zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Adaptive stabilization of uncertain nonholonomic systems by state and output feedback. (English) Zbl 1038.93079
This paper addresses constructive adaptive state feedback control strategies for stabilizing a class of uncertain non-holonomic chained systems without imposing any restrictions on the system order or the growth of drift nonlinearities. Control laws are developed that use state scaling and backstepping. An innovative adaptive switching approach is proposed to prevent possible escape to infinity in finite time of system states and to guarantee boundedness of all signals in the system. A nonlinear observer-based output feedback design is proposed when only partial system states are measurable. A filtered observer rather than the customary linear observer is used to handle technical problems associated with the presence of unavailable states in the regressor matrix. The authors prove that all system states converge globally to the origin and that the estimated parameters remain bounded. Simulation results with a bilinear model of a mobile robot demonstrate the effectiveness of the authors’ approach.
93D21Adaptive or robust stabilization
70F25Nonholonomic systems (particle dynamics)
93C85Automated control systems (robots, etc.)