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)
On an optimal control design for Rössler system. (English) Zbl 1123.49300
Summary: An optimal control strategy that directs the chaotic motion of the Rössler system to any desired fixed point is proposed. The chaos control problem is then formulated as being an infinite horizon optimal control nonlinear problem that was reduced to a solution of the associated Hamilton-Jacobi-Bellman equation. We obtained its solution among the correspondent Lyapunov functions of the considered dynamical system.

49N35Optimal feedback synthesis
93C10Nonlinear control systems
Full Text: DOI
[1] Ott, E.; Greboggi, C.; Yorke, J. A.: Phys. rev. Lett.. 64, 1196 (1990)
[2] Kapitaniak, T.: Controlling chaos. (1996) · Zbl 0883.58021
[3] Sinha, S. C.; Henrichs, J. T.; Ravindra, B. A.: Int. J. Bifur. chaos. 10, No. 1, 165 (2000) · Zbl 1090.37528
[4] Bellman, R.: Dynamic programming. (1957) · Zbl 0077.13605
[5] Bryson, A. E.; Ho, Y.: Applied optimal control. (1975)
[6] Rössler, O. E.: Phys. lett. A. 57, 397 (1976)
[7] Bardi, M.; Capuzzo-Dolcetta, I.: Optimal control and viscosity solutions of Hamilton -- Jacobi -- Bellman equations. (1997) · Zbl 0890.49011
[8] Osher, S.; Shu, C. W.: SIAM J. Numer. anal.. 28, 907 (1991)