On Separating Points for Ensemble Controllability
نویسندگان
چکیده
منابع مشابه
On Separating Points by Lines
Given a set P of n points in the plane, its separability is the minimum number of lines needed to separate all its pairs of points from each other. We show that the minimum number of lines needed to separate n points, picked randomly (and uniformly) in the unit square, is Θ̃(n), where Θ̃ hides polylogarithmic factors. In addition, we provide a fast approximation algorithm for computing the separa...
متن کاملControllability Issues for Continuous-Spectrum Systems and Ensemble Controllability of Bloch Equations
We study the controllability of the Bloch equation, for an ensemble of non interacting half-spins, in a static magnetic field, with dispersion in the Larmor frequency. This system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum, whose controllability is not well understood. We provide several mathematical answers, with discrimination between approxi...
متن کاملSeparating Points by Parallel Hyperplanes - Characterization Problem
This paper deals with partitions of a discrete set S of points in a d-dimensional space, by h parallel hyperplanes. Such partitions are in a direct correspondence with multilinear threshold functions which appear in the theory of neural networks and multivalued logic. The characterization (encoding) problem is studied. We show that a unique characterization (encoding) of such multilinear partit...
متن کاملFixed Points and Controllability in Delay Systems
Schaefer’s fixed point theorem is used to study the controllability in an infinite delay system x′(t)=G(t,xt) + (Bu)(t). A compact map or homotopy is constructed enabling us to show that if there is an a priori bound on all possible solutions of the companion control system x′(t) = λ[G(t,xt) + (Bu)(t)], 0 < λ < 1, then there exists a solution for λ = 1. The a priori bound is established by mean...
متن کاملSeparating points by axis-parallel lines
We study the problem of separating n points in the plane, no two of whi h have the same xor yoordinate, using a minimum number of verti al and horizontal lines avoiding the points, so that ea h ell of the subdivision ontains at most one point. Extending previous NP-hardness results due to Freimer et al. we prove that this problem and some variants of it are APX-hard. We give a 2-approximation a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2020
ISSN: 0363-0129,1095-7138
DOI: 10.1137/19m1278648