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)
Adaptive synchronization of chaotic systems and its application to secure communications. (English) Zbl 0967.93059
The aim of this paper is to derive an adaptive observer-based driven system via a scalar transmitted signal which can attain not only chaos synchronization but can also be applied to secure communication of chaotic systems in the presence of the system’s disturbances and unknown parameters. Section 2 presents the class of chaotic systems considered and formulates the problem. Section 3 develops an adaptive observer-based driven system to synchronize the driving system with disturbances and unknown parameters. By appropriately selecting the observer gain vector such that the strictly positive real condition is satisfied, the synchronization and stability of the overall system are guaranteed by the Lyapunov stability theory with certain structural conditions. In Section 4, two well-known chaotic systems, Rösler-like and Chua’s circuit, are considered as illustrative examples to demonstrate the effectiveness of the proposed scheme. Moreover, in Section 5, the considered scheme is applied to a secure communication system whose process consists of two phases: the adaptive phase in which the chaotic transmitter’s disturbances are estimated, and the communication phase in which the information signal is transmitted and then recovered on the basis of the estimated parameters. Promising simulation results illustrate the proposed scheme in the communication application.
MSC:
93C40Adaptive control systems
93D21Adaptive or robust stabilization
37D45Strange attractors, chaotic dynamics
94A05Communication theory
93C10Nonlinear control systems