相关论文: Controllability of random systems: Universality an…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
We consider a bilinear control problem for the wave equation on a torus of arbitrary dimension. We show that the system is globally approximately controllable in arbitrarily small times from a dense family of initial states. The control…
The goal of the present article is to study controllability properties of mixed systems of linear parabolic-transport equations, with possibly non-diagonalizable diffusion matrix, on the one-dimensional torus. The equations are coupled by…
We consider control systems of the type $\dot x = A x +\alpha(t)bu$, where $u\in\R$, $(A,b)$ is a controllable pair and $\alpha$ is an unknown time-varying signal with values in $[0,1]$ satisfying a persistent excitation condition i.e.,…
There is a strong interest in optimal manipulating of quantum systems by external controls. Traps are controls which are optimal only locally but not globally. If they exist, they can be serious obstacles to the search of globally optimal…
The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of…
We show how a linear control systems theory for the backward nabla differential operator on an arbitrary time scale can be obtained via Caputo's duality. More precisely, we consider linear control systems with outputs defined with respect…
A joint characterisation of the observability and controllability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a…
In this paper, we consider the well-known Fattorini's criterion for approximate controllability of infinite dimensional linear systems of type $y'=A y+Bu$. We precise the result proved by H. O. Fattorini in \cite{Fattorini1966} for bounded…
In the present work we investigate topological properties of the set of controllable differential-algebraic systems of the form $\tfrac{\text{d}}{\text{d}t}Ex = Ax+Bu$ with real matrices $E,A\in\mathbb{R}^{\ell\times n}$ and…
Kalman's fundamental notion of a controllable state space system \cite{k} has been generalised to higher order systems by Willems \cite{w}, and further to distributed systems defined by partial differential equations \cite{ps}. It turns…
This paper addresses a structural design problem in control systems, and explicitly takes into consideration the possible application to large-scale systems. More precisely, we aim to determine and characterize the minimum number of…
This paper deals with strong structural controllability of structured networks. A structured network is a family of structured systems (called node systems) that are interconnected by means of a structured interconnection law. The node…
Using a compactness-uniqueness approach, we show that the Fattorini criterion implies the exact controllability of general compactly perturbed controlled linear systems. We then apply this perturbation result to obtain new controllability…
In recent years complex networks have gained increasing attention in different fields of science and engineering. The problem of controlling these networks is an interesting and challenging problem to investigate. In this paper we look at…
The controllability of a network is a theoretical problem of relevance in a variety of contexts ranging from financial markets to the brain. Until now, network controllability has been characterized only on isolated networks, while the vast…
Reparable systems are systems that are characterized by their ability to undergo maintenance actions when failures occur. These systems are often described by transport equations, all coupled through an integro-differential equation. In…
Let $A \in \mathbb{R}^{n \times n}$ be invertible, $x \in \mathbb{R}^n$ unknown and $b =Ax $ given. We are interested in approximate solutions: vectors $y \in \mathbb{R}^n$ such that $\|Ay - b\|$ is small. We prove that for all $0<…
Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust…