zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
UAV formation control: theory and application. (English) Zbl 1201.93089
Blondel, Vincent D. (ed.) et al., Recent advances in learning and control. Festschrift for Mathukumalli Vidyasagar on the occasion of his sixtieth birthday. London: Springer (ISBN 978-1-84800-154-1/pbk). Lecture Notes in Control and Information Sciences 371, 15-33 (2008).
Summary: Unmanned Airborne Vehicles (UAVs) are finding use in military operations and starting to find use in civilian operations. UAVs often fly in formation, meaning that the distances between individual pairs of UAVs stay fixed, and the formation of UAVs in a sense moves as a rigid entity. In order to maintain the shape of a formation, it is enough to maintain the distance between a certain number of the agent pairs; this will result in the distance between all pairs being constant. We describe how to characterize the choice of agent pairs to secure this shape-preserving property for a planar formation, and we describe decentralized control laws which will stably restore the shape of a formation when the distances between nominated agent pairs become unequal to their prescribed values. A mixture of graph theory, nonlinear systems theory and linear algebra is relevant. We also consider a particular practical problem of flying a group of three UAVs in an equilateral triangle, with the centre of mass following a nominated trajectory reflecting constraints on turning radius, and with a requirement that the speeds of the UAVs are constant, and nearly (but not necessarily exactly) equal.
MSC:
93C95Applications of control theory
93A14Decentralized systems