literature for nonlinear, heterogeneous networked systems is comparatively less. In this paper we…
We consider nonlinear scalar-input differential control systems in the vicinity of an equilibrium. When the linearized system at the equilibrium is controllable, the nonlinear system is smoothly small-time locally controllable, i.e.,…
We consider the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. First a number of foundational results on…
In this paper we stated a condition for the controllability of discrete-time linear systems for the case when the Lie group has finite semisimple center and provided a example in the Lie group $SL_2(\mathbb{R})$.
This paper examines stability properties of distance-based formation control when the underlying topology consists of a rigid graph and a flex node addition. It is shown that the desired equilibrium set is locally asymptotically stable but…
This paper presents a generalization of conventional sliding mode control designs for systems in Euclidean spaces to fully actuated simple mechanical systems whose configuration space is a Lie group for the trajectory-tracking problem. A…
This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes $N$, the number of leaders $N_L$, and diameter $D$,…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
Motivated by the development and deployment of large-scale dynamical systems, often composed of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. In this work…
Control systems of interest are often invariant under Lie groups of transformations. For such control systems, a geometric framework based on Lie symmetry is formulated, and from this a sufficient condition for dynamic feedback…
In this paper we investigate a relaxed concept of controllability, known in the literature as herdability, namely the capability of a system to be driven towards the(interior of the) positive orthant. Specifically, we investigate…
In this work, we study the controllability of the bilinear Schr\"odinger equation on infinite graphs for periodic quantum states. We consider the bilinear Schr\"odinger equation $i\partial_t\psi=-\Delta\psi+u(t)B\psi$ in the Hilbert space…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
The purpose of this paper is to describe explicitly the solution for linear control systems on Lie groups. In case of linear control systems with inner derivations, the solution is given basically by the product of the exponential of the…
In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as the set of singularities of the drift…
For bilinear control systems in $\mathbb{R}^d$ we prove, under an accessibility hypothesis, the existence of a nontrivial compact set $D\subset\mathbb{R}^d$ satisfying $\mathcal{O}_t(D)=e^{tR}D$ for all $t>0$, where $R\in\mathbb{R}$ is a…
In structural rigidity, one studies frameworks of bars and joints in Euclidean space. Such a framework is an articulated structure consisting of rigid bars, joined together at joints around which the bars may rotate. In this paper, we will…